The Many Voices of Modern Physics: Written Communication Practices of Key Discoveries 0822947587, 9780822947585

Table of contents :
Contents
Acknowledgments
Introduction
1. Special Relativity
2. General Relativity
3. Quantum Mechanics
4. Unification Physics
5. Cosmic Conjectures
6. Quantum Magic
7. Transistor Actions
8. Astronomical Value
9. The Atomic Bomb: Anticipated and Unanticipated Consequences
Epilogue
Afterword by Randy Allen Harris
Notes
Bibliography
Index

Citation preview

The

MANY VOIC ES

of

MODERN PHYSICS

U N I V E R S I T Y of PI T T SBURGH PR ES

S

The

MANY VOIC ES

MODERN PHYSICS

of of

WRIT TEN

KEY

COMM UNICA TION

DISCOV

JOSEPH E. HARM and

with

an

PRAC T ICE S

ERIES

ON

AL AN G. GROS S

afterword by S EN HARRI L L A Y D N RA

Published by the University of Pittsburgh Press, Pittsburgh, Pa., 15260 Copyright © 2023, University of Pittsburgh Press All rights reserved Manufactured in the United States of America Printed on acid-free paper 10 9 8 7 6 5 4 3 2 1 Cataloging-in-Publication data is available from the Library of Congress ISBN 13: 978-0-8229-4758-5 ISBN 10: 0-8229-4758-7 Cover art: Artistic rendering of shapes of strings in string theory for several subatomic particles via Shutterstock; higher-resolution Hubble Space Telescope image of the Pillars of Creation, taken in 2014 as a tribute to the original photograph. Cover design: Alex Wolfe

In memory of Alan G. Gross, 1936–2020

CONTENTS

acknowledgments  ix

Introduction   3 1. Special Relativity  14 2. General Relativity   38 3. Quantum Mechanics  63 4. Unification Physics   86 5. Cosmic Conjectures   112 6. Quantum Magic  137 7. Transistor Actions   159 8. Astronomical Value   181 9. The Atomic Bomb: Anticipated and Unanticipated Consequences  207 Epilogue   226 Afterword by Randy Allen Harris  240 notes  255 bibliography  275 index  289

ACKNOWLEDGMENTS

On Friday, October 16, 2020, Alan Gross died suddenly. I had spoken to him at length over Zoom that very morning, as we were nearing completion of the first draft of the present book. Fortunately for me, over the course of the period after Alan’s death, our collaboration continued as I read and reread our text while finishing up various chapters, revised the draft extensively in response to reviewer and editor comments while imagining Alan watching over my shoulder, and proofed the final copy. Now, after close to three decades, we part company as writing partners forever. I want to express my sincere gratitude to Jermey Matthews, who provided me with much needed critical insights in the very early stages of manuscript development. This book would never have come to fruition without his feedback at that embryonic time. Special thanks go to editor Abby Collier at the University of Pittsburgh Press. Through her choice of readers, we received excellent critical feedback on the initially submitted manuscript—feedback that helped reshape the manuscript to its present state. Also to be thanked are her team members Jessica LeTourneur Bax and Amy Sherman for their outstanding copyediting. An extra special acknowledgment goes to Randy Allen Harris not only for critical feedback but also for his contribution of an afterword, written with his usual flair for melding the scholarly and personal. Much of what I know about the practical side of scientific communication I learned while working for the US Department of Energy’s Argonne National Laboratory; however, I performed the research and writing for this book independent of Argonne. Finally, I am certain Alan would have wanted to thank his wife and literary executor, Suzanne Gross, for her unfailing support, love, and encouragement over the years. He would also have expressed gratitude to his children—Sarah, Joshua, and Jessica—for having enriched his life.

ix

The

MANY VOIC ES

of

MODERN PHYSICS

INTRODUCTION

A revolution in science began in 1905 when Albert Einstein published two papers on relativity and one on quantum theory. For the latter, he built upon a paper published in 1900 by Max Planck suggesting that energy can be thought of as produced in discrete miniscule bundles. In The Many Voices of Modern Physics, we trace the key discoveries of physics and astrophysics from then to now. Unlike Newtonian physics, this new physics often departs wildly from common sense, a radical divorce that presents a unique communicative challenge to physicists when writing for other physicists or for the general public, and to journalists and popular science writers as well. Our focus is not on the history of modern physics, but on its communication. We are not historians like Peter Galison, telling the story of the bubble chamber.1 Nor are we sociologists like Andrew Pickering, delving deeply into the social construction of quarks,2 or philosophers like Thomas Kuhn, revealing the structure of scientific revolutions.3 In our two long careers, we have explored how scientists communicate with each other and with the general public. That is our main concern here. Our book is a tribute to the written communication practices of the physicists who convinced their peers and the general public that the universe is a place far more complex, far more bizarre, and far more interesting than their

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THE MANY VOICES OF MODERN PHYSICS

nineteenth-century predecessors ever could have imagined. In our survey of the communicative practices concerning modern physics, we move from peak to peak of scientific achievement. By means of extensive and frequent quotation, our persistent focus is how physicists use the communicative tools available— words, equations, graphs, diagrams, photographs, and thought experiments— to convince others that what they say is not only true but significant, that it must be incorporated into the body of scientific and general knowledge. We especially favor the many celebrated physicists, including Einstein, who have devoted considerable time and ingenuity to communicating their discoveries and those of others not only to the physics community but also science enthusiasts in general. We also make use of extracts by others: science journalists in particular, but also philosophers, sociologists, historians, even an opera composer and a patent lawyer. Each chapter is thus a chorus of voices, including ours, of course. While our polyphonic approach is distinctive, we are not breaking new ground. We have models we hope to imitate and improve upon. First, there is Rom Harré, whose Great Experiments: Twenty Experiments That Changed Our View of the World is still in print after four decades.4 Its contents stretch from Aristotle on chick embryos to Albert Michelson and Edward Morley on the nature of light and Otto Stern on molecular beams. Strategically interspersed within his chapters are passages from relevant scientific texts and images published over the last millennium. Harré divides his twenty experiments into three unequal groupings: those illustrating different aspects of experiment, its importance in theory development, and its use in technique development. We find Harré’s exposition exemplary; his choices, admirable; and his range, too broad for such short a book. Readers are left with no clear impression of change over time. Nevertheless, his is a feast for any science enthusiast. There is also Alan Lightman’s The Discoveries: Great Breakthroughs in 20th-Century Science, which covers such important twentieth-century milestones as Alexander Fleming’s discovery of penicillin and Niels Bohr’s theory of the atom.5 For each milestone, after an introductory essay, Lightman reproduces the entire relevant scientific article when reasonably short and a large proportion when not. But Lightman jumps in chronological order from one discipline to another without any other connecting threads. As a result, Max Planck’s 1900 paper on the quantum is jarringly followed by the 1902 paper by William Bayliss and Ernest Starling on hormones. Moreover, while his introductory essays are exemplary, they can be of marginal use in understanding the scientific papers that follow. These comments aside, the book should be on every science enthusiast’s reading list. 4

INTRODUCTION

Finally, there is Laura Garwin and Tim Lincoln’s A Century of Nature: TwentyOne Discoveries That Changed Science and the World, which covers significant discoveries that appeared in Nature magazine, such as seafloor spreading and DNA sequencing.6 For each, Garwin and Lincoln reproduce an article in its entirety. They also preface each article with an essay by a world-leading expert in the subject matter. Unfortunately, the Nature papers reproduced are for the most part impenetrable to all but those with specialized knowledge. Although T. H. Maimon’s paper on his discovery of the laser is preceded by an informative introduction by Nobel Prize winner Charles H. Townes, for instance, Townes gives the reader little help in understanding the paper itself. This defect is general. Still, the introductions are illuminating and much can be learned from them about discoveries that changed science and the world. In writing The Many Voices of Modern Physics, we set out to exploit to our own ends what we learned from these three books’ experiments in exposition. For ease of comprehension, we quote passages of varying lengths from technical and popular accounts that are either self-explanatory, or that we are careful to try to explain. We readers are blessed in that many celebrated physicists have devoted considerable time and ingenuity to communicating their discoveries to science enthusiasts in general. In each chapter, we quote from popular accounts by these physicists liberally, and sometimes at length. But also quoted are scientific papers, journalistic accounts, history of physics books and articles, press releases, letters, memoirs, declassified technical documents, a patent application, and even Senate committee testimonies. For thematic consistency, we employ these texts as exemplary illustrations of the use of words and pictures in communicating physics to diverse audiences. For narrative consistency, we place our choices in a limited historical framework: highlights in physics and astrophysics from 1900 to the present, with a few detours into earlier centuries. Our emphasis throughout is the verbal and visual communications related to not only the theories of modern physics—a dominant topic in popular science books in general—but also the discovery machines and novel materials with strange and remarkable properties. In the course of the time span covered in this book, written communications in physics have radically transformed the picture of the world around us. Those on relativity theory revised the definitions of time, space, mass, energy, and gravity. Those on quantum mechanics revealed an incommensurability between the nature of the hidden microworld and the visible macroworld. Those on grand unification theories and modern cosmology radically reshaped and are still reshaping our understanding of the origin of matter and the picture of the universe we inhabit. Those on materials of science like semiconductors and superconductors changed the meaning of what a thing is and can do. 5

THE MANY VOICES OF MODERN PHYSICS

Key Written Communication Practices In communicating this new science-based picture of the world, physicists and science writers frequently rely upon analogy. Classical rhetoric defines analogy as a linguistic structure constructed from pairs, where meaning emerges from the interactions between their similarities and contrasts. As one example, Aristotle offers “the cup is related to Dionysus as the shield to Ares,” where a cup used for alcohol consumption is linked with the Greek god of unrestrained consumption, and a shield used in battle is linked with the Greek god of war and valor.7 This analogy hinges on the similarity of two common man-made implements, the similarity of two Greek gods, and the contrast between the lack of impulse control of one god and the military discipline of the other god. Aristotle’s second example is “old age is to life as evening is to day,” where the similar pairs are old age/evening and life/day and the contrasting pairs are old age/life and evening/day. For this example, Aristotle shows how one can combine the third and second elements to give “the evening of life,” a metaphor for the first element, “old age.” These analogical elements can also be combined into a simile, “old age is like the evening of life.” In The New Rhetoric Chaïm Perelman and Lucie Olbrechts-Tyteca define analogy in a mathematical way consistent with Aristotle: “As a resemblance of structures, the most general formulation of which is: A is to B as C is to D. This conception of analogy is in line with a very ancient tradition.”8 Perelman and Olbrechts-Tyteca give analogy a lofty place as a rhetorical device: “No one will deny the importance of analogy in the workings of the intellect.”9 Moreover, they add that “analogies are important in invention and argumentation fundamentally because they facilitate the development and extension of thought.”10 In a book on Perelman commenting on The New Rhetoric, Alan Gross and Ray Dearin offer a precise explanation of a possible argumentative function of analogy: “To create, strengthen, or intensify the adherence of minds to a persuasive thesis.”11 The importance of analogy to scientific discourse and argument has long been recognized.12 Such analogies are often expressed as a comparison between the abstract world of science and the world the reader is assumed to know through experience or common knowledge. As Marcello Pera notes in The Discourses of Science,13 for example, running throughout Charles Darwin’s Origin of Species are analogies in support of an argument for natural selection as the ruling mechanism behind biological evolution. One such potent example is natural selection is to all organic beings in the wild as artificial selection is to domesticated animals and plants. And when Lise Meitner and Otto Frisch discovered nuclear fission 6

INTRODUCTION

and reported it in Nature magazine, they analogized uranium bombarded with neutrons as comparable to an unstable liquid drop that divides into two.14 Analogy has tremendous communicative utility because it can transform the abstractions of science into more easily comprehended language. Even certain equations of physics can be thought of as having an analogy-like flavor on occasion, comparing mathematical operations with physical processes. To give a fairly simple example, the equation E = mc2 is analogous to the statement that energy is interchangeable with mass. Of special import to the physics literature is another analogy-like linguistic construction, the thought experiment, a fiction that has the unusual property of telling us something significant about the real world. Philosophers continue to make a living disagreeing about what one is. Typically, thought experiments involve the author setting up some imaginary scenario with an analogy to the real world, letting it run its course before the readers’ eyes—consistent with laws of science— and drawing some conclusions about it.15 These have been a way of science at least since the days of Galileo.16 In a break with the past, an escape from Aristotle’s long shadow, for example, Galileo created a thought experiment. Aristotle believed heavy bodies fall faster than lighter ones; that they must do so is a clear dictate of common sense. So let’s think—just think—about a cannon ball tied to a musket ball and dropped from the Leaning Tower of Pisa. This combination must fall faster than the cannon ball alone because it is heavier, right? On the other hand, it must also fall slower because the attached musket ball must impede its downward movement, right? Aristotle’s view cannot be correct if it leads to a contradiction. QED: regardless of weight, all objects must fall at the same speed. This “experiment” is notable because Galileo could not have performed it with any precision using real cannon and musket balls dropped from a real leaning tower. Just try. Thought experiments are a notable exception to the rule that scientific theories must be tested against the world. At the start of the twentieth century, faced with understanding and explaining the bizarre behavior of moving objects in a relativistic world, Einstein repeatedly turned to thought experiments. The same was true for the quantum physicists confronted with the even more bizarre behavior of motion in the microworld. Another central communicative device in popular science books, just as in scientific articles, is visual representation, which also can have an analogy-like foundation, comparing a diagram or schematic with some aspect of the real or a theoretical world. Actual scientific visuals have not been much discussed in the literature on rhetoric. The ancient Greek rhetorician Longinus did write that “weight, grandeur, and urgency in writing are very largely produced . . . by the use of ‘visualizations’ (phantasiai). That at least is what I call them; others call 7

THE MANY VOICES OF MODERN PHYSICS

Figure I.1. Illustration of Darwin’s theory of the evolution of an atoll from volcanic island with fringing coral reef. From Charles Darwin, Structure and Distribution of Coral Reefs (1842). Images on separate pages (98 and 100) combined into one here.

them ‘image productions.’”17 But of course, Longinus was referring to verbal “image productions” that vividly evoke some scene before the eyes of an audience. As we mention in Science from Sight to Insight,18 pictures are an integral part of scientific communications, where meaning typically emerges from the interactions between the words in the text and the pictures integrated therein. As an example from evolutionary theory, in Science from Sight to Insight, we chose to analyze a pair of visuals from Charles Darwin’s 1842 The Structure and Distribution of Coral Reefs (figure I.1), a monograph meant to be understandable by any reasonably well-informed amateur naturalist. These two diagrams visually represent Darwin’s theory that volcanic islands subside into the sea over many millions of years until all that remains is an atoll, a circular reef with lagoon inside. In the top image, we see the geology of a volcanic island in the distant past as the sea level rises from the solid horizontal line (A-A) to the dotted one (A´- A´). Important to note is that a barrier reef spreads out from the volcano (below A´- B´). In the bottom image, fast forward many millions of years later, we see the volcano having subsided completely, and the barrier reef having swollen to become an atoll enclosing a lagoon with ship anchored in the middle where the island once stood (see C´ near the dotted line at the top of the image). 8

INTRODUCTION

In Science from Sight to Insight, one of our visual examples from physics comes from Galileo’s Two World Systems, as part of his argument that the apparent retrograde motion of Jupiter (forward, then backward, then forward again) in the night sky is an illusion that can be explained geometrically if the planet circles the sun.19 This masterful diagram can be viewed as Galileo’s visual analogy for the illusion of planetary retrograde motion. It shows a complicated arrangement of lines and circles bearing little physical resemblance at all to Jupiter in its orbit. Yet, if we scan the lines from right to left in the way Galileo guides us in his verbal text, we can mentally reconstruct the orbit of Jupiter as it deceptively appears from Earth to reverse directions twice, even though it is doing nothing of the kind. According to Galileo, along with the other evidence he presents, that “ought to be enough to gain ascent for the . . . [Copernican] doctrine from anyone who is neither stubborn not unteachable.”20 It is important to caution that while thought experiments, analogies, and visuals have many positive attributes, there are limitations as well. As pointed out by John Norton, thought experiments can dupe readers into drawing flawed “conclusions about fundamental matters from bizarre imaginings.”21 And as mentioned by Gross and Dearin, analogies “are important but precarious techniques of argument.”22 Those questioning an analogy can simply claim that it is either wrong-headed or too vague, while the author may claim that it is no more than a metaphor. The result is that the analogy is caught between the “disavowal by its opponents and disavowal by its supporters.”23 Analogies also have their limits in another sense. There is never a one-to-one correspondence between things of the everyday and some physics abstraction. There are always differences, and those differences can outweigh the similarities to the point of distortion. The commonplace analogy between the workings of our solar system and the atom is one of the more obvious examples. This meme-like analogy is certainly poetic and seductive and still very much alive today in popular science writing and on the internet. The spoiler is that quantum mechanics tells us electrons definitely do not orbit the nucleus like planets, but in accord with probabilistic instead of deterministic laws. Visual representations of the atom as a miniscule solar system (figure I.2) further spreads the false impression for the unwary. An often overlooked but enormously important communicative device in combatting false impressions in science is use of qualifications and hedging language—that is, words like maybe, probably, perhaps, and so on.24 By this means, scientists and science writers can separate already established science (“this is so”) from the frontier of science (“this may be so, but only time will tell”). When writers leave out or misuse qualifications and hedges, they can confer far 9

THE MANY VOICES OF MODERN PHYSICS

Figure I.2. Visual representing an atom as similar to miniature solar system.

greater certainty than the situation warrants. Studies have found, for example, that journalistic writing tends to shape the narrative as a race with clear winners and losers, redacting qualifications and hedges.25 Even when hedges are handled with care, some readers can easily be persuaded by the authority of the voices of distinguished scientists. After all, who are we readers to doubt them on matters of science, whatever the hedging? But as we will address in several chapters, the spectacularly successful strange theories of the past like relativity and quantum mechanics do not by any means guarantee current ones will hold water, no matter how seductive or convincing the analogies, visuals, or thought experiments. Communicating science also requires the act of definition, carefully tuned to a particular audience. A term like Standard Model requires no definition in 10

INTRODUCTION

a physics journal, but for any popular exposition, it does demand some level of definition, even though it is one of the monumental achievements of twentieth-century physics. One might describe it for readers with firm knowledge of elementary physics as “a field theory of all matter in which the nongravitational forces arise by exchange of a force particle with substance particles.” But others less well versed would understandably want to know: What is a field theory? What are the nongravitational forces? What are force and substance particles? Luckily for those interested in the Standard Model, popular science writers have employed various inventive communicative strategies to more fully explicate what the Standard Model is. For example, in Knocking on Heaven’s Door, physicist Lisa Randall gives much greater insight into the meaning of Standard Model by systematically arranging all the force and substance particles along with the nongravitational forces in a periodic-table-like table.26 (We have more to say about that table in chapter 4.) As rhetoricians Perelman and Olbrechts-Tyteca maintain,27 definition can also be an element in argumentation of all kinds. For example, Einstein’s argument for the validity of his new definition of simultaneity is central to his classic 1905 paper on special relativity.28 And in his popular science book A Brief History of Time, Stephen Hawking first defines black holes, then pictures them, then expounds upon the strong evidence for their existence at that time, despite no one having yet observed one directly.29 We find it convenient to lump the majority of written scientific communications into two broad genres: (1) specialized scientific articles and books and (2) popular science ones. The purpose of the former is the communication of claims to new knowledge aimed at an audience of experts for their evaluation and possible use. Stylistically, authors of such communications heavily rely on a vast specialized terminology, which improves communicative efficacy at the expense of intelligibility. In fact, it is not hard to find passages in which everyday English words are banished, with the exception of verbs and connecting words like prior to and because. In such passages, most of the nouns and their modifiers are of a highly technical nature; even everyday words are enlisted in the service of science, words such as force and particle. Three other prominent contributors to cognitive and semantic complexity here are quantifications, abbreviations, and noun strings. The first confronts the reader with a sea of numbers; the other two make an already information-rich text even more compact.30 The language of physics in journal articles and technical books is not just words—it also is the language of mathematics. The common symbolism physicists now employ was invented in the seventeenth century. Gottfried Leibniz was the chief architect: “Among Leibniz’ symbols which at the present time enjoy 11

THE MANY VOICES OF MODERN PHYSICS

universal, or well-nigh universal, recognition and wide adoption are [in the calculus] his dx, dy [for differentials], his sign of integration, his colon for division, his dot for multiplication, his geometric signs for similar and congruence, his use of the Recordian sign of equality when writing proportions, his double-suffix notation for determinants.”31 Today, specialized communications on physics theory are typically a steady mathematical stream, equation after equation with connecting text moving toward a climax, a solution to a problem established in the introduction. They typically conclude with an argument for the theory’s validity by comparison, a deceptively simple analogy-like communicative strategy. This comparison typically involves comparing predictions from the theory with experimental measurements or calculations by a different theory.32 The focus of most of our book, popular science books and articles in physics, constitutes a different genre for a different audience, with few if any equations and far more limited number of technical terms. We use the word popular as a catchall to encompass almost any communication on physics aimed at an audience beyond the very narrow one for specialized journal articles. The purpose of popular expositions is to spread the word to this audience about the most newsworthy discoveries of science, whether or not they have reached the stage of accepted knowledge. Here, the prominent communicative tools include analogy, thought experiment, visual representation of theory, hedging, and definition of technical terms. Also, unlike scientific articles, popular physics expositions are not striving for approval of new discoveries from a jury of peers, who would expect mathematics and data and a heavy dose of technical language. Nevertheless, they do seek to convince the science-interested public that the seemingly implausible physics described therein is not pie in the sky. The default position is that at least some popular science readers are highly skeptical about the claims being made, even ones long accepted ones by the scientific community, like the warping of space and relativity of time in physics, and that those doubts need to be assuaged by means more than just quantitative comparison of theory and experiment. That is where persuasive communicative devices like analogy, thought experiment, and visual representation come to the fore.

We organized the first part of this book around communications related to the main theoretical achievements in modern physics, with separate chapters on relativity theory, quantum mechanics, unification theories on the road to a “theory of everything,” and various cosmological theories for the origin and evolution of the universe. Then, turning away from bold theories that repeatedly defy our perceptions of the world around us—the topic dominating most popular physics 12

INTRODUCTION

books—the later chapters treat communications on physics-based technologies and materials that have significantly affected nearly everyone’s life or may do so in the future. Throughout, our emphasis is not the theories or technologies and materials per se or their historical context, but their communication with the tools outlined above, plus others that we will introduce later. In the end, we do not tell the story of physics starting in the early twentieth century, but a story—one told partly through the words and pictures of the discoverers as well as other physicists and science writers. Our hope is that our story will be read by physicists, who do not usually think of themselves as the master communicators they can be, by communications scholars interested professionally in the doings of these master communicators, and by scholars in science studies. Our book might also be of interest to anyone curious about a developing science-based view of the universe that persistently defies common sense. While we will not pretend that our book is beach reading, our intent is that readers with little or no education in physics will not find this a handicap so long as they are willing to expend some effort in return for understanding some of the greatest intellectual achievements in science.

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1 SPECIAL RELATIVITY

Where better to begin a book on communicating modern physics than with Albert Einstein in 1905, a miraculous year for a young patent examiner in Bern, Switzerland, who is really a theoretical physicist in disguise? Having published no paper of consequence in previous years, he burst on the physics scene with four remarkable papers in Annalen der Physik, papers that would over the next few years catapult him into the upper echelon of physics. The most important had the nondescript title “On the Electrodynamics of Moving Bodies.” This paper had astonishing and counterintuitive implications for our understanding of length, time, and velocity and introduced to the world what would later become known as special relativity. For Einstein, one key to communicating his counterintuitive deductions was the thought experiment, of which he was a grand master. “On the Electrodynamics of Moving Bodies” opens with a thought experiment, establishing a serious problem with then-current electrodynamics theory, a preeminent physics theory of the late nineteenth century. His solution required a rejection of many centuries of past physics assuming absolute time and space. Thought experiments aplenty also appear in Einstein’s popular science book, Relativity: The Special and General Theory (1917). Their purpose is to disillusion readers about certain commonsense notions they might have regarding space, time, and motion. Since this book, other prominent scientists have written popular science books about the theory, 14

SPECIAL RELATIVITY

also relying heavily on thought experiment. The extracts reproduced here are taken from books by physicists Max Born, Arthur Eddington, George Gamow, and Sander Bais, plus an outlier—the mathematical philosopher Bertrand Russell. As the following expositions of the quoted texts bring forth, all these writers appropriated, revised, and extended each other’s thought experiments and even created new ones. Our expositions also reveal how several of them made effective use of illustrations of relativistic space-time effects to accompany their thought experiments.

Einstein on Special Relativity for Physicists In his entertaining and readable biography Einstein: His Life and Universe, Walter Isaacson said of  Einstein’s 1905 paper on special relativity, one of the key papers ushering in the age of modern physics: “Most of its insights are conveyed in words and vivid thought experiments, rather than in complex equations. There is some math involved, but it is mainly what a good high school senior could comprehend.”1 We do not agree. True, the first paragraph is a thought experiment, but not too long thereafter “vivid thought experiments” fade away as the math behind the thought experiments takes over. It is true that the equations involve only high school–level mathematics, but it is doubtful that many high school (or college) students could follow the sequence of equations to their remarkable conclusion. Einstein wrote in the highly condensed mathematical style typical of theoretical physics papers; he expected readers to go to the blackboard and work out all the many unstated steps and assumptions involved in navigating the sequence. We doubt even Einstein’s math-less introduction is comprehensible by most high school students. Its first paragraph fulfills the duty of any good introduction to a scientific paper—it establishes a research problem. Somewhat unusually, Einstein does so through the communicative vehicle of a thought experiment: It is known that Maxwell’s electrodynamics—as usually understood at the present time—when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion. For if the magnet is in motion and the conductor at rest, there arises in the neighborhood of the magnet an electric field with a certain definite energy, producing a current at the places where parts of the

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THE MANY VOICES OF MODERN PHYSICS conductor are situated. But if the magnet is stationary and the conductor in motion, no electric field arises in the neighborhood of the magnet. In the conductor, however, we find an electromotive force, to which in itself there is no corresponding energy, but which gives rise—assuming equality of relative motion in the two cases discussed—to electric currents of the same path and intensity as those produced by the electric forces in the former case.2

Einstein clearly composed this passage with other physicists in mind. The first sentence expands on the title, repeating “electrodynamics” and “moving bodies” in order to establish a major problem with physics at the turn of the twentieth century: the laws governing electricity, magnetism, and optics—first formulated by James Clerk Maxwell—lead to a glaring asymmetry when applied to bodies in uniform motion. Einstein instantiates this asymmetry by means of a thought experiment involving a magnet and a conductor (such as a copper wire), seen from the point of view of then-status quo physics. The asymmetry is simply that the physical explanation should be the same whether the magnet or conductor is considered to be moving relative to the other, but that was not the case at the time. Identification of this problem did not originate with Einstein. The title “The Electrodynamics of Moving Bodies” echoes an 1894 textbook chapter by physicist August Föppl, “The Electrodynamics of Moving Conductors.” 3 Föppl questioned the then-different physical explanations given for a conductor of electricity moving relative to a stationary magnet, and a magnet moving relative to a stationary conductor. Einstein’s first paragraph does the same. The asymmetry lies in the different theoretical explanations given for the two cases. In the first, an electric field appears around the moving magnet and induces a current in the stationary conductor (Faraday’s law), while in the second, the moving conductor experiences an electrical force due to the stationary magnet (Lorentz’s law). Yet, both cases of relative motion generate an identical current. Einstein asked, should simply changing the body being moved really have different effects? Einstein’s next somewhat less dense paragraph elaborates, giving the knowledgeable reader a first hint at his radical solution to the asymmetry problem: Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that . . . the same laws of electrodynamics and optics will be valid for all frames of

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SPECIAL RELATIVITY reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body. These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies.4

Evident in the first sentence is that Einstein assumes his physicist readers have some familiarity with two widespread beliefs at the time. One is the existence of a universal luminescent ether, a medium needed for light to move through space, just as sound waves need the atmosphere to propagate. The other is the notion of “absolute rest,” with the ether itself providing a medium to fix any object as being absolutely stationary. Without those beliefs, the justification for the different physics in the two magnet-conductors cases withers on the vine.5 In that compact first sentence, Einstein dismisses the universal light medium, since no one had been able to detect any effect from it despite repeated attempts. He mentions these null experiments but does not reference them, the norm within the scientific community for referencing not being as onerous as it would soon become. And with no light medium, the justification for the existence of absolute rest goes by the wayside too. Thus, it should not matter which object one chooses to be at rest. The law of physics should be the same for the case of the moving magnet and conductor. Also embedded in that first sentence is the first hint that Einstein’s thought experiment links both visible moving objects like magnets and conductors (“mechanics”) and the invisible electromagnetic fields they generate (“electrodynamics”). This is an important claim because Einstein asserts in a third introductory paragraph that he will be merging Galileo’s principle of the relative motion of objects with those for electrodynamics, an astonishing claim, given the then-settled beliefs of the physics community. A brief digression on mechanics might help with added context. In Dialogue Concerning the Two Chief World Systems, Galileo communicated his principle of relative motion by means of a thought experiment involving a sailing ship.6 He asks us to imagine we are in a windowless cabin belowdecks, docked in a perfectly calm sea. Insects would fly about and fish in a bowl would swim as though they were on terra firma. In a game of catch, the ball would fly through the air just as it would on land. Now we are to imagine the ship moving at a 17

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uniform velocity on a perfectly smooth and calm sea. We would find no difference. Flies would still fly, fish would swim, and balls would sail through the air just as before. The surroundings inside the cabin would give us no sign whatever whether the ship was moving or still on this idealized smooth sea. So, whether we choose as a stationary frame of reference the docked or so-called moving ship relative to a docked ship should make no difference to the laws of physics—a ball would still fall straight to the deck if dropped in both cases; a fly would buzz about in the same way. Einstein’s radical thought was that the laws of relative motion for a ship should be consistent with the laws of electrodynamics with magnets and conductors as well as light. This is the first of the two fundamental “postulates” from which he would construct his argument. The second is that the speed of light in a vacuum is constant, always 186,000 miles per second, or 671 million miles per hour. An observer traveling at near to the speed of light will measure light speed to be exactly the same as that of a stationary observer or an observer traveling half the speed of light. Einstein provides no justification for that assertion, though earlier experiments had suggested that the speed of light is constant, as did Maxwell’s electrodynamic equations. This startling second postulate creates an asymmetry between the laws of electrodynamics and mechanics. Why would the Galilean principle of relative motion for sailing ships apparently not hold for light as well, whose velocity never varies? The last sentence in the second paragraph hints at the solution Einstein embeds in the article title: “These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell’s theory for stationary bodies” (emphasis added). Key terms in that sentence are the antonyms moving and stationary, terms that are later central to all of Einstein’s thought experiments on relativity. In Einstein’s brief introduction, he accomplishes much. He first establishes an asymmetry in current electrodynamics through a thought experiment. Then, he connects that thought experiment, which assumes classical electrodynamics with a light medium and absolute rest, to the two founding postulates of a new physics sans the light medium or absolute rest. After this introductory thought experiment, in the main body of the text, Einstein continues with brief and abstract thought experiments involving clocks, a train, and measuring sticks, imaginary tools he will also make great use of in later writings. Applying mathematics to them he derives a set of simple algebraic equations (the so-called Lorentz transformation, named for Hendrik Lorentz) that mathematically account for the change in time and length for one object in uniform motion relative to another consistent with the two postulates. A truly 18

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startling consequence of his solution is that time slows and length contracts for a body in uniform motion, though these effects are not in any way noticeable at speeds we typically experience. After much more math, Einstein then plugs his Lorentz transformation equations into Maxwell’s equations for electricity and magnetism, the climax of the article. These climatic equations resolve the thought experiment problem and remove the asymmetry mentioned in the first paragraph. The same physics must hold whether the magnet or conductor is the one in motion. In the last part of the paper, Einstein argues for the wide explanatory scope of his theory to other physics problems. All this is done in only about 7,000 words, but nearly 180 displayed equations. What distinguishes Einstein’s paper and makes it, in Isaacson’s accurate phrase, “one of the most spunky and enjoyable papers in all of science,”7 is not only the thought experiments or its simple mathematics for a highly theoretical physics paper but also the remarkable argument at its core. By following that we can peek behind the screen of words and equations into the mind of a young genius. Good scientific arguments—especially those that run counter to current thinking—do not guarantee immediate attention, much less acceptance. It is perfectly understandable that some of Einstein’s first readers viewed his radical conclusions with suspicion, given that they lacked experimental support or even any obvious way of testing at the time and set aside well-established beliefs. Nevertheless, within four or five years, thanks in no small part to Max Planck’s advocacy, Einstein’s paper did sway a large cohort of the German physics community, altering forever their picture of time, space, and velocity.8 The next publications to be discussed did the same for the scientifically curious layperson.

Einstein Turns from Physicists to the General Public In 1919 a New York Times foreign correspondent interviewed Einstein in his library on the top floor of a “fashionable apartment house on one of the few elevated parts of Berlin.” The correspondent asked Einstein to explain his theory of relativity. His reply reflects just how deeply he had thought about how to answer that question for any learned person interested in his theory. In his response, Einstein focuses on his merger of the Galilean law of relative motion with electrodynamics: “The term relativity refers to time and space,” Dr. Einstein replied. “According to Galileo and Newton time and space were absolute entities, and the moving systems of the universe were dependent on the absolute time and space. On this conception was built the science of mechanics [motion

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THE MANY VOICES OF MODERN PHYSICS of objects]. The resulting formulas sufficed for all motions of a slow nature; it was found, however, that they could not conform to the rapid motions [some large percentage of the speed of light] apparent in electrodynamics [interactions of electric currents and magnetics fields].” “This led to Dutch professor, Lorenz [sic], and myself to develop the theory of special relativity. Briefly, it discards absolute time and space and makes them in every instance relative to moving systems. By this theory all phenomena in electrodynamics, as well as mechanics, hitherto irreducible by the old formulae—and there are multitudes—were satisfactorily explained.”9

Several years before that interview, Einstein had written what we consider the first important popular science book on modern physics by a major physicist, Relativity: The Special and General Theory, originally published in German in 1917 and first translated into English in 1920. It opens with an analogy: “In your schooldays most of you who read this book made acquaintance with the noble building of Euclid’s geometry, and you remember—perhaps with more respect than love—the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers.”10 The analogy here is that Euclid’s geometry is analogous to a noble school building with lofty staircase. Einstein formulated this analogy only to identify a weakness in it. He will soon shake his readers’ “feeling of proud certainty” by repeatedly demonstrating that certain prior certainties—for example, that two points on a measuring rod remain at the same distance independent of velocity—are, quite simply, false. Having questioned a certainty well embedded in his reader’s past, in the following pages Einstein will substitute for it special relativity, a set of ideas so bizarre that only an argument readers can follow step by inevitable step, will convince them, perhaps even against their will, that Einstein might be right. When, at the end of the journey, the trap is sprung, they may find themselves caught, believing the unbelievable. The vehicle for this persuasive maneuver is the substitution for a mathematical proof a set of familiar things: trains, embankments, lightening, clocks, and so on. But beware: minefield ahead! As wisely noted by historians Hanoch Gutfreund and Jürgen Renn, Einstein’s exposition “may be popular in its format, in its dialogues with the reader, in its examples from daily life, and in the lack of mathematical formulas, but it does not compromise on intellectual rigor, and the reader soon discovers that an intellectual effort is required to follow the flow of Einstein’s thoughts and arguments.”11 As an example, we quote Einstein’s thought experiment regarding the meaning of simultaneous. We might think we know what it means for two or more 20

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Figure 1.1. Schematic showing relationship between passenger in train and stationary observer on embankment. M is midpoint; A and B are lightning strikes. From Albert Einstein, Relativity: The Special and General Theory (2016), 36.

events to occur at the same time. By means of his thought experiment, Einstein argues we must think again: Up to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity v and in the direction indicated in [figure 1.1]. People travelling in this train will with a vantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.12

Our commonsense notion of simultaneity is that the answer should be positive. The following thought experiment demonstrates common sense makes no sense: When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A → B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A → B on the travelling train. Just when the flashes (as judged from the embankment) of lightning occur, this point M' naturally coincides with the point M but it moves towards the right in the diagram

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THE MANY VOICES OF MODERN PHYSICS with the velocity v of the train. If an observer sitting in the position M' in the train did not possess this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event. Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity.13

Before reading this passage for the first time, we thought we knew the meaning of simultaneous events. They are the same whether we are a train passenger or standing on the nearby embankment. Einstein’s thought experiment demonstrates that, contrary to our preconceived notion, simultaneous lightning strikes A and B on the train would not be simultaneous on the embankment, and vice versa. Simultaneity is relative to the observer because of the different lengths of time required for a light signal to reach a moving versus stationary observer. Einstein’s new explanation for simultaneous shakes our “proud certainty” of what we thought it meant to be simultaneous. This is only one of numerous similar thought experiments involving trains in the special relativity part of Relativity, all intended to shake our confidence in the notion of absolute time and space. Others involve a dropped stone from a moving train, a raven flying at uniform speed with respect to a moving train, a passenger walking in the train compartment, a beam of light sent through the compartment, and measurements of length in the moving train versus that measured from the embankment. The thought experiment with magnet and conductor that opens Einstein’s 22

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“Electrodynamics of Moving Bodies” is nowhere to be found in his popular science book, and the word electrodynamics, so central to his paper, only appears a handful of times. The change in intended audience demanded a change in emphasis away from a new theory of electrodynamics, of interest to theoretical physics, to the shocking discovery of the relativity of space and time, of possible interest to the wider world. When we arrive at the turning point in Einstein’s overall chain of thought experiments in Relativity, mathematics cannot be avoided despite the broadening in intended audience. The result is not his equations of electrodynamics, the climax to his 1905 paper, but his equations of mechanics in the form of the Lorentz transformation—four equations with which to separately determine spatial position (x, y, z) and time (t) for a uniformly moving frame of reference relative to a stationary one. These simple algebraic equations tell us that among other things, in Einstein’s words, “Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa.” Taken together, Einstein’s four equations constitute mathematical solutions to the problems posed by his train thought experiments. Using the same revelatory equations, Einstein then derives the equation most closely associated with him: E = mc2. In Relativity and his other writings, Einstein made sparing use of visuals to aid readers in seeing the world anew in the light of his theory. Others would quickly fill that gap.

Visualization of Simultaneity Max Born was a founding father of quantum mechanics and close friend of Einstein’s. In his Einstein’s Theory of Relativity, first published in German in 1920, Born presents a thought experiment on simultaneity combined with a geometric visual that will be repeated and modified by countless others over the next century in explaining relativity. He begins by introducing a general principle (in italics), followed by his visual with accompanying text proving it: There is no such thing as absolute simultaneity. Whoever has once grasped this will find it difficult to understand why it took many years of exact research until this simple fact was recognized. It is a repetition of the old story of the egg of Columbus [a brilliant solution to a problem that in retrospect seems obvious]. The next question is whether the method of comparing clocks which we have introduced [synchronization of clocks using light signals] leads to a consistent relative conception of time.

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Figure 1.2. Minkowski graphs showing time versus distance (“xt-plane”) in the x-direction for both stationary (left) and moving points (right). From Max Born, Einstein’s Theory of Relativity (1922), 196, 197. This is actually the case. To see this, we shall use Minkowski’s representation of events or world-points in an xt-plane, in which we restrict ourselves to motions in the x-direction and thus omit those in the y- and z-directions.14

The two graphs in figure 1.2 are Born’s variations on Hermann Minkowski’s graphs for the space-time continuum.15 Minkowski’s great insight was that classical physics locates an event in space with the three spatial dimensions—x, y, z—with time being absolute and independent of the location or velocity. In accord with the Lorentz transformation and Einstein’s new physics, however, for Minkowski an event in space has four dimensions—x, y, z, and t—where “time is robbed of its independence” from the spatial dimensions. Most important, he devised a method for visualizing this time relationship. Unlike the two-spatial-dimensional Cartesian graph it resembles, Minkowski’s is dynamic—t is constantly advancing, as time never stops, even for a stationary object. For simplicity, Born here only plots the x-direction and leaves out the y- and z-directions. In his book, Born does not position the two graphs side by side as we have. Displayed as in figure 1.2, readers can more easily perceive the striking differences in simultaneous time for the cases of stationary and moving points, even before they have puzzled through all the complex geometric details that follow. The points A, B, and C, at rest on the x-axis, are represented in the xt-coordinate system as three parallels to the t-axis [figure 1.2, left side]. Let the point C lie midway between A and B. At the moment t = 0 a light-signal is to be sent out from it in both directions.

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SPECIAL RELATIVITY We assume that the system S is “at rest,” that is, that the velocity of light is the same in both directions. Then the light-signals moving to the right and left are represented by straight lines which are equally inclined to the x-axis, and which we call “light-lines.” We shall make their inclination 45°; this evidently amounts to saying that the same distance which represents the unit length 1 cm. on the x-axis in the figure signifies the very small time 1/c secs. [one divided by the speed of light] on the t-axis, which the light takes to traverse the distance 1 cm. The t-values of the points of intersection A 1, B1, of the light-lines with the world-lines of the points A and B give the times at which the two light-signals arrive. We see that A 1 and B1 lie on a parallel to the x-axis, that is, they are simultaneous. The three points, A, B, C, are next to be moving uniformly with the same velocity [figure 1.2, right side]. Their world-lines are then again parallel, but inclined to the x-axis. The light-signals are represented by the same light-lines, proceeding from C, as above, but their points of intersection, A 1', B1' with the world-lines A, B do not now lie on a parallel to the x-axis; thus they are not simultaneous in the xt-co-ordinate system, and B1' is later than A 1'. On the other hand an observer moving with the system can with equal right assert that A 1', B1' are simultaneous events (world-points). He will use an x't'-coordinate system S' in which the points A 1', B1' lie on a parallel to the t'-axis. The world-lines of the points A, B, C are, of course, parallel to the t'-axis, since A, B, C are at rest in the system S' and hence their x'-co-ordinates have the same values for all t' ’s.16

Born’s version of a Minkowski graph constitutes a stunning representation of Einstein’s new definition of simultaneity taking into account stationary and moving observers. On the x-axis of the left graph in figure 1.2, as Born explains, C lies midway between A and B, and we are to imagine these as stationary. No point advances in the x-direction, but all three advance t in the y-direction, the direction of time. On the plot, Born instructs us to draw what he calls world lines parallel to the t-axis at A, B, and C. We then imagine someone at C shining a light in the x-direction simultaneously to the right and left. The path of the light conforms to the 45 degree lines passing through A 1 and B1. Born calls these light lines. We are then to draw over to the t-axis a horizontal dashed line from B1 through A 1. In this condition, the light sent from C will always be observed at A and B at exactly the same time. Thus, A and B simultaneously receive the light pulse sent at C consistent with “the most natural definition of simultaneity.” No surprise there. 25

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Figure 1.2 at the right reflects the difference in simultaneity that occurs with Einstein’s new definition. In this graph, A, B, and C are in uniform motion in the x-direction (x’-t’ coordinate system). Because of the movement forward in the x-direction, the world lines A, B, and C shift at an angle to the right, but remain parallel and straight. Next, we draw the light lines from C at a 45 degree angle to world lines A and B and connect A’1 and B’1 with a dashed line. As readily apparent, B’1 is always later than A’1 with respect to the t-axis. In short, what is simultaneous for stationary points is not so for uniformly moving points, and vice versa. In the course of Born’s heavily illustrated book (a robust 135 figures in a book under three hundred pages), he covers relativity’s “empirical physical foundations.” So Born traces relativity back to the mathematics and physics of ancient Greece, through the classical physics of the scientific revolution, and on to the work on electrodynamics and optics by James Clerk Maxwell and Hendrik Lorentz. Even though still lacking thorough experimental confirmation at the time, relativity is thus represented as the most recent grand physics theory in a line of theories dating back many centuries, each theory being an advance on a previous one that expands the explanatory reach of physics to the material world.

Embellishing Einstein’s Postulate with a Thought Experiment Besides the first English version of Albert Einstein’s Relativity and the German edition of Max Born’s Einstein’s Theory of Relativity, the year 1920 saw the publication of astrophysicist Arthur Eddington’s Space, Time and Gravitation: An Outline of the General Relativity Theory, the first important popular science book on relativity by a major British scientist. In this popular exposition, Eddington adds to the growing stockpile of inventive thought experiments on special relativity and fills in details of the experimental evidence in favor of general relativity, about which he possessed firsthand knowledge (see chapter 2). Eddington’s thought experiment with a swimmer illustrates Einstein’s postulate regarding the constancy of the velocity of light, leading to the inference that a universal luminiferous ether and absolute rest can be discarded. It has a much less complex visual than Born’s, which lacks any strong connection to daily life. It rests on an easily comprehended analogy between the common experience of swimming upstream and a simple geometric visual, as well as between the current in an ordinary stream and the current from a hypothetical ether: Will it take longer to swim to a point 100 yards up-stream and back, or to a point 100 yards across-stream and back? In the first case there is a long toil up against the current, and then a quick return helped by the current, which is all too short to compensate.

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SPECIAL RELATIVITY Figure 1.3. Path of swimmer in stream. From Arthur Eddington, Space, Time and Gravitation (1920), 17. In the second case the current also hinders, because part of the effort is devoted to overcoming the drift downstream. But no swimmer will hesitate to say that the hindrance is the greater in the first case. Let us take a numerical example. Suppose the swimmer’s speed is 50 yards a minute in still water, and the current is 30 yards a minute. Thus the speed against the current is 20, and with the current 80 yards a minute. The up journey then takes 5 minutes and the down journey 1 ¼ minutes. Total time, 6 ¼ minutes. Going across-stream the swimmer must aim at a point E above the point B where he wishes to arrive, so that OE represents his distance travelled in still water, and EB the amount he has drifted down [figure 1.3]. These must be in the ratio 50 to 30, and we then know from the right-angled triangle OBE that OB will correspond to 40. Since OB is 100 yards, OE is 125 yards, and the time taken is 2 ½ minutes. Another 2 ½ minutes will be needed for the return journey. Total time, 5 minutes. In still water the time would have been 4 minutes. The up-and-down swim is thus longer than the transverse swim in the ratio 6 1/4: 5 minutes. Or we may write the ratio 1

√ 1 – ( 3050 )

2

which shows how the result depends on the ratio of the speed of the current to the speed of the swimmer, viz. 30/50. A very famous experiment on these lines was tried in America in the year 1887. The swimmer was a wave of light, which we know swims through the aether with a speed of 186,330 miles a second. The aether was flowing through the laboratory like a river past its banks. The light-wave was divided, by partial reflection at a thinly silvered surface, into two parts, one of which was set to perform the up-and-down stream journey and the other the across-stream journey. When the two waves reached their proper turning-points they were sent back to the starting-point by mirrors.

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THE MANY VOICES OF MODERN PHYSICS To judge the result of the race, there was an optical device for studying interference fringes; because the recomposition of the two waves after the journey would reveal if one had been delayed more than the other, so that, for example, the crest of one instead of fitting on to the crest of the other coincided with its trough. To the surprise of Michelson and Morley, who conducted the experiment [in 1887], the result was a dead-heat [no effect from an ether detected in the lab].17

The implied analogy here is that this swimmer in a stream is to the water current as a beam of light is to the universal ether. The same geometric relationship should hold for both. But, as Eddington then points out, the Michelson-Morley experiment had demonstrated that the time for light to traverse the up-anddown route is exactly the same as for its transverse route. The swimmer analogy with light moving through a river-like ether does not hold, and the universal ether carrying light can be permanently dispensed with on the scrap heap with phlogiston and the four humors. Because even the fastest trains can only reach an insignificant percentage of the speed of light, Eddington later imagines a spaceship moving near that velocity where the effects of relativity actually would affect time and space. One journey involves a cigar-smoking passenger passing by a cigar-smoking stationary observer at close to 90 percent the speed of light. Although the spaceship passenger would appear only three feet high to the observer, the passenger would appear to himself to be normal, totally unaware of his “undignified appearance.” At the same time, because time slows with increasing velocity, the passenger’s cigar would appear to the observer to last twice as long, while from the passenger’s frame of reference, the observer’s cigar would last twice as long. Eddington continues the thought experiment with a spaceship traveling at close to the speed of light to a nearby star, Arcturus. By Earth time it would take the ship a century to reach its destination, but since it would be moving at close to the speed of light, time would have come to a near standstill for any passengers according to the time equation in the Lorentz transformation. So if the spaceship returned to Earth, it would be some two centuries later on Earth, but the spaceship passengers would not be significantly older. In a footnote, Eddington addresses an obvious question. Why could we not assume the spaceship is stationary and Earth moving away and returning? Would not the earthlings then be the ones to have escaped the ravages of time? Is that not a deep flaw in relativity? We will later deal with that apparent conundrum shortly with another version of a Minkowski graph. 28

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A Philosopher’s Take on Relativity In 1925, Bertrand Russell, the preeminent British philosopher of his time, published a slim popular science volume on relativity, titled ABC of Relativity. The reader will find it teeming with ingenious thought experiments, used by Russell to illustrate the strange character of relativity, like the constancy of the speed of light, the slowing of time and contraction of length with motion, curving of space around masses, and so on. Some appear to be of Russell’s invention, others borrowed and modified from Einstein, Born, and Eddington, all meant to be less technically expressed than those quoted earlier by Einstein and Born. One somewhat silly example asks readers to imagine themselves walking or just riding on an escalator moving at the speed of light, “which it does not do even in New York.” We are to address the question: Does walking get you to the top any faster according to special relativity? Russell’s answer is that “you would reach the top at exactly the same moment whether you walked up or stood still.”18 Of course, even in New York, nothing but a massless subatomic particle like the photon can actually go the speed of light. This next more serious example illustrates both the effects of relative motion on time and space (the Lorentz transformation in Einstein’s paper and book) and the principle that the speed of light cannot be exceeded. It summons an imaginary amusement park ride as the site of the experiment and is of Russell’s invention as far as we could determine: There are other curious things about the velocity of light. One is, that no material body can ever travel as fast as light, however great may be the force to which it is exposed, and however long the force may act. An illustration may help to make this clear. At exhibitions one sometimes sees a series of moving platforms, going round and round in a circle. The outside one goes at four miles an hour; the next goes four miles an hour faster than the first; and so on. You can step across from each to the next, until you find yourself going at a tremendous pace. Now you might think that, if the first platform does four miles an hour, and the second does four miles an hour relatively to the first, then the second does eight miles an hour relatively to the ground. This is an error; it does a little less, though so little less that not even the most careful measurements could detect the difference. I want to make quite clear what it is that I mean. Suppose that, in the morning, when the apparatus is just about to start, you paint a white line on the ground and another one opposite it on each of the first two platforms. Then you stand by the white mark on the first platform and travel with it. The first platform moves at the rate of four miles an hour with respect

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THE MANY VOICES OF MODERN PHYSICS to the ground, and the second platform moves at the rate of four miles an hour with respect to the first. Four miles an hour is 352 feet in a minute. After a minute by your watch, you note the position on your platform opposite to the white mark on the ground behind you, and the position on your platform, and on the ground, opposite to the white mark on the second platform in front of you. Then you measure the distances round to the two positions on your platform. You find that each distance is 352 feet. Now you get off the first platform onto the ground. Finally you measure the distance, on the ground, from the white mark you started with, round to the position which you noted, after one minute’s travelling, opposite to the white mark on the second platform. Problem: how far apart are they? You would say, twice 352 feet, that is to say, 704 feet. But in fact it will be a little less, though so little less as to be inappreciable. The discrepancy results from the fact that according to relativity theory, velocities cannot be added together by the traditional rules. If you had a long series of such moving platforms, each moving four miles an hour relatively to the one before it, you would never reach a point where the last was moving with the velocity of light relatively to the ground, not even if you had millions of them. The discrepancy, which is very small for small velocities, becomes greater as the velocity increases, and makes the velocity of light an unattainable limit.19

The second sentence above expresses in a simple declarative statement what the Lorentz transformation in Einstein’s scientific paper tells mathematically—the speed of light is the speed limit of the universe. The moving platform thought experiment then illustrates that mathematical deduction. As the platform incrementally increases in speed, its length continuously contracts and time slows in accord with the math. At close to the speed of light, the platforms keep contracting to almost nothing, and the time slows to a near standstill, but both length and time still continue. As a result, even if there were trillions and trillions of such platforms, the thought experimenter could approach closer and ever closer but never reach the speed of light, in keeping with the Lorentz transformation equations. (Mathematica programmer Enrique Zeleny created an interactive animated version of Russell’s thought experiment, relieving readers of the burden of mentally visualizing it.)20 From a philosopher, you would also expect some discussion of the philosophical implications of relativity. Russell does not disappoint. In ABC of Relativity, for example, he asserts that despite the claims of some misguided “philosophers and uneducated people” that “everything is relative,” such is definitely not the 30

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philosophical lesson of Einstein’s theory.21 What special relativity does tell us is that, with uniform motion relative to a stationary observer, mass and energy increase, length contracts, and time slows, although these effects are not evident in our daily lives. Special relativity also tells us the velocity of light is an exception: it is not relative to the speed of the observer. Russell brings these insights vividly to life with a panoply of thought experiments and analogies. At the end of ABC of Relativity, he spells out the philosophical consequences—the need to rethink common technical terms like mass, energy, velocity, length, and time.

Special Relativity in Story Form The above abstract thought experiments taken from what we might loosely categorize as “popular science” books do require considerable cognitive processing by most readers (ourselves included). Popular science writing does not necessarily imply light reading or a truly universal audience, only a particular audience much wider than the typical very narrow one for scientific articles. In their prefaces, the physicist authors of the above excerpted books alert prospective readers as much. In Relativity, Einstein imagines his readers as having attained “a standard of education corresponding to that of a university matriculation examination” and warns that this book will require, at times, “a fair amount of patience and force of will.”22 In Space, Time and Gravitation, Eddington comforts potential readers that they will not be faced with “anything very technical in the way of mathematics, physics, or philosophy,” but they can expect “unusual mental exercise.”23 In Einstein’s Theory of Relativity, Born goes into some detail about his expectations with regard to the math at least: “The reader is assumed to have but little mathematical knowledge. I have attempted to avoid not only the higher mathematics but even the use of elementary functions, such as logarithms, trigonometrical functions, and so forth. Nevertheless, proportions, linear equations, and occasionally squares and square roots had to be introduced. I advise the reader who is troubled with the formulae to pass them by on the first reading and to seek to arrive at an understanding of the mathematical symbols from the text itself.”24 In Mr. Tompkins in Wonderland, George Gamow, a prominent physicist who would later make a significant contribution to the big bang theory, takes a more reader-friendly approach to explaining relativity theory. Aiming at a young adult audience with interest in science, he translates the abstract thought experiments of Einstein and the others into a series of stories starring “a little clerk in a big city bank” named Mr. C. G. H. Tompkins. (Gamow chose those initials because they correspond to three fundamental constants important to relativity and quantum theory: C for speed of light, G for the gravitational constant, and 31

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H for the Planck constant in quantum mechanics.) 25 Also co-starring in the story is a physics professor. In the opening story, Mr. Tompkins decides to attend a lecture on relativity theory. He falls asleep during the lecture and dreams he is in a relativistic wonderland where the speed of light is only ten miles per hour. Because the laws of special relativity hold, the fastest any object can move is less than ten miles per hour; effects of the theory are thus magnified many times over. Gamow’s story thought experiment illustrates what life would be like in this virtual reality, bringing the effects of Einstein’s theory to life in a different way from the earlier thought experiments. What began life near the beginning of the century as abstract thought experiments has morphed into a story in which science fiction becomes science fact: It was a beautiful old city with medieval college buildings lining the street. He suspected that he must be dreaming but to his surprise there was nothing unusual happening around him; even a policeman standing on the opposite corner looked as policemen usually do. The hands of the big clock on the tower down the street were pointing to five o’clock and the streets were nearly empty. A single cyclist was coming slowly down the street and, as he approached, Mr. Tompkins’s eyes opened wide with astonishment. For the bicycle and the young man on it were unbelievably shortened in the direction of the motion, as if seen through a cylindrical lens. The clock on the tower struck five, and the cyclist, evidently in a hurry, stepped harder on the pedals. Mr. Tompkins did not notice that he gained much in speed, but, as the result of his effort, he shortened still more and went down the street looking exactly like a picture cut out of cardboard [figure 1.4, left]. Then Mr. Tompkins felt very proud because he could understand what was happening to the cyclist—it was simply the contraction of moving bodies, about which he had just heard. “Evidently nature’s speed limit is lower here,” he concluded, “that is why the bobby on the corner looks so lazy, he need not watch for speeders.” In fact, a taxi moving along the street at the moment and making all the noise in the world could not do much better than the cyclist, and was just crawling along. Mr. Tompkins decided to overtake the cyclist, who looked a good sort of fellow, and ask him all about it. Making sure that the policeman was looking the other way, he borrowed somebody’s bicycle standing near the curb and sped down the street. He expected that he would be immediately shortened, and was very happy about it as his increasing figure had lately caused him some anxiety. To his great surprise, however, nothing happened to him or to his cycle. On

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Figure 1.4. Illustrations of effects of time and space in Gamow’s relativistic wonderland. From George Gamow, Mr. Tompkins in Paperback (1965), 3–4. Reproduced with permission of Cambridge University Press through PLSclear.

the other hand, the picture around him completely changed. The streets grew shorter, the windows of the shops began to look like narrow slits, and the policeman on the corner became the thinnest man he had ever seen [figure 1.4, right].26

These Lewis Carroll–like stories vividly depict the relativity of space only. Next Gamow illustrates the relativity of both space and time. When Mr. Tompkins hops on a bicycle in pursuit of the cyclist, he finds that nothing about his shape seems to change. He looks the same as always. When Mr. Tompkins overtakes the cyclist, he asks him why he seemed to be moving at a snail’s pace. The cyclist tells him they both had in fact just covered five blocks in the short time of their encounter, since, while in motion, the blocks appear to be very short. The distance of each block contracts the closer he approaches the 10 mph speed limit. Having driven for ten blocks to the local post office, the two characters stop. Mr. Tompkins notes the clock outside the post office says half past five, suggesting the trip took half an hour. But the cyclist asks him to check his wristwatch, which has only advanced five minutes. Later, still in the relativistic city, Mr. Tompkins meets a very old woman whose grandfather is much younger than she, only in his forties. This is because the grandfather has a job in which he was constantly traveling while his granddaughter lived a sedentary existence. When Mr. Tompkins encounters a physics professor on a train ride, the professor tells him the point behind this part of the narrative: “It was shown by Einstein, on the basis of his analysis of new . . . notions of space and time, that all physical processes slow down when the system in which they are taking 33

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place is changing its velocity. In our world the effects are almost unobservably small, but here [in the relativistic city], owing to the small velocity of light, they are usually very obvious.”27 In the next section and in chapters to come, we will be examining a number of other narrative-driven thought experiments like this, including a brilliant one from Gamow’s book, where Mr. Tompkins learns about a bizarre effect of general relativity.

Visualization of the Paradox in the Twin Paradox Since Einstein, so many distinguished physicists have written about special relativity for a general audience that it might seem that there is nothing new to say. In 2007, however, theoretical physicist Sander Bais threw this pessimism overboard. Very Special Relativity: An Illustrated Guide is full of thought experiments concerning this theory, each of which is tied to a variation on the Minkowski space-time diagram discussed earlier. One of these concerns the twin paradox, an enduring puzzle special relativity has left in its wake. Bais conveys this paradox in a hybrid thought experiment, combining the amusing story form of Gamow and the geometric type visual of Born: The twin paradox shows that the time dilation effect, the fact that moving clocks run at a slower rate, is real. Time dilation as a real physical effect appears to be yet another paradox. After all, doesn’t relativity say that motion is relative? If A’s clock runs more slowly than B’s because A is moving with respect to B, shouldn’t we also require that B’s clock run more slowly than A’s, as B is moving with respect to A just as well? This is the paradox underlying the following thought experiment. Nora and Vera, two identical twins, are given identical, perfectly calibrated clocks. Vera then goes on a space trip, moving through the galaxy at great velocity, to return home after a long journey. Nora stays at home. At a certain time, Vera comes back. Because she has been moving, her clock has been running more slowly and therefore for her less time has elapsed since she left. She will find her sister much more aged than herself. Depending on the length of her trip and the relative velocity she traveled at, she may even find that Nora has died long ago! Now that is drama. Is this brilliant fiction or harsh reality? And if it is for real, how can we reconcile this asymmetry with the basic postulate of relativity? That is the question! 28

The twin paradox is a consequence of the time equation in the Lorentz transformation. It predicts that if thirty years elapse for Nora on Earth, and 34

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Figure 1.5. Graph illustrating twin paradox. Original image is in color. The Minkowski graph we have reproduced is slightly modified from original. In particular, we substituted the letter w for t representing the various points in time along the y-axis. From Sander Bais, Very Special Relativity (2007), 61. Reproduced with permission of Amsterdam University Press.

Vera’s spaceship travels at four-fifths the speed of light, only eighteen years pass by for Vera. Figure 1.5 visually represents Bais’s explanation. In this figure Nora’s time on Earth is represented by an advance straight up the y-axis (time elapsed) from 0 to t1. At the same time, Vera travels to a distant point two squares to the right and three squares up, turns around, and returns home to Earth at t1. At t = 0, the twins are the same age; at t = t1, Vera is twelve years younger. How is that possible? By quick visual inspection of the two paths, readers might understandably and mistakenly conclude that Vera and Nora should be the same age at the end since they both have ascended the time axis the exact same distance. The shaded triangle represents why that is not the case. It shows the differences in times between the twins at the point when Vera 35

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hits the midpoint in her journey. According to Bais, “Just before the turning point [triangle apex], Vera considers ta to be simultaneous to her time [light line from apex to that point], but an infinitesimally small amount of time later she sees tb as simultaneous [light line from apex to other point]. So somehow she has jumped instantaneously from ta to tb.”29 Similar triangles constructed with light lines could be drawn all the way along Vera’s path up to t1. The time differences between the twins add up to twelve years at the end. There is another twist to the twin paradox, mentioned earlier. Would not relativity be contradicted if we assume that Vera in her spaceship is stationary and Nora on spaceship Earth is moving relative to her? Shouldn’t Nora then be twelve years older than Vera? Would not that mean curtains for Einstein’s theory? Bais’s explanation is that Vera still experiences the acceleration and deceleration of her spaceship as it reverses direction to head home, even though she is assumed to be stationary, while Nora on the spaceship Earth would experience no sense of a change in direction at the turning point. Since special relativity only applies to uniform motion, it would not apply in this case. That asymmetry, according to Bais, is what resolves that paradox in the twin paradox. There is a continuing controversy concerning the twin paradox. Some have offered alternative explanations not involving the acceleration and deceleration argument;30 others, solutions that purport to eliminate the age difference altogether.31 But we will let Bais have the last word: “The twin paradox is an entirely real physical effect.” So, time travel is possible if you can build a Star Trek–like spaceship!

In his popular science book Relativity, Einstein designed his thought experiments with trains to upset our “feeling of proud certainty” about our existing notions of absolute space and time, especially with regard to simultaneous time. They had a tremendous influence on not only his own thinking and writing but also all subsequent popular science accounts of special relativity and beyond. One of their minor shortcomings is that no train can approach anywhere near the speed of light, where the effects of relative motion noticeably affect time and space. For that reason, Eddington switched the mode of transportation to spaceships; Russell concocted an imaginary amusement park ride consisting of an indefinite number of linked platforms, each moving four miles per hour faster relative to the one that preceded it; and Gamow imagined an alternative universe in which the speed of light is only ten miles per hour. Also lacking in Einstein’s accounts but introduced by other physicists are Minkowski space-time diagrams. Born and Bais applied them to central concepts behind special relativity, visually 36

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representing Einstein’s new definition of simultaneity and the twin paradox in conjunction with thought experiments. Worth emphasizing is that Einstein’s 1905 special relativity paper contains a thought experiment fundamentally different from any popular account in that it is integral to a mathematical argument aimed only at other physicists, many of whom after several years delay acknowledged its truth. While all the subsequent popular thought experiments bring out seemingly impossible aspects of special relativity which, if true, apply to the real world—at least in the extreme case of a velocity approaching the speed of light—general readers have no way of judging with any expertise if these actually are true. As in any popular science book, readers have to trust the physicists, while recognizing at the same time that the physicists’ theories could one day be proved flawed or incomplete.

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2 GENERAL RELATIVITY

At the beginning of the last century, Western Europe underwent a radical shift in the way creative men and women viewed the world. In physics, there was not only Albert Einstein but also Erwin Schrödinger and Werner Heisenberg; in the novel, there were Gertrude Stein and Virginia Woolf; in poetry, T.S. Eliot and Ezra Pound; in painting, Hilma af Klint and Pablo Picasso; in classical music, Arnold Schoenberg and Igor Stravinsky; in jazz, Jelly Roll Morton and Louis “Satchmo” Armstrong. It is within this Weltanschauung, this new worldview, that Einstein lived and labored. In the miracle year of 1905, he worked with astonishing speed to develop special relativity and lay the groundwork for quantum theory. With painful effort over the following decade, he then labored strenuously as he developed his theory of general relativity. Just three years after its publication, one of this theory’s predictions showed impressive agreement with solar measurements by a team of British scientists who rose above partisanship to pay tribute to the work of an exceptional physicist, a citizen of an enemy nation. In Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc, historian of science Arthur I. Miller links as parallel the quests of these two ambitious young men: In the intellectual atmosphere of 1905 it is not surprising that Einstein and Picasso began exploring new notions of space and time almost

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Figure 2.1. Pablo Picasso’s Les Demoiselles d’Avignon (1907). coincidentally. The main lesson of Einstein’s relativity theory is that in thinking about these subjects, we cannot trust our senses. Picasso and Einstein believed that art and science are means for exploring worlds beyond perceptions, beyond appearances. Direct viewing deceives, as Einstein knew by 1905 in physics, and Picasso by 1907 in art. Just as relativity theory overthrew the absolute status of space and time, the cubism of Georges Braque and Picasso dethroned perspective in art.1

Les Demoiselles d’Avignon (figure 2.1), Picasso’s most notorious painting, which now hangs in the Museum of Modern Art in New York City, depicts five 39

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nudes (or one nude five times), each a far cry from the classical and romantic ideals of feminine beauty. As our eyes move across the canvas, both the women and their background are victims of a chaos of perspectives, the table laden with fruit in the lower center indicating clearly the complete absence of a single point of view. No other work of art could better represent Picasso’s rejection of past notions of what representations of the human form should accomplish. Einstein shared Picasso’s need to cast the past aside. Most famously, he did that for time and space related to relative uniform motion in a straight line with his special relativity paper of 1905, as just discussed in the previous chapter. He also did it even more spectacularly for gravity and acceleration in his climatic paper on general relativity in 1916, which includes his gravitational field equation governing the relative motion of all large bodies in the heavens and on Earth. At the beginning of both of Einstein’s papers appear thought experiments purposely designed to shake the readers’ beliefs in the nature of time, space, and motion as part of his overthrow of both Newtonian physics and Euclidean geometry. Einstein’s 1916 paper starts with no less than three thought experiments, all laying the foundation for the avalanche of equations to follow as Einstein works toward the climax of a compact equation capturing the essence of general relativity. These same thought experiments and variations on them would be the inspiration for many subsequent popular expositions, including Einstein’s own. And in the latter half of the twentieth century, the underlying principles embedded within these thought experiments would find impressive application in the development of modern cosmology, including black hole theory.

Contra Newton The “A. Einstein” listed as the sole author of Einstein’s 1916 paper on general relativity2 is a very different scientist from the one listed on the special relativity paper. In 1905 Einstein was a young patent examiner who practiced physics in stolen free time at work and at home, and in 1916 he was a middle-aged professor at the University of Berlin and a star of German physics. As mentioned in chapter 1, the title to Einstein’s 1905 paper, “On the Electrodynamics of Moving Bodies,” alludes to the latest and most important physics theory of that time, Maxwell’s electrodynamics. The title to this 1916 paper, “The Foundation of the General Theory of Relativity,” also alludes to the latest and most important physics theory of that time, Einstein’s own theory. Einstein begins this paper with the rhetorical tactic we found with special relativity in his popular science book: start with a fundamental assumption no sane person would question, then throw that assumption into doubt. Einstein’s opening, seemingly totally reasonable assumption is that the distance between 40

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two points on a rigid body at rest is always the same independent of where you measure it. Moreover, also independent of place is the time interval between two ticks on a clock at rest. For example, when measuring length or time while at rest, it should not matter a jot where you are: deep in a coal mine, on Earth’s surface, atop the Empire State Building, or on the moon. But, Einstein concludes, “The general theory of relativity cannot adhere to this simple physical interpretation of space and time.”3 To begin the process in shaking our confidence in what seems obvious, Einstein turns to a variation on a thought experiment of Isaac Newton’s invention related to circular motion, a form of acceleration where the direction of motion changes over time while the velocity remains constant. Newton’s original thought experiment involves a rotating bucket partially filled with water. Almost two centuries after its first expression, Ernst Mach argued for a seemingly ludicrous alternative interpretation to Newton’s, as physicist Tony Rothman explains: In his magnum opus, Principia Mathematica, Newton proposed a thought experiment to prove that rotation takes place with respect to absolute space. He imagined a bucket partially filled with water and hanging from a rope, which an experimenter has twisted up. When the experimenter releases the bucket, the rope untwists, and the bucket begins to spin. At first the water remains flat, but as the pail speeds up and drags along the water, its surface eventually becomes concave due to the centrifugal force of the rotation. At that stage, the water and vessel are rotating together, and there is no relative motion between them. Yet somehow the water “knows” to create a concave surface. Newton insisted that the concavity must be due to the water’s rotation with respect to something else—absolute space. Rotation is absolute, not relative. That answer stood largely unchallenged for two centuries, until the Austrian physicist Ernst Mach flatly declared Newton to be wrong. In his 1883 book Science of Mechanics, Mach wrote that Newton’s thought experiment “simply informs us, that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the Earth and the other celestial bodies.” . . . He dismissed absolute space as an “arbitrary fiction of our imagination.” Mach never gave a precise formulation of what became known as Mach’s Principle. Nevertheless, the essential idea is simple enough. According to Mach, Newton’s conception of absolute space lacks all meaning. Inertia—that tendency of massive objects to move at constant velocity—must depend on other bodies, because motion itself must be measured relative

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THE MANY VOICES OF MODERN PHYSICS to other bodies. Rotations and accelerations along straight paths take place with respect to the reference frame of the distant stars and galaxies. The centrifugal forces that throw you to the side of an automobile as it rounds a corner arise because you are accelerating with respect to the distant matter in the universe.4

Rothman’s first paragraph begins with a thought experiment that poses a puzzle—why is the water still concave, even though the water and bucket are rotating in synch? Newton’s solution to his thought experiment identified spinning relative to absolute space as the reason. Mach dismissed that solution. Popular science physicist Brian Greene expressed Mach’s principle succinctly in modern terms: “When the airplane you are on accelerates down the runway, when the car you are in screeches to a halt, when the elevator you are in starts to climb, Mach’s ideas imply that the force you feel represents the combined influence of all the other matter making up the universe. If there were more matter, you would feel greater force. If there were less matter, you would feel less force. And if there were no matter, you wouldn’t feel anything at all.”5 Einstein found Mach’s argument about Newton’s thought experiment compelling and the starting point for communicating his new theory. Einstein’s actual thought experiment in his 1916 paper is a major rethinking of Newton’s original and Mach’s variation. In it, we are to imagine two fluid spheres of equal size separated from each other by so large a distance that gravitational forces between them would be negligible. We are next to set one of the spheres into uniform rotation about an imaginary axis joining the two spheres. We know from experience that the rotating sphere will assume an ellipsoidal shape, and the other will remain unchanged. But what if we switch our frame of reference from the stationary sphere to the ellipsoidal one? In this case, Einstein conjectures that the sphere shapes would remain unchanged: the “stationary” ellipsoidal sphere would remain the same shape as would the other sphere, even though now “rotating.” How to explain the asymmetry—or in Einstein’s own charming phrase, “inherent epistemological defect”? In keeping with Mach’s interpretation, Einstein contends that, whatever the cause, it must arise from distant masses “outside the system” of the two fluid bodies, which would later be assumed to mean all the other matter in the universe rotating around the ellipsoid sphere if it is the one assumed to be stationary. In this case, imagine if you will the dizzying picture of a “stationary” ellipsoidal sphere being circled by the planets, sun, all the stars and galaxies whose combined gravitational pull causes the shape formation. With no such masses, there would presumably be no shape change at all. 42

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In other popular science versions of this thought experiment after Einstein’s paper, physicist authors have favored the spinning water bucket analogy as Rothman did,6 not Einstein’s two liquid spheres. The judgment of time appears to be that the water bucket version more vividly communicates the main message for popular expositions—just as the uniform motion of special relativity has no absolute frame of reference, any generalization of it to accelerated motion must do likewise. Newton’s interpretation has to go. That is the first postulate in Einstein’s opening argument.

Einstein’s Happiest Thought Experiment After the two-sphere thought experiment in his 1916 paper, Einstein turns to a more abstract and technical thought experiment involving an object accelerating in a straight line relative to a stationary observer. His conclusion from this thought experiment is what has come to be known as the “equivalence principle”—the effects of accelerated motion are equivalent to those from a gravitational field. In his paper, Einstein did not express this thought experiment in the language the common reader can be expected to grasp, one involving things of everyday experience, a very large container and rope. But he did do that at some length in Relativity: The Special and General Theory, his popular science book published in 1917: We imagine a large portion of empty space, so far removed from stars and other appreciable masses, that we have before us approximately the conditions required by the fundamental law of Galilei. It is then possible to choose a Galileian [sic] reference-body for this part of space (world), relative to which points at rest remain at rest and points in motion continue permanently in uniform rectilinear motion. As reference-body let us imagine a spacious chest resembling a room with an observer inside who is equipped with apparatus. Gravitation naturally does not exist for this observer. He must fasten himself with strings to the floor, otherwise the slightest impact against the floor will cause him to rise slowly towards the ceiling of the room [like an astronaut in space]. To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion. In course of time their velocity will reach unheard-of values—provided that we are viewing all this from another reference-body which is not being pulled with a rope.

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THE MANY VOICES OF MODERN PHYSICS But how does the man in the chest regard the Process? The acceleration of the chest will be transmitted to him by the reaction of the floor of the chest. He must therefore take up this pressure by means of his legs if he does not wish to be laid out full length on the floor. He is then standing in the chest in exactly the same way as anyone stands in a room of a home on our Earth. If he releases a body which he previously had in his hand, the acceleration of the chest will no longer be transmitted to this body, and for this reason the body will approach the floor of the chest with an accelerated relative motion. The observer will further convince himself that the acceleration of the body towards the floor of the chest is always of the same magnitude, whatever kind of body he may happen to use for the experiment. Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time. Of course he will be puzzled for a moment as to why the chest does not fall in this gravitational field. Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field. Ought we to smile at the man and say that he errs in his conclusion? I do not believe we ought to if we wish to remain consistent; we must rather admit that his mode of grasping the situation violates neither reason nor known mechanical laws. Even though it is being accelerated with respect to the “Galileian [sic] space” first considered, we can nevertheless regard the chest as being at rest. We have thus good grounds for extending the principle of relativity to include bodies of reference which are accelerated with respect to each other, and as a result we have gained a powerful argument for a generalised postulate of relativity.7

Unlike the train thought experiment that so dominated the special relativity part of Relativity, this crucial one was not repeated with variations by Einstein in the general relativity part of his book, but it would later be repeated again and again in various ways over the decades by other physicists and science writers attempting to explain general relativity to a general audience.8 Like the train thought experiment, it takes place in a large enclosed space—Einstein refers to it as a “chest” the size of a room—that moves in a straight line as it is pulled by a rope and is occupied by a passenger (figure 2.2). In executing this thought experiment, we find that the effects on the stick figure are equivalent whether the 44

GENERAL RELATIVITY Figure 2.2. Visualization of thought experiment illustrating the equivalence principle between gravity and acceleration. From Prokaryotic Caspase Homolog, April 16, 2018, https://commons.wikimedia.org/w/index. php?curid=68363516.

chest is being accelerated by some extraterrestrial yanking a rope at uniform acceleration or suspended at rest in some gravitational field, such as that of the Earth. This second thought experiment deftly dramatizes the second postulate of general relativity, and it along with the first thought experiment makes for “a powerful argument for a generalized postulate of relativity.” Einstein milks this thought experiment for further startling insights.9 Along with the equivalence of acceleration and gravity, one of the truly startling inferences from this thought experiment is the bending of light. To illustrate Einstein imagines a ray of light having been shot across the freely falling chest. With respect to an observer in the accelerated chest, the light would move downward due to the chest having been yanked upward a slight distance in the time the light crossed from one side of the chest to the other. So, given the equivalence of acceleration and gravity, to an observer inside a chest that is at rest in a powerful gravitational field, the light beam would move downward by the exact same distance as it would if the chest were accelerating. The analogy between acceleration and gravity thus leads to the truly astonishing conclusion that the path of a light beam is curved under both conditions. Continuing the same fecund thought experiment, Einstein also concludes that the curvature of a light ray in a gravitational field can only happen if its velocity changes with position. So in the chest, the speed of light is not constant when the light is bent. This is so whether the chest is accelerating or resting in a gravitational field. With good reason, then, Einstein later referred to the equivalence principle as “the happiest thought” of his life.10 Never has a single thought experiment provided so many profound insights. 45

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Contra Newton and Euclid Having established the equivalence principle in his 1916 scientific paper, Einstein then proceeds with a thought experiment that argues for the warping of space and time with accelerated circular motion, constituting Einstein’s third postulate. The thought experiment must have been a favorite child of Einstein’s, because it also appeared in Relativity in 1917 and the published lectures he gave at Princeton University in 1921, “The Meaning of Relativity.”11 All three versions share the same rotating disc. We reproduce the selection from his 1917 book. While Einstein’s account is addressed to the general reader, we would hesitate to call it popular. It is not to be read in a few minutes, but rather studied. Readers who pay the text the full attention it deserves will be propelled forward in a powerful argumentative tide, one created by a master teacher lecturing to high school physics students. This opening paragraph sets up the thought experiment to follow. Because there is no absolute frame of reference, Einstein must carefully establish for us a relative one: Let us consider a spacetime domain in which no gravitational field exists relative to a reference body K whose state of motion has been suitably chosen. K is then a Galileian [sic] reference body as regards the domain considered, and the results of the special theory of relativity hold relative to K. Let us suppose the same domain referred to a second body of reference K', which is rotating uniformly with respect to K. In order to fix our ideas, we shall imagine K' to be in the form of a plane circular disc, which rotates uniformly in its own plane about its center. An observer who is sitting eccentrically on the disc K' is sensible of a force which acts outwards in a radial direction, and which would be interpreted as an effect of inertia (centrifugal force) by an observer who was at rest with respect to the original reference body K. But the observer on the disc may regard his disc as a reference body which is “at rest”; on the basis of the general principle of relativity he is justified in doing this. The force acting on himself, and in fact on all other bodies which are at rest relative to the disc, he regards as the effect of a gravitational field. Nevertheless, the space distribution of this gravitational field is of a kind that would not be possible on Newton’s theory of gravitation. But since the observer believes in the general theory of relativity, this does not disturb him; he is quite in the right when he believes that a general law of gravitation can be formulated—a law which not only explains the motion of the stars correctly, but also the field of force experienced by himself.12

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Here, Einstein sets up a frame of reference for a similar thought experiment to his earlier rotating sphere thought experiment illustrating Mach’s principle. In this case, he replaces the spheres with a single circular disc rotating with respect to a stationary body in a space with no gravitational field like Earth to rest on. He also adds anonymous observers: one on the rotating disc; the other stationary. Newtonian physics attributes the outward (centrifugal) force experienced by the circling observer to the rotation of the disc. But if we set the stationary frame of reference as the figure on the disc periphery, then general relativity attributes the force experienced by that figure to “a gravitational field,” which is not possible with Newton’s theory. This gravitational field is presumably the same one evoked in the first thought experiment with the ellipsoid sphere chosen as being stationary—that is, all the mass in the universe. Einstein caps off the paragraph with an astounding leap—the same general theory that explains his rotating disc experiment explains the motions of the stars. The rotating disc thought experiment then continues merrily along with more actions and a dramatic conclusion. Einstein arms the rotating observer with clocks and measuring rods, the first to test the effect of special relativity of time, the second, length. We know from special relativity that length contracts and time slows for a uniformly moving body in a straight line. Einstein takes that as given. So what does that mean if we apply the same principle to someone on a rotating disc at uniform speed? We rejoin Einstein’s thought experiment in Relativity: The observer performs experiments on his circular disc with clocks and measuring rods. In doing so, it is his intention to arrive at exact definitions for the signification of time- and space-data with reference to the circular disc K', these definitions being based on his observations. What will be his experience in this enterprise? To start with, he places one of two identically constructed clocks at the center of the circular disc, and the other on the edge of the disc, so that they are at rest relative to it. We now ask ourselves whether both clocks go at the same rate from the standpoint of the nonrotating Galileian [sic] reference body K. As judged from this body, the clock at the center of the disc has no velocity, whereas the clock at the edge of the disc is in motion relative to K in consequence of the rotation. According to a result obtained in Section XII [on the time and space effects of special relativity], it follows that the latter clock goes at a rate permanently slower than that of the clock at the center of the circular disc, i.e. as observed from K. It is obvious that the same effect would be noted by an observer whom we will imagine sitting alongside his clock at the center of the circular disc. Thus on our

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THE MANY VOICES OF MODERN PHYSICS circular disc, or, to make the case more general, in every gravitational field, a clock will go more quickly or less quickly, according to the position in which the clock is situated (at rest). For this reason, it is not possible to obtain a reasonable definition of time with the aid of clocks which are arranged at rest with respect to the body of reference. . . . Moreover, at this stage the definition of the space coordinates also presents insurmountable difficulties. If the observer applies his standard measuring rod (a rod which is short as compared with the radius of the disc) tangentially to the edge of the disc, then, as judged from the Galileian [sic] system, the length of this rod will be less than 1, since, according to Section 12, moving bodies suffer a shortening in the direction of the motion. On the other hand, the measuring rod will not experience a shortening in length, as judged from K, if it is applied to the disc in the direction of the radius. If, then, the observer first measures the circumference of the disc with his measuring rod and then the diameter of the disc, on dividing the one by the other, he will not obtain as quotient the familiar number π = 3.14 . . . , but a larger number, whereas of course, for a disc which is at rest with respect to K, this operation would yield π exactly. This proves that the propositions of Euclidean geometry cannot hold exactly on the rotating disc, nor in general in a gravitational field, at least if we attribute the length 1 to the rod in all positions and in every orientation. Hence the idea of a straight line also loses its meaning.13

In the aforementioned passage, Einstein leads his imagined audience of young physics students step by step from what they have already learned—the point of the cross-references to section 12 (on special relativity)—to a rejection of both Newtonian physics with regard to absolute time and space and Euclidean geometry with regard to a simple circle and straight line. His is a world in which circumference equals pi times the diameter may (or may not) be the formula for a circle, one in which even the notion of a straight line is relative. Much of the framework for the mathematics that follows in Einstein’s general relativity paper rests on the postulate that space bends and time slows under accelerated motion or a gravitational field. Just as special relativity radically redefined space and time, so too general relativity, but even more so.

Gamow Visualizes Einstein’s Thought Experiment After Einstein, many popular science physicists explaining general relativity have spun out some variation on the rotating disc in explicating curved space-time in general relativity, normally adding circumstantial details to make it more 48

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Figure 2.3. Three experimenters measuring different dimensions in a rotating platform. Mr. Tompkins and professor are the stationary observers. Hookham is the name of the illustrator for many of the book’s drawings. From George Gamow, Mr. Tompkins in Paperback (1965), 33. Reproduced with permission of Cambridge University Press through PLSclear.

realistic and entertaining and less abstract. In Mr. Tompkins in Paperback, for example, George Gamow visualizes Einstein’s thought experiment in figure 2.3, then discusses it.14 That’s a stationary Mr. Tompkins on the right, a stationary physics professor on the left explaining the physics, and four experimenters working on the rotating disc, one of whom appears to be there just to enjoy the ride, a typical humorous Gamow touch. Gamow calls his disc a “platform” and locates it in the relativity wonderland we first encountered in the special relativity chapter. Experimenters No. 3 and 4 illustrate Einstein’s thought experiment for length measurements. Euclid’s formula for the circle (C/D = p) does not hold here because the measuring rod shrinks for the rotating experimenter measuring the circumference but not for the one measuring the diameter. The key difference is that the former moves uniformly in the direction of motion while the latter is always perpendicular to that motion. Einstein’s thought experiment makes a strong verbal argument that Euclidean geometry fails in the case of a rotating circle. But it does not really communicate 49

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what that means in terms of actual physical space. Experimenter No. 2 in Gamow’s figure does. He is measuring a triangle formed with the apexes touching the circumference of the platform. The dotted lines show us a normal Euclidean triangle when the platform is not rotating while the solid lines show the warped space measured when it is spinning. This single picture thus demonstrates the violation of Euclidean geometry for the circle, triangle, and straight line. Of course, Gamow’s wonderland example greatly magnifies the non-Euclidean effects of relativity. In our everyday world, the effects on such a small scale are essentially nonexistent.

The Most Beautiful Equation in Physics Einstein’s trio of thought experiments in his 1916 paper upends past notions of space, time, accelerated motion, and gravity. Afterward, a seismic shift in the prose occurs. The thought experiments cease entirely, and the math part kicks into high gear as Einstein derives a set of equations for the various relationships that transform those cherished notions. The climax is the following presentation of mathematical symbols:15 R μν = –κ (Tμν – 1/2 gμνT) In an essay appearing in a book called It Must Be Beautiful: Great Equations of Modern Science, Roger Penrose accurately characterized this equation as “of unprecedented elegance and geometric simplicity.”16 It stands in for our usual quotation of a long passage or picture here. We will not try to fully explain all the symbols in this beautiful equation. Suffice to say, the subscripted symbols are called tensors (gμν, R μν, and Tμν), which are special because they describe many more dimensions than just “east-west or north-south, but also up-down, forward or backward in time, and so forth.”17 For Einstein, tensors function like a trope called “synecdoche.” In classical rhetoric, synecdoche is a figure of speech where a part is shorthand for the whole, as in “All hands on deck!” The hands represent all sailors present on the boat, not just their hands. In synecdoche-like fashion, symbols for tensors like gμν, R μν, and Tμν stand for much more elaborate mathematical equations, the symbol being much easier to manipulate mathematically and conceptually than the equation it represents in full. (The Greek symbols μ and ν represent all possible combinations of pairs of numbers from 1 to 4: 11, 12, 13, 14, 21, 22, 23, 24, etc. The numbers 1–4 reflect the four dimensions of space-time. Since pairs like 12 and 21 are considered equivalent, the sixteen possible combinations boil down to ten unique combinations. [see equations below]) 50

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Simply defining the symbols in Einstein’s equation does not actually communicate to us non-physicists much of anything. It’s all Greek to us. In a later publication, Einstein rearranged and revised his epoch-making equation into an expression that is more psychologically satisfying and physically meaningful:18 R μν – 1/2 gμνR = –κTμν The reformulation expresses a clear analogy between Einstein’s equation and the physical world. (For those wanting to check the algebra, note that R = κT.) In the words of Penrose, Einstein’s equation “tells us how space-time curvature (left-hand side) is directly related to the distribution of mass in the universe (right-hand side).”19 According to the slightly more elaborate interpretation of physicists S. James Gates Jr., Frank Blitzer, and Stephen Jacob Sekula, the equation has a finely balanced chiasmic grammatical structure: the left-hand side represents “how space-time curves in response to the presence of matter and energy,” while the right-hand side expresses “how matter and energy are moved by this curvature of space-time.”20 Important to bear in mind here is that the space-time curvature is what we call gravity. Today, physicists sometimes express Einstein’s above equation in even simpler, more compressed form: G μν = κTμν Physicists call the G μν on the left side the “Einstein tensor.” It has become a symbol representing all of general relativity. It expands into ten simple-looking equations: G11 = T11, G12 = T12, G13 = T13, G14 = T14, G22 = T22, G23 = T23, G24 = T24, G33 = T33, G34 = T34, G44 = T44 Each of these equations also expands into a more complicated mathematical expression. Einstein’s history-making equation may thus look simple on the surface, but most of the hands have gone below the deck and are out of sight. Besides hidden complex mathematical equations, enmeshed in it is the warping of space-time as expressed through the communicative vehicle of the thought experiments with rotating disc and chest. 51

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From Theory Prediction to Proof As in his 1905 paper, the end of theory development in Einstein’s 1916 paper is not the end of his story. Einstein devotes the last parts to convincing his physicist readers that the theory and its equation are credible. Typical physics papers end with an argument by comparison between theory calculations and actual measurements of some property, or at least the future promise of one. Einstein does just that with a calculation of the deviation in the orbit of Mercury caused by the gravitational fields of all the other planets plus the sun, and comparison with the latest measurement of it in the previous century. To Einstein’s everlasting satisfaction, “Calculation [with general relativity] gives for the planet Mercury a rotation of the orbit of 43´´ [arc seconds] per century, corresponding exactly to astronomical observation.”21 On that affirmative note ends Einstein’s “General Theory of Relativity.” Obviously, a monumental achievement, an achievement that left Einstein happy but “kaput.” But wait. The gold standard for the proof of any theory is not the calculation of an already known quantity, but the successful prediction of an unknown one. Also in the conclusion to his paper, Einstein thus makes one of the boldest predictions in the history of science: “According to [general relativity], a ray of light going past the Sun undergoes a deflection of 1.7 seconds; and a ray going past the planet Jupiter a deflection of about 0.02 seconds.”22 In his theory, light rays passing by the sun during an eclipse should bend by exactly the aforementioned amount from a straight line (figure 2.4), the bending being a real-world manifestation of one of the implications from Einstein’s chest and disc thought experiments. In Relativity (1917 edition), Einstein pleaded for an astronomical expedition to measure this bending of starlight during an eclipse: “The examination of the correctness or otherwise of this deduction [1.7 arc-seconds] is a problem of the greatest importance, the early solution of which is to be expected of astronomers.”23 Shortly after the end of World War I, he got his wish. Two separate British teams set out to distant ports to observe a solar eclipse on May 29, 1919, in separate parts of the world—South America and Africa—and measure the bending of starlight. The African expedition was an undertaking under the leadership of Arthur Eddington, an astrophysicist and Quaker whose inner light had determined that he must give the distinguished citizen of an enemy nation his due. If there is any doubt about the courage this act of generosity took, we need only hear from Wilfred Owen, a fine poet killed in action just a week before the Armistice: 52

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Figure 2.4. Diagram illustrating light from a distant star (P) being deflected by the sun (S) and reaching Earth (E). From Arthur Eddington, Space, Time and Gravitation (1920), 112. Shall they return to beatings of great bells In wild trainloads? A few, a few, too few for drums and yells, May creep back, silent, to still village wells Up half-known roads.24

Owen is reflecting on the decimation soon to include himself. He was one of the 880,000 British combat dead. After the solar expedition’s conclusion, on November 6, 1919, a scientific paper heralding the expedition’s success was read before a combined meeting of the Royal Society of London and the Royal Astronomical Society. A “deflection of 1.7 arc-seconds” is a vanishingly small amount to measure (there are 1,296,000 seconds in a circle). In the publication, we experience the difficulty of measuring this minute deflection in the three minutes and five seconds the eclipse lasted. The expedition report from Principe—a small island off the coast of West Africa, one of the two expedition sites—captures the vicissitudes of field work in a style providing circumstantial details more typical of scientific papers in the nineteenth than twentieth century: The days preceding the eclipse were very cloudy. On the morning of May 29 there was a very heavy thunderstorm from about 10 a.m. to 11.30 a.m.—a remarkable occurrence at that time of year. The sun then appeared for a few minutes, but the clouds gathered again. About half-an-hour before totality the crescent sun was glimpsed occasionally, and by 1:55 it could be seen continuously through drifting cloud. The calculated time of totality was from 2h. 13m. 5s. to 2h. 18m. 7s. G.M.T. [Greenwich Mean Time]. Exposures were made according to the prepared program, and 16 plates were obtained. Mr. Cottingham gave the exposures and attended to the driving mechanism [a coelostat reflecting the eclipse into the telescope], and Prof. Eddington [expedition leader] changed the dark slides. It appears from the results that the cloud must have thinned considerably during the last third of totality, and some star images were shown on the later plates.

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Figure 2.5. Displacement measurements in Dyson et al. paper on the solar eclipse expedition to Sobral. From F. W. Dyson, A. S. Eddington, and C. Davidson, “A Determination of the Deflection of Light” (1920), 309. The cloudier plates give very fine photographs of a remarkable prominence which was on the limb of the sun. A few minutes after totality the sun was in a perfectly clear sky, but the clearance did not last long. It seems likely that the break-up of the clouds was due to the eclipse itself, as it was noticed that the sky usually cleared at sunset. It had been intended to complete all the measurements of the photographs on the spot; but owing to a strike of the steamship company it was necessary to return by the first boat, if we were not to be marooned on the island for several months. By the intervention of the Administrator berths, commandeered by the Portuguese Government, were secured for us on the crowded steamer. We left Principe on June 12, and after trans-shipping at Lisbon, reached Liverpool on July 14.25

Back in England, the two teams compared their findings, confirming Einstein’s prediction of 1.7 seconds of arc due to the effect of the sun’s strong gravitational pull. Figure 2.5 summarizes the results from the second observational station in Sobral, Brazil—the agreement between the observed and calculated values for the seven stars is obviously far from perfect but was good enough to convince the authors (Eddington as well as Frank Watson Dyson and Charles Rundle Davidson) and physics community at the time of the accuracy of the measurements. The authors did not consider their findings the final word. In the paper’s conclusion, they note that “the observation is of such interest that it will probably be considered desirable to repeat it at future eclipses.”26 Understandably, 54

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Einstein was delighted with the team’s measurements, as he reproduced them in an appendix to Relativity added in 1920, proclaiming that they “confirmed the theory in a most satisfactory manner.”27 (Note that either Einstein, or, more likely, the typesetter, incorrectly copied the calculated displacement of star 11 in the right ascension—0.22 instead of the actual number 0.32 given in figure 2.5—more in the theory’s favor.)

General Relativity Hits the Front Page On November 7, 1919, four days before the first anniversary of the Armistice, there appeared on the front page of the Times of London, news of Parliament, the bank rate, a coal strike, and under the headline the glorious dead, King George V’s declaration of two minutes of commemorative silence two days hence. On the column farthest to the right, there also appeared the headlines revolution in science—new theory of the universe—newtonian ideas overthrown. This story reports on the scientific meeting the day before, when the astronomical expedition paper by Eddington and colleagues had been read before the Royal Society of London and the Royal Astronomical Society. With internet-like speed, this communication catapulted Einstein and his esoteric theory into international fame.28 A crucial paragraph summarizes Einstein’s three sources of verification for his theory: When the discussion began, it was plain that the scientific interest centered more in the theoretical bearings of the results than in the results themselves. Even the President of the Royal Society, in stating that they had just listened to “one of the most momentous if not the most momentous pronouncements of human thought,” had to confess that no one had yet succeeded in stating in clear language what the theory of Einstein really was. It was accepted, however, that Einstein on the basis of his theory, had made three predictions. The first, as to motion of the planet Mercury, had been verified. The second as to the existence and the degree of deflection of light as it passed the sphere of influence of the sun had now been verified [emphasis added]. As to the third, which depended on spectroscopic observations [to test effect of gravitational field on time] there was still uncertainty. But he was confident that the Einstein theory must now be reckoned with, and that our conceptions of the fabric of the universe must be fundamentally altered.

Although the author is anonymous, his identity is now known: Peter Chalmers Mitchell, a Fellow of the Royal Society, a prominent Scottish zoologist with 55

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a strong interest in physics.29 His interest was not strong enough, however, to avoid a misstatement concerning the anomaly in the orbit of Mercury. Einstein did not predict this anomaly as it was well-known and had been measured in the nineteenth century. Newton’s gravitational theory could not account for it. Einstein’s theory could. The statement by the president of the Royal Society, physicist J. J. Thomson, was also not entirely accurate. As discussed earlier, in 1917 Einstein had published a book on his theory “in clear language,” the language being German, since the book had yet to be translated into English. These minor slips aside, more noteworthy from a communications perspective is the absence of any hedging language regarding the sentence on the deflection of light. The reporter’s unqualified statement about the verification of Einstein’s theory accurately reflects the general opinion expressed at the meeting on November 6. In his 1920 popular science book on relativity, however, expedition leader Eddington gave a more nuanced interpretation of the astronomical results, an interpretation more in keeping with the norm for hedging in the standard scientific literature: “The results from this plate [photograph of eclipse taken with a telescope] gave a definite displacement, in good accordance with Einstein’s theory [1.7 arc-seconds] and disagreeing with the Newtonian prediction [0.83 arc-seconds]. Although the material [data taken from plates] was very meagre compared with what had been hoped for, the writer (who it must be admitted was not altogether unbiassed) believed it convincing.”30 Indeed, subsequent attempts by others to reproduce the measurements over the next two decades proved problematic.31 In the many decades since the “verification” of general relativity, some have thus questioned the handling and reliably of the 1919 results. Had Eddington and others indeed been biased in favor of Einstein’s theory? Whatever the case, the results have held up in subsequent far more accurate astronomical measurements starting in the 1960s, firmly establishing that space bends around the Sun and other astronomical bodies in a way predictable with general relativity. Einstein’s thought experiments with rotating disc (bending of space) and accelerating chest (bending of light) were indeed much more than thoughts. Next, we jump ahead many decades to application of general relativity to cosmology development, an embodiment of the lessons learned from Einstein’s thought experiments regarding the bending of light.

From Confirmation to Cosmological Application The conclusion of the bending of space, preliminarily confirmed by the British astronomical expedition, would cast a whole new light on the nature of the universe when—after Einstein’s death on April 18, 1955, aged seventy-six (“I have 56

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done my share; it is time to go”32)—a new generation of gifted theoretical physicists led by Stephen Hawking, Roger Penrose, and Kip Thorne applied general relativity theory to the behavior of collapsed stars or black holes. In his runaway best-seller A Brief History of Time, Hawking gives us a clear picture of the role of general relativity in the creation of black holes. A collapsing star’s ever more concentrated mass distorts space-time, eventually creating a gravitational field of enormous power, one that consumes any stars or anything else that ventures too near. His is a story, not of any particular black hole, but of black holes in general, an appropriate perspective for the instantiation of a natural law. In the following passage, Hawking is careful to define such technical terms as “light cone” and “event horizon” and to remind his readers of the speed limit for light. He does not identify the bending of light as a prediction of general relativity, but he does make use of it: The gravitational field of the [collapsing] star changes the paths of light rays in space-time from what they would have been had the star not been present. The light cones [defined and visualized earlier by Hawking], which indicate the paths followed in space and time by flashes of light emitted from their tips, are bent slightly inward near the surface of the star. This can be seen in the bending of light from distant stars observed during an eclipse of the sun. As the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a distance. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes so strong that the light cones are bent inward so much that light can no longer escape [figure 2.6]. According to the theory of relativity, nothing can travel faster than light. Thus, if light cannot escape, neither can anything else; everything is dragged back by the gravitational field. So one has a set of events, a region of space-time, from which it is not possible to escape to reach a distant observer. This region is what we now call a black hole. Its boundary is called the event horizon and it coincides with the path of light rays that just fail to escape from the black hole.33

Definition of technical terms is de rigueur in effectively communicating science to a broad audience. Rhetoricians define definition as a statement of a thing’s essence.34 Its typical three-part syntactic form is the term to be defined, followed by genus, followed by differentia. Take the definition that a “black hole is a region of spacetime where gravity is so strong that nothing—no particles 57

Figure 2.6. Hawking’s diagram for formation of a black hole from a dying star. From Stephen Hawking, The Illustrated A Brief History of Time (1996), 111. Original Illustration, copyright © 1996 by Moonrunner Design, UK. Reproduced with permission of Bantam Books.

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or even electromagnetic radiation such as light—can escape from it, predicted by general relativity” (adapted from Wikipedia). In this example, “a region of spacetime” is the genus, and “where gravity is so strong that . . .” the differentia. (Worth noting here is that, in another part of A Brief History of Time, Hawking amends that definition—black holes can theoretically emit small quantities of radiation, an insight based on quantum mechanics that constitutes one of his most important contributions to the history of physics.) Popular science writing is not just a matter of defining technical details in a succinct manner but expanding on the differentia. In doing so, Hawking defines black hole, its components, its origin, and its astronomical effects, and even visualizes one for us to better follow his exposition and picture in our minds how they form. As shown in figure 2.6, the size of the collapsing star decreases with time until it reaches a point where the bending of space-time due to the extraordinary density of matter prevents light from escaping beyond the event horizon (vertical dotted lines bordering lightly shaded strip). At the event horizon, Hawking communicates the serious distortion of space-time by a badly distorted light cone. A few normal light cones hover nearby. At the center of the black hole sits a singularity—a point of space-time curvature similar to what might have existed at the origin of the universe, a region of “infinite density and the end of time”!35 Our entire universe is dotted with these invisible mini universes.

Translating Relativity into Science News Following the groundbreaking work of Hawking and others, black holes have been a hot topic in both specialized and popular science communications ever since. In a scientific paper appearing in Astrophysical Journal Letters, astrophysicists Christopher Evans, Pablo Laguna, and Michael Eracleous mathematically simulate with a computer an astronomical process that transpires in a matter of hours what might otherwise take years, a process in which a disintegrating star forms a thick accretion disc in the vicinity of a black hole. While filled with undefined technical jargon—a component one must remember in the everyday talk of astrophysicists—the prose style is well within the acceptable norms of scientific writing for specialized journals: A bright flare from a galactic nucleus followed at late times by a t−5/3 decay [time] in luminosity is often considered the signature of the complete tidal disruption of a star by a massive black hole. The flare and power-law decay are produced when the stream of bound debris returns to the black hole self-intersects, and eventually forms an accretion disc or torus. In the canonical scenario of a solar-type star disrupted by a 106 M⊙ black hole [one

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THE MANY VOICES OF MODERN PHYSICS million solar mases], the time between the disruption of the star and the formation of the accretion torus could be years. We present fully general relativistic simulations of a new class of tidal disruption events involving ultra-close encounters of solar-type stars with intermediate mass black holes. In these encounters, a thick disc forms promptly after disruption, on timescales of hours. After a brief initial flare, the accretion rate remains steady and highly super-Eddington [with a high rate of loss of mass] for a few days at ~102 M⊙yr−1.36

Although the final version of this paper was published on June 1, 2015, this is not the date at which it was first shared with the astrophysics community. On February 19, 2015, it was first published on arXiv.org, a website created by Paul Ginsparg, who won a MacArthur “genius” grant for his efforts.37 ArXiv is not peer-reviewed, but it is moderated, a far swifter process of quality control. Its home is now Cornell University; its financial support comes from the Simons Foundation and from member institutions. While a paper in the humanities may linger for years in peer review and publication limbo, papers in science are breaking news, bulletins from the research front. The paper’s title, “Ultra-Close Encounters of Stars with Massive Black Holes,” must have caught the attention of Science News reporter Jacob Aron while scanning arXiv for papers of interest. What happens when this up-to-the-minute result is published as news for the general public? A magazine for scientists and science enthusiasts, Science News, published Aron’s news article, titled “Black Holes Devour Stars in Gulps and Nibbles,” even before the original scientific paper appeared in Astrophysical Journal Letters. Aron opens with an arresting analogy between eating at a buffet and a star being eaten by a black hole: It’s like a buffet where no one agrees on table manners. When a black hole encounters a star, it seems there is more than one way for this cosmic enigma to chow down. Stars can safely orbit a black hole if they keep their distance, but if they cross a line called the Roche limit, they get torn apart in a so-called tidal disruption event (TDE). This is when the black hole loads up its plate by stretching the star in one direction and squeezing it in the other, gradually distributing hot gas from the star in a disc around itself. Once it has finished the task, the black hole can gorge on the star’s remains until nothing is left. Normally, forming the disc and eating it both take years, but Pablo Laguna of the Georgia Institute of Technology in Atlanta and his colleagues

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Having formulated his buffet analogy in the first paragraph, Aron then expertly weaves it into the language of the following paragraphs. In the process, he defines two technical terms—tidal disruption event and relativistic precession—by describing their relativity-related spatial effects. Comparing the above two quoted passages makes for a good illustration of the difference between scientific writing for a science journal and a science news outlet. There is no question that Aron read the original paper with care, as those key terms appear in it. He not only read the paper, he also spoke to one of its authors and worked a quotation into the text, a standard move for adding a personal touch and credibility to news articles. Aron’s headline and central analogy might seem sensationalist or even silly. But Aron does a good job of justifying such comparisons when used thoughtfully and in consultation with the scientists who wrote the paper: “Analogies in science writing are like forklift trucks—when used correctly they do a lot of heavy lifting, but if you don’t know what you’re doing you’ll quickly drive them into a wall of labored metaphors and cause some major damage (a bit like that sentence). I find the best analogies pop into my head as I try to form my own understanding of whatever a researcher is explaining, so I repeat them back . . . to make sure they check out.”39

As was the case for special relativity, thought experiments figure prominently in general relativity, which extends the uniform straight motion of objects in special relativity to include accelerated motion both circular and straight. In Einstein’s various publications, a thought experiment with a pair of rotating spheres around a common axis illustrates a problem with Newton’s thought experiment related to circular motion; a rotating disc illustrates Einstein’s reasoning behind the warping of space and time due to gravity; and an accelerated chest in a straight line, 61

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as contrasted with one resting in a gravitational field, illustrates the equivalence of acceleration and gravity as well as the bending of light. Collectively, these thought experiments explicate the logical reasoning behind general relativity, strengthen Einstein’s case that the counterintuitive claims of relativity are not mere fantasies, and alter the readers’ imaginative picture of space in a gravitational field from flat everywhere in the universe to undulating, fluctuating, bending, contorting, and rippling around large masses, accompanied by time warping.40 The generations of popular science physicists on relativity after Einstein have continued in their books to appropriate, modify, massage, extend, visualize, and add to his imaginative thought experiments. We are fortunate that Arthur I. Miller has placed Einstein beside Picasso in a wider cultural context devoted entirely to fundamental innovation, always a stony path to follow. While it is not an overwhelming task to appreciate the impact of a Picasso at the Museum of Modern Art, it is difficult indeed to wrap your head around a concept as abstruse as general or special relativity. Luckily, Einstein and those who followed in his footsteps have provided explanations in book-length popular expositions on relativity any diligent reader can follow with a little effort (well, sometimes more than a little). When it comes to the proof of Einstein’s hypothesis of the bending of light in his thought experiments and confirmation of his prediction of its exact extent, Eddington, Dyson, and Davidson give even general readers a transparent explanation of their crucial astronomical measurements in Philosophical Transactions, deemed front-page news in highly abbreviated form in the Times of London and sparking Einstein’s ascent from distinguished German physicist to worldwide household name. The principles behind Einstein’s thought experiments and the resulting mathematics, verified by experiment, spawned great leaps forward in our understanding of the evolution of our universe, discussed further in chapter 5. One of the bizarre astronomical bodies predicted by general relativity in the 1930s was black holes. Hawking’s definitions of them in A Brief History of Time—including their horizons and their singularities—along with his illustration cannot be bettered in terms of bringing complex science to the public; in this regard at least, he is Einstein’s heir. To this day black holes remain a favorite topic for journalists looking to translate relativity-related theory and experiment into news.

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And Coleridge, too, has lately taken wing, But like a hawk encumber’d with his hood, Explaining Metaphysics to the nation— I wish he would explain his Explanation. —Lord Byron, Don Juan

Relativity lends itself to explanation by means of analogies between its main principles and real-world situations as communicated with thought experiments involving speeding trains and spaceships, clocks and measuring rods, rotating spheres and disks, and light beams both straight and bent. But there is a fundamental problem in explaining quantum mechanics, as amusingly expressed by a New York Times science reporter in 1927: “To explain the quantum theory and its modification by Dr. Heisenberg and others is even more difficult than explaining relativity. It is much like trying to tell an Eskimo what the French language is like without talking French. In other words, the theory cannot be expressed pictorially and mere words mean nothing. One is dealing with something that can be expressed only mathematically.”1 Along the same line, Paul Dirac, a founding father of quantum mechanics, warned readers of his equation-ridden 1930 textbook for fellow physicists that it cannot be “built up from physical concepts known to the student, which cannot be explained adequately in words at all.”2 In his similarly equation-laden textbook on the same subject published the same year, another founding father 63

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of quantum mechanics, Werner Heisenberg, elaborated: “It is not surprising that our language should be incapable of describing the processes occurring within the atoms, for . . . it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. Furthermore, it is very difficult to modify our language so that it will be able to describe these atomic processes, for words can only describe things of which we can form mental pictures, and this ability, too, is a result of daily experience.”3 In his undergraduate textbook of 1965, Richard Feynman, a scientific offspring of Dirac and Heisenberg, sums up, asserting that no one really understands quantum mechanics, not even Richard Feynman: “Because atomic behavior is so unlike ordinary experience, it is very difficult to get used to, and it appears peculiar and mysterious to everyone—both to the novice and to the experienced physicist.”4 This is not to say that quantum mechanics is a very poor theory fit only to be thrown in the scrap heap along with the light ether and cold fusion. It is, in fact, a superb theory when the question is: How does the subatomic world behave? Suppose, however, the question is: what exactly does that world look like? Quantum theory is silent on that question. We are all in Lord Byron’s shoes. The machinery of explanation in quantum mechanics, as in all science, consists of words, equations, and visual representations. This is true whether the audience is the community of physicists or the general public. In the case of the birth of quantum mechanics as with relativity, one means of communication was of signal importance: the thought experiment. In contrast to the case of the relativity thought experiments, however, our quantum mechanical thought experiments consistently bump into the language problem mentioned above. Scholar Jennifer Burwell has a slightly different take on that problem independent of the mathematics: “Existing by way of discontinuities, probabilities, mutually exclusive or multiple simultaneous states, quantum phenomena can only ever be said to be incompletely and intermittently ‘there.’ As a result, the quantum world challenges our conventional assumption that nature consists of discrete, coherent substances that persist over time, and the challenge in turn strikes at our assumptions about the reliability of language.”5 Undaunted by the linguistic challenges, many of those involved in the creation of quantum mechanics attempted to communicate its foundational mysteries—the quantum itself, the uncertainty principle, wave-particle duality, superposition, and entanglement—by means of thought experiments, as well as analogies and visuals. In this chapter we intend to demonstrate that, although the effects of the quantum world can be vividly depicted through these communicative means, the quantum world itself consistently defies depiction. 64

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Quantum Theory Begins We begin with a thought experiment in the mind of a scientifically conservative physicist in the grip of an unconventional idea—modeling light as countless tiny clumps of energy, not as a continuously flowing stream. The mathematical constant used in dealing with these clumps—a product of energy and time now known as Planck’s constant—is 6.62 · 10 –27 erg · sec, an incredibly low number, a billionth of a billionth of a billionth. The passage we take from a 1900 scientific paper by Max Planck—who would later become Albert Einstein’s famous mentor and win a Nobel Prize for his quantum research—describes this experiment, the one that takes place only in the laboratory of his mind. It involves imaginary miniscule vibrating resonators stationed within an imaginary enclosed apparatus. It is not easy reading. This is at least partly because theoretical physicists show an inordinate fondness not only for the equations we would expect but also for the Greek alphabet. Planck’s ν is the Greek nu and stands for frequency, his c is the speed of light (the Latin celeritas), his ε is the Greek epsilon, the energy element. Physicists also have a fondness for abbreviations, sometimes arbitrary. While Et is the total energy in an imaginary enclosed system, N is the number of imaginary resonators stationed within it, h is Planck’s constant, and P is an energy element. Planck’s very technical and abstract thought experiment follows: Let us consider a large number of monochromatically vibrating resonators—N of frequency n (per second), N' of frequency ν', N'' of frequency ν' . . . with all N large numbers—which are properly separated and are enclosed in a diathermic medium with light velocity c and bounded by reflecting walls. Let the system contain a certain amount of energy, the total energy Et (erg) which is present partly in the medium as travelling radiation and partly in the resonators as vibrational energy. The question is how in a stationary state this energy is distributed over the vibrations of the resonator and over the various colors of the radiation present in the medium, and what will be the temperature of the total system. To answer this question we first of all consider the vibrations of the resonators and try to assign to them certain arbitrary definite energies, for instance, an energy E to the N resonators ν, E' to the N' resonators ν' . . . The sum

E + E' + E'' + . . . = E0 must, of course, be less than E t. The remainder Et — E0 pertains then to the radiation present in the medium. We must now give the distribution of the

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THE MANY VOICES OF MODERN PHYSICS energy over the separate resonators of each group, first of all the distribution of the energy E over the N resonators of frequency ν. If E is considered to be continuously divisible quantity, this distribution is possible in infinitely many ways. We consider, however—this is the most essential point of the whole calculation—E to be composed of a very definite number of equal parts and use thereto the constant of nature h = 6.55.10 –27 erg · sec [current value is slightly higher than the value determined by Planck]. This constant multiplied by the common frequency ν of the resonators gives us the energy element ε in erg, and dividing E by ε we get the number P of energy elements which must be divided over the N resonators. If the ratio is not an integer, we take for P an integer in the neighborhood [that is, approximately].6

Planck’s imaginary “experimental apparatus” consists of a black box, a completely enclosed space that, when heated to a given temperature, emits radiation whose source is the atoms within the walls, modeled as vibrating resonators.7 It is a contraption meant to analogize the behavior of “blackbody radiation.” At constant temperature, a blackbody emits energy at the same rate as it is absorbed. This was a hot area of experimental inquiry at the time in which predictive theory lagged behind. Readers might find the technical complexity of the thought experiment daunting, but it makes sense given Planck’s goal: to say something fundamental about the relationship between energy and temperature, the principal problem of thermodynamics.8 You are free to think instead of an oven, its resonators—the atoms in its walls—emitting and absorbing quanta when the oven is at a steady temperature, energy packets that bounce back and forth and eventually reach equilibrium. Planck’s apparatus functions as a series of constraints necessary and sufficient to create the blackbody effect Planck desires. This does not mean that his conjecture about tiny energy packets, later called quanta, is real; it does mean that this thought experiment will be worth the time of physicists to take seriously as a fruitful analogy. For Planck the puzzle was that, under the reigning assumption of continuous energy from classical theory, the distribution of the energy at a given wave frequency among all the resonators would be “possible in infinitely many ways.” To eliminate that infinity mathematically, he decided to see what happens when he assumed that the energy was divisible into “a very definite number of equal parts.” That led him to one of the most famous equations in all physics, hidden in plain sight within Planck’s thought experiment, E = h · f, or in his notation ε = h · ν. That is, each energy packet equals Planck’s constant times the frequency 66

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of the resonators. In the remainder of his paper, Planck made the bold leap of incorporating this simple equation into the physics and mathematics of blackbody radiation. Given that Planck’s thought experiment yielded the concept of a quantum of energy, it deserves consideration as one of the most fruitful ever created. But there is a historical point worth mentioning. While the discovery of hypothetical energy quanta—and of a theory that fully accounted for the behavior of blackbody radiation—initiated the quantum revolution, Planck was no revolutionary. Apparently, at the time of publication, he did not believe that, in the real world as opposed to his thought experiment and equations, energy is discontinuous and divisible into unimaginably tiny bits of energy. The somewhat vague last sentence in the quoted passage suggests as much. It hedges by asserting that the number of energy elements could be “in the neighborhood” of an integer. Yet, key to the conclusion that energy is discontinuous—and not divisible into smaller and smaller chunks indefinitely—is that this number must be an integer, not approximately or in the neighborhood of one. For many years after his 1900 paper, Planck remained uncomfortable with the microworld conjured by the writings of Einstein, Niels Bohr, Werner Heisenberg, and others.9 In the previous two chapters we emphasized the argumentative and pedagogical functions of thought experiment. In terms of its practical utility for physicists, we can add Thomas Kuhn’s insight: “The function of the thought experiment is to assist in the elimination of prior confusion by forcing the scientist to recognize contradictions that have been inherent in his way of thinking from the start.”10 This insight fits exactly Planck’s example, plus several others we will look at in this chapter, a cascade of fundamental reimaginings that leapt beyond the deterministic physics at the end of the nineteenth century, along with any sense that physics was a discipline with no interesting problems to solve.

Heisenberg’s Uncertainty Thought Experiment A 1927 scientific paper by Werner Heisenberg, then a young assistant to Niels Bohr at the University of Copenhagen, established the uncertainty principle, a law of nature that changed forever the deterministic picture of the microworld. In a thought experiment in the manner of Planck and Einstein as part of a scientific argument, Heisenberg uses an imaginary gamma-ray microscope to determine an imaginary electron’s position. Why gamma rays? Because of their short wavelength, physicists should be able to detect the electron’s position with great precision. His attempt fails. (There is, by the way, no such thing as a gamma-ray microscope, but it is possible in principle.) A gamma ray that collides with the electron knocks it out of its current position: the very act of observing the 67

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electron has altered that position. This thought experiment leads to the famous uncertainty principle: “The more precisely the position is determined, the less precisely the momentum is known, and conversely.” Heisenberg’s actual thought experiment, like Einstein’s for simultaneity, hinges on a redefinition of a common term meant to foster an entirely new way of thinking about it: When one wants to be clear about what is to be understood by the word “position of the object,” for instance of the electron (relative to a given frame of reference), then one must specify definite experiments with whose help one plans to measure the “position of the electron” with arbitrary accuracy. For example, let one illuminate the electron and observe it under a microscope. Then, the highest attainable accuracy in the measurement of position is governed by the wavelength of the light. However, in principle one can build, say, a g-ray microscope and with it carry out the determination of position with as much accuracy as one wants. In the measurement there is an important feature, the Compton effect. Every observation of scattered light coming from the electron presupposes a photoelectric effect (in the eye, on the photographic plate, in the photocell) and can therefore also be so interpreted that a light quantum hits the electron, is reflected or scattered, and then, once again bent by the lens of the microscope, produces the photoelectric effect. At the instant when position is determined—therefore, at the moment when the photon is scattered by the electron—the electron undergoes a discontinuous change in momentum. This change is greater the smaller the wavelength of the light employed—that is, the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known up to magnitudes which correspond to that discontinuous change. Thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely [emphasis ours]. In this circumstance we see a direct physical interpretation of the equation pq − qp = −iℏ. Let q1 be the precision with which the value q is known (q1 is, say, the mean error of q), therefore here the wavelength of the light. Let p1 be the precision with which the value p is determinable: that is, here, the discontinuous change of p in the Compton effect. Then, according to the elementary laws of the Compton effect, p1 and q1 stand in the relation

p1q1 ~ h.  (1)

That this relation (1) is a straightforward mathematical consequence of the rule pq − qp = −iℏ will be shown below.11

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Before we can read this long paragraph with any understanding, we need to familiarize ourselves with its abbreviations and its symbolism, and with the experimental results and theories Heisenberg takes for granted. In Heisenberg’s symbols, p is position, q is momentum, g is the Greek gamma, the symbol ∼ means “approximately,” iℏ is a version of the Planck constant, and the bold letters (pq, qp) indicate use of a specialized branch of mathematics called matrix theory. The Compton effect occurs when a charged particle scatters photons; the photoelectric effect is the ejection of electrons from a surface when light falls on it. From “de Broglie waves,” we infer that particles might have wave properties. In the remainder of his paper Heisenberg will mention the Ramsauer effect, a factor important in understanding the electron’s wave-like nature; magnetic moment, the force a magnet can exert on electrical currents; the Doppler effect, observed when a receding siren changes its pitch; the Stern-Gerlach experiment, which reveals quantum properties on an atomic scale; and the Franck-Hertz experiment, which shows the quantum nature of atoms. He will also refer to papers by Niels Bohr, Wolfgang Pauli, Paul Dirac, Max Born, Albert Einstein, Pascual Jordan, and himself, a rogue’s gallery of quantum geniuses. These mentions are not simply a matter of giving credit where credit is due; they are not simply a matter of placing the paper in the appropriate theoretical context. Rather, it is these contexts that give Heisenberg’s thought experiment credibility with those he would like to convince, the older contingent—Bohr, Born, and Einstein, as well as the younger contingent—Dirac, Pauli, and Jordan. Heisenberg initially expresses his uncertainty principle mathematically as pq − qp = h/2πi, where the boldface indicates matrices in the form of rows and columns of numbers representing an infinite number of possible positions and momenta for an electron. In ordinary mathematics, the order of multiplication makes no difference whatsoever: two times three always equals three times two; but in matrix mathematics, that order can make a difference. Translated into ordinary but somewhat clunky English, Heisenberg’s equation tells us that the position times the momentum is not equivalent to the momentum times the position, the difference being a very small non-zero number (h/2πi). Heisenberg then makes the assertion that this equation—together with the “basic equations for the Compton effect” for the scattering of X-ray photons in collision with electrons—leads by mathematical reasoning to the simpler algebraic p1 q1 ≈ h (in modern notation, ∆p ∆q ≈ h), where p1 represents the uncertainty in the momentum (velocity times mass), q1 is the uncertainty in position, and h is Planck’s constant. What this algebraic equation tells us is that, since Planck’s constant is fixed at a very small quantity, increasing the accuracy in the position determination proportionally decreases the accuracy 69

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of the momentum determination in compensation, and vice versa. A gain in one produces a precisely calculable loss in the other, and they both cannot be determined with high accuracy at the same time. In the aforementioned passage, Heisenberg establishes the uncertainty principle, visualizes it in words with a thought experiment, and represents it with a deceptively simple-looking equation. Having redefined the meaning of position and momentum at the microscale, he subsequently continues in the same vein to redefine energy and time, yielding the bonus landmark equation ∆E . ∆t ~ h. In other words, the more precise the energy determination, the wider the time interval over which it must be measured, and vice versa. With his thought experiments and equation, Heisenberg has redefined for all time position, momentum, velocity, and energy, just as Einstein had earlier redefined time, space, motion, and gravity. While Heisenberg’s paper has few visuals, visualization is an important factor in it. The German title is “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik.” The key phrase there is anschaulichen Inhalt, which is difficult to translate into English in a few equivalent words. The noun Anschaulichkeit and its adjective anschaulich imply “visualization or intuition through mechanical models.”12 Louisa Gilder summarizes scholarly opinion on its meaning among physicists in the 1920s: “The physical naturalness of an idea, so that it can be pictured in the mind’s eye.”13 In his paper, Heisenberg sought to make the then highly abstract quantum mechanics visualizable and intuitively graspable by the communicative means of his thought experiment. In his 1933 Nobel Prize lecture, however, Heisenberg maintained that visualization can actually impede intuitive understanding of quantum mechanics: “The natural phenomena in which Planck’s constant plays an important part can be understood only by largely foregoing a visual description of them.”14 The problem with the visual description of quantum phenomenon reveals itself in George Gamow’s figure illustrating Heisenberg’s thought experiment in Thirty Years That Shook Physics.15 To our knowledge, this is the first book-length popular account of quantum theory by a major physicist—first published in 1966, more than three decades after the physics it describes.

Gamow’s Visualization of Heisenberg’s Thought Experiment Gamow’s problematic visual representation of Heisenberg’s thought experiment (figure 3.1) sets up an analogy meant to compare and contrast the visible “real” world with the invisible quantum world.16 In the macroworld, a tiny cannon C shoots a shell in a horizontal direction. The shell follows a parabolic path—the solid and dashed line. This is in accord with classical physics for motion in the Earth’s gravitational field. A theodolite T—a surveying and navigational 70

QUANTUM MECHANICS Figure 3.1. Gamow’s drawing for Heisenberg’s thought experiment for the uncertainty principle. From George Gamow, Thirty Years That Shook Physics (1966), 108. Reproduced with permission of Dover Publications.

instrument commonly used in determining the precise position of an object—tracks this path by capturing the photons emitted from the light bulb B and reflected from the flying object into the theodolite. Based on data from the theodolite, we can easily determine the shell’s exact position and momentum at any given time, since the photons from the light bulb would have no measurable effect on the shell’s trajectory. The quantum side of the analogy tells a contrasting story. An electron (e) follows the shell’s parabolic path as far as the solid line extends. A photon from the light bulb strikes the electron; in compensation, the electron ejects a photon that strikes the theodolite, and simultaneously the electron dramatically alters its trajectory—the solid line ending with downward arrow. The hν above the photon path is Planck’s formula for the energy of a single light quantum or photon (from his 1900 thought experiment discussed earlier), enough to knock an electron out of its smooth trajectory. Gamow explains later that, as many photons would be striking the electron, it will wildly fly to and fro in all directions. Gamow’s picture of Heisenberg’s idealized experiment is vivid but somewhat misleading. It treats the electron as though it were a point following a classical parabolic trajectory until struck by a quantum of light, which itself follows a wavy but straight trajectory. But the electron would follow a discontinuous path even without the photons from the light bulb present, as would the photons streaming from the light bulb when present. In quantum theory, as Gamow observes, physicists can only determine the “probability that the particle will be found in one or another part of space and will move with one or another velocity.”17 71

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Heisenberg biographer David Cassidy explains Gamow’s failure: “The true quantum interaction, and the true uncertainty associated with it, cannot be demonstrated with any kind of picture that looks like everyday colliding objects. To get the actual result you must work through the formal mathematics that calculates probabilities for abstract quantum states.”18 As Heisenberg implies in his Nobel Prize lecture, there is no way to visualize the principle of indeterminacy without seriously misleading the viewer.

Another Spin on an Uncertainty Thought Experiment In Quantum Mechanics: The Theoretical Minimum, quantum physicist Leonard Susskind and software engineer Art Friedman attempt to explain the basics of quantum mechanics to a mathematically sophisticated lay audience with what they consider the “minimum” of theory.19 In presenting that theory, they do not stint on equations and, on occasion, call upon thought experiments to better explain their mathematics. Our example here is their opening thought experiment, which focuses on a primary property of quantum particles, their spin. True to the many paradoxes of quantum mechanics, particle spin is measurable, but the particles themselves do not actually spin like planets or billiard balls as the term suggests. Unlike the Planck and Heisenberg thought experiments in the service of scientific arguments, the purpose of Susskind and Friedman’s is pedagogical. And like the earlier thought experiments on relativity written in the form of a lecture for imaginary high school or college physics students, Susskind and Friedman’s combines geometry and visuals. Their experimental tool is an imaginary apparatus that measures spin. While science writers often visualize quantum spin as a stationary sphere rotating around an axis,20 Susskind and Friedman forego that shaky analogy here. It runs into similar communicative problems as the colliding particles in figure 3.1. Instead, they picture spin abstractly as a little arrow that can be pointed any direction indicating the direction of spin rather than spin itself. In executing their quantum spin thought experiment, we start in the realm of classical physics. Our first step is to orient a spin arrow in our imaginations as pointing straight up along the z-axis (see figure 3.2, left) and then measure the spin with the apparatus pointed up as well. The apparatus will register +1 (figure 3.2, center). Having done so, we will find that we can repeat this measurement as many times as we like, and the outcome will always read +1. No surprise there. If we flip the apparatus 180 degrees so the arrow now points straight down, then it will read the other possible value, -1. No matter how many times we repeat this measurement, even in the quantum world of probabilities, the outcome is predictably the same. 72

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Figure 3.2. Susskind and Friedman’s thought experiment for quantum spin oriented to z-direction: (center) after initial measurement with apparatus pointed up and (right) after apparatus rotated by ninety degrees. From Leonard Susskind and Art Friedman, Quantum Mechanics (2014), 6, 8. Reprinted by permission of Basic Books.

For this initial state, the apparatus A will thus display only two possible numbers, +1 or -1. Susskind and Friedman represent this binary state by the Greek symbol s, which reflects a measurement of spin. This symbol figures prominently as the thought experiment continues, segueing into the quantum realm only in the last paragraph: Now let’s do something new. After preparing the spin by measuring it with A, we turn the apparatus upside down and then measure s again. What we find is that if we originally prepared s = +1, the upside-down apparatus records s = -1. Similarly, if we originally prepared s = -1, the upside-down apparatus records s = +1. In other words, turning the apparatus over interchanges s = +1 and s = -1. From these results, we might conclude that s is a degree of freedom that is associated with a sense of direction in space. For example, if s were an oriented vector of some sort [represented as an arrow whose length indicates magnitude and arrowhead, the direction], then it would be natural to expect that turning the apparatus over would reverse the reading [arrow direction]. A simple explanation is that the apparatus measures the component of the vector along an axis embedded in the apparatus. Is this explanation correct for all configurations? If we are convinced that the spin is a vector, we would naturally

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THE MANY VOICES OF MODERN PHYSICS describe it by three components: sz, sx, and sy. When the apparatus is upright along the z axis [figure 3.2, left side], it is positioned to measure sz. So far, there is still no difference between classical physics and quantum physics. The difference only becomes apparent when we rotate the apparatus through an arbitrary angle, say . . . 90 degrees. The apparatus begins in the upright position (with the up-arrow along the z axis). A spin is prepared with s = +1 [figure 3.2, middle]. Next, rotate A so that the up-arrow points along the x axis [figure 3.2, far right], and then make a measurement of what is presumably the x component of the spin, sx. If in fact s really represents the component of a vector along the up-arrow, one would expect to get zero. Why? Initially, we confirmed that s was directed along the z axis, suggesting that its component [spin] along x must be zero. But we get a surprise when we measure sx: Instead of giving sx = 0, the apparatus gives either sx = +1 or sx = -1. A is very stubborn—no matter which way it is oriented, it refuses to give any other answer than sx = ± 1. If the spin really is a vector, it is a very peculiar one indeed.21

If the arrow (vector) for spin direction is pointing straight up along the z-axis, common sense—at least if we think of an actual spinning sphere—dictates that there should be no spin component at all along any other axis. Therefore, in the x direction, sx should be 0. The initial experiment also suggests that repeated measurement of spin should always yield the same value. We find instead that the system has gone quantum: in repeated measurements, the apparatus rotated by 90 degrees always reads sx = +1 or -1, not zero (as in figure 3.2, right). Stranger still, if we repeat this measurement many times, the average value comes out to zero: “Instead of the classical result—namely, that the component of s along the x axis is zero—we find that the average of these measurements is zero.”22 So measuring some aspect of a system disrupts some other aspect, in accord with Heisenberg’s principle. Despite the success of the above thought experiment in giving some sense of the math and the strangeness of quantum mechanics, Susskind and Friedman forewarn that it has a flaw: quantum particles do not spin in the same way as spheres, nor do they correspond exactly to an arrow (vector) pointing in some spin direction, as all attempts to visualize spin classically “badly miss the point.”23

Schrödinger’s Wave-Particle Duality Equation In 1926 Erwin Schrödinger presented an equation that described the wave function or state function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantum theory. This equation 74

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mathematically treats the behavior of electrons and other particles in atoms or molecules as though they were waves, represented by the symbol y, the wave function. That is paradoxical in the sense that one would think that microscopic particles, in analogy with macroscopic particles, should behave like single points moving through space with a predictable velocity and position, not like waves. In Mr. Tompkins Explores the Atom, Gamow gives us a thought experiment in story form that illustrates the equation in operation. He dreams up another world in which Planck’s constant is boosted to a relatively high number like one instead of its actual miniscule ∼10 –27. He then works out what consequences this would have in his dream world. In that dream, Mr. Tompkins and his physics professor friend find themselves in a pub watching a game of billiards. To his great astonishment, Mr. Tompkins observes that two colliding billiard balls act like quantum particles “rushing about within an angle of 180° round the direction of the original impact. It resembled rather a peculiar wave spreading from the point of collision.”24 As the professor also explains, “You cannot actually indicate the position of a ball exactly; the best you can say is that the ball is ‘mostly here’ and ‘partially somewhere else.’”25 In other words, they behave according to the equation Schrödinger discovered. Physicist Jim Al-Khalili also created a Gamow-like narrative thought experiment to illustrate the behavior the Schrödinger equation describes: Let us consider a single electron trapped in a box. Suppose we know exactly where it is to begin with, and we feed the location into the Schrödinger equation. We will thus be able to calculate its wavefunction at some later time. Now, let us assume that we have tabulated in a computer file or on a sheet of paper, an array of numbers that represent the values of the electron’s wavefunction at various grid points around the volume of the box. We cannot use this information to locate the electron with any certainty any more. Instead, we must make do with knowing where it is most likely to be found. . . . The probabilistic nature, and therefore the built-in unpredictability of quantum mechanics, requires a little more discussion about the nature of the wavefunction. For instance, it is helpful to give you a rough idea of how a wavefunction changes with time by considering a useful analogy. A burglar has just been released from prison, but the local police are convinced he has not turned over a new leaf and, by studying a map of the city, can trace his likely whereabouts from the moment he is freed. While they cannot pinpoint his exact location at a given time, they can assign probabilities to burglaries being committed in various districts. To begin

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THE MANY VOICES OF MODERN PHYSICS with, houses close to the prison are most at risk, but the area under threat grows over time. They can also say with some confidence that wealthier areas are more at risk than poorer ones. This one-man crime wave spreading through the city can be thought of as a wave of probability. It is not tangible or real, just a set of abstract numbers assigned to every part of the city. In a similar way, a wavefunction spreads out from the point where the electron was last seen and knowledge of the wavefunction allows us to assign probabilities to where it might show up next. The police soon find out that their hunches have been accurate when a burglary is reported from some address. This alters their probability distribution since they know the thief cannot be far away from the scene of the crime. Likewise, if an electron is detected in a certain location then its wavefunction is instantly altered. At the moment of detection there will be zero probability of finding it anywhere else. Leave it be, and its wavefunction evolves and spreads out.26

Initially, Schrödinger tried to give his wave function a physical interpretation in keeping with classical physics, asserting that its square (y2) corresponded to the distribution of the particle’s charge density in the surrounding space. It was Max Born who—out of left field and somewhat to Schrödinger’s consternation—asserted instead that the wave function squared actually determines the probability of finding a single particle in a particular place if one were to search for it there.27 It is this condition that Al-Khalili visualizes with the thought experiment in the form of a detective story, comparing the wave function to the crime-spree path of a recidivist burglar. Unlike a quantum particle, however, the burglar moving through time and space always has a definite position and velocity and mass, and the aforementioned Susskind-Friedman qualification comes into effect. Al-Khalili notes that while a quantum particle has wave-like behavior, it can be detected experimentally just like any macroscopic particle. Upon detection, the probability of the microworld “collapses,” and the probability that the particle is at a specific position jumps to 100 percent. Burwell puts this quantum paradox succinctly: “Unobserved, the electron behaves according to the wavefunction. Observed, it becomes a particle.”28 But why should observing a particle make a difference? And where is the particle when it is not being observed? These and other puzzles of quantum mechanics led Schrödinger as well as Einstein to challenge the completeness of quantum mechanics by means of ingenious thought experiments. Before exploring these, however, we turn to a famous visualized thought experiment of wave-particle duality. We consider it the most successful ever in the quantum realm. 76

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Figure 3.3. Interference (“double-slit”) experiment with electrons. Probability graphs on right indicate wave-like behavior even though electrons are particles. From Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, vol. 3 (1965), 4. Copyright © 2011. Reprinted by permission of Basic Books.

Feynman’s Visualizations of Wave-Particle Duality According to the Nobel Prize–winning physicist Steven Weinberg, you must never say that a light wave is just like a water wave, because “electron waves are not waves of electronic matter, in the way that ocean waves are waves of water. Rather . . . the electron waves are waves of probability.”29 In one of his famous physics lectures, Richard Feynman ingeniously illustrates this crucial point in a series of connected thought experiments, each with accompanying visual. Here is one: Now we imagine [an] experiment with electrons. It is shown diagrammatically in [figure 3.3]. We make an electron gun which consists of a tungsten wire heated by an electric current and surrounded by a metal box with a hole in it. If the wire is at a negative voltage with respect to the box, electrons emitted by the wire will be accelerated toward the walls and some will pass through the hole. All the electrons which come out of the gun will have (nearly) the same energy. In front of the gun is again a wall (just a thin metal plate) with two holes in it. Beyond the wall is another plate which will serve as a “backstop.” In front of the backstop we place a movable detector. The detector might be a Geiger counter or, perhaps better, an electron multiplier, which is connected to a loudspeaker.

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THE MANY VOICES OF MODERN PHYSICS We should say right away that you should not try to set up this experiment. . . . This experiment has never been done in just this way. The trouble is that the apparatus would have to be made on an impossibly small scale to show the effects we are interested in. We are doing a “thought experiment,” which we have chosen because it is easy to think about. We know the results that would be obtained because there are many experiments that have been done, in which the scale and the proportions have been chosen to show the effects we shall describe. The first thing we notice with our electron experiment is that we hear sharp “clicks” from the detector (that is, from the loudspeaker). And all “clicks” are the same. There are no “half-clicks.” We would also notice that the “clicks” come very erratically. Something like: click . . . click-click . . . click . . . click . . . click-click . . . click . . . , etc., just as you have, no doubt, heard a Geiger counter operating. If we count the clicks which arrive in a sufficiently long time—say for many minutes— and then count again for another equal period, we find that the two numbers are very nearly the same. So we can speak of the average rate at which the clicks are heard (so-and-so-many clicks per minute on the average). As we move the detector around, the rate at which the clicks appear is faster or slower, but the size (loudness) of each click is always the same. If we lower the temperature of the wire in the gun, the rate of clicking slows down, but still each click sounds the same. We would notice also that if we put two separate detectors at the backstop, one or the other would click, but never both at once. (Except that once in a while, if there were two clicks very close together in time, our ear might not sense the separation.) We conclude, therefore, that whatever arrives at the backstop arrives in “lumps.” All the “lumps” are the same size: only whole “lumps” arrive, and they arrive one at a time at the backstop. We shall say: “Electrons always arrive in identical lumps.”30

The double-slit thought experiment is definitely not Feynman’s original invention, but he certainly created his own highly illuminating variations. He prefaced the above thought experiment with two similar ones involving the world of classical physics. The first involves a spray of bullets from a machine gun, and the second, water ripples. Both come with structurally similar diagrams to figure 3.3: in all three diagrams, the left half visualizes the components of the experiment and their actions during its execution, while the right half displays the corresponding probabilities in graphical and equation form—a beautiful amalgamation of thought experiment, visual, and math. 78

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Figure 3.4. Electron experiment through two slits with a particle detector and light source. Probability graphs on the right indicate particle-like behavior. From Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, vol. 3 (1965), 7. Copyright © 2011. Reprinted by permission of Basic Books.

In the two earlier thought experiments, the machine gun diagram displays a smooth probability curve with a single peak signifying particle-like behavior, while the rippling water diagram has an undulating probability curve with multiple peaks signifying wave-like behavior. Paradoxically, even though figure 3.3c is for a thought experiment involving electron particles, the resulting undulating probability curve is the same as that for the wave-like behavior of the rippling water experiment. Susskind and Friedman remind us that “real quantum mechanics is not so much about particles and waves but the non-classical logical principles that govern their behavior.”31 To illustrate this difference at its most extreme, Feynman has us repeat the electron experiment with a slight wrinkle (figure 3.4). Into the experimental setup, we insert behind the wall between slits 1 and 2 a light source that can detect electrons as they pass through one of the slits. Lo and behold, the probability curve is the same as the particle-like behavior of the machine gun experiment with a random spray of bullets! This last thought experiment illustrates Heisenberg’s uncertainty principle: observing the movement of an electron changes its behavior in some essential way. In Feynman’s words, “We must conclude that when we look at the electrons the distribution of them on the screen [backstop] is different than when we do not look.”32 So when we do not look, the curve undulates, as in figure 3.3c, but when we do look, it is smooth, as in figure 3.4c. 79

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There is another point of interest. Figure 3.3 does not display the trajectory of the electrons after they leave the gun, pass through the slit, and strike the backdrop. That region is blank for a reason. How can one visualize the path of something that is simultaneously like a wave and particle? Feynman wisely does not try. As for figure 3.4, Feynman draws one path (A) of an indefinite number possible to emphasize the particle-like behavior of an electron only when observed. Yet, as good as Feynman’s illustrated thought experiments are, they still come up short in capturing wave-particle duality, as science writer Philip Ball explains: Quantum objects are what they are, and we have no reason to suppose that “what they are” changes in any meaningful way depending on how we try to look at them. Rather, all we can say is that what we measure sometimes looks like discrete little ball-like entities [Feynman’s bullets], while in other experiments it looks like the behavior expected of waves of the same kind as those of sound travelling in the air, or that wrinkle and swell of the sea surface [Feynman’s water ripples]. So the phrase “wave-particle duality” doesn’t really refer to quantum objects at all, but to the interpretation of experiments—which is to say, to our human-scale view of things.33

Thought Experiments against Quantum Theory No physicist is against quantum theory; no theory in the history of physics has yielded a greater harvest. Moreover, today few physicists question the theory’s completeness; that is, few ask whether there is some underlying theory that, like classical physics, can simultaneously predict with exactness the position and momentum of each object in the microworld. One would be excused, then, if one thought the issue is settled: there is no such theory and there never will be. The issue is not at all settled; perhaps it never will be. When doubts about completeness surfaced, in fact, two of the doubters were two of the founders of quantum theory, Einstein and Schrödinger. Each expressed his doubts in a brilliant thought experiment. Which thought experiment contra quantum theory is Einstein’s? “EPR”— named after him and his coauthors, Boris Podolsky and Nathan Rosen—is the common and mistaken answer. Because his English was better, Podolsky, one of Einstein’s assistants, was asked to write the thought experiment up. He did so. Before Einstein had a chance to approve the draft, however, Podolsky sent it off for publication in Physical Review. Since Einstein was first author, it is understandable that the paper’s contention that there are hidden variables controlling quantum behavior, a theory that no longer holds water, was viewed as 80

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Einstein’s own. In fact, the possibility of hidden variables was a view Einstein entertained only fleetingly, one he never endorsed or advocated. In a letter to Schrödinger, he presents another thought experiment whose conclusion he does fully endorse: The system is a substance in chemically unstable equilibrium, perhaps a charge of gunpowder that, by means of intrinsic forces, can spontaneously combust, and where the average life span of the whole setup is a year. In principle this can quite easily be represented quantum-mechanically. In the beginning the y-function [the wave function in the Schrödinger equation] characterizes a reasonably well-defined macroscopic state. But, according to your equation, after the course of a year this is no longer the case. Rather, the y-function then describes a sort of blend of not-yet and already exploded systems. Through no art of interpretation can this y-function be turned into an adequate description of a real state of affairs; in reality there is no intermediary between exploded and not-exploded.34

This thought experiment bears a startling resemblance to Schrödinger’s own far more famous one, at the center of which is a diabolically clever contraption for questioning quantum mechanics: One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat). In a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The y-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.35

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According to quantum theory, Schrödinger’s cat is in a state of superposition: it is neither alive nor dead until we look inside the box, at which point the wave function collapses, and the cat is suddenly alive or dead without question. Until that time “the living and dead cat (pardon the expression) [is] mixed or smeared out in equal parts.”36 Once we open the box, the wave function collapses, and we know the cat’s fate. Einstein insists that there is no such thing as exploded and unexploded gunpowder—gunpowder must be one or the other. Schrödinger points to the difference between a “shaky out-of-focus photograph and a snapshot of clouds and fog banks.” He insists that there is a difference between “the living and dead cat . . . mixed or smeared out in equal parts,” a cat that is actually in a state of superposition, in his view an unlikely occurrence, and a cat whose state of superposition is no more than a product of the quantum equations, an imaginary cat, one that does not really exist. It is hardly irrational for both these men to infer that quantum theory is incomplete. In quantum theory, can realism be maintained? Can we have both cats, the living and the dead? Philosopher Donald Davidson argues that Thomas Kuhn’s idea, that after Copernicus we all lived in a different world, is just a way of talking. Because “there is at most one world,” he maintains, “talk about another world is at best metaphorical and at worst seriously misleading.”37 Physics theorist Hugh Everett would beg to differ. In 1957 he maintained that there are in fact many worlds, all of them quite real. The quantum superposition does not collapse, leaving the unexploded gunpowder and the live cat.38 The gunpowder has also exploded and the cat is also dead, but in another world. If this sounds more like science fiction than science fact—Bohr’s position—we should not be surprised. Over the years, however, there has been a sea change. For some, science fiction has become at least plausible science. Some physicists and philosophers of science now take seriously an interpretation that sidesteps the paradox Einstein and Schrödinger so tellingly revealed.39 According to the many-worlds interpretation, there is no superposition of exploded and unexploded gunpowder or of dead and living cats; there is no collapse of the wave function; there are branching worlds instead. If on inspection the gunpowder has exploded and the cat is dead, there exists another branching world, alike in all respects to the world we know, except that in that world the gunpowder has not exploded and the cat is still alive. Moreover, quantum formalism is no formalism at all: “The approximately classical world that we see around us ultimately emerges from the wave function of the universe, spacetime and all.”40 To quell those like Bohr who might dismiss this as science fiction, Everett argued that 82

QUANTUM MECHANICS as any fool can plainly see [he writes with intentional irony], the earth doesn’t really move because we don’t experience any motion. However, a theory which involves the motion of the earth is not difficult to swallow if it is a complete enough theory that one can also deduce that no motion will be felt by the earth’s inhabitants (as was possible with Newtonian physics). Thus, in order to decide whether or not a theory contradicts our experience, it is necessary to see what the theory itself predicts our experience to be. [While you might object to branching worlds,] I can’t resist asking: Do you feel the motion of the earth [66,658 mph around the sun and that doesn‘t count the movement of the solar system and the expansion of the universe]?41

A Spooky Thought Experiment One of the counterintuitive logical consequences of quantum mechanics is something Einstein later called “spooky action at a distance,” nowadays referred to by the technical term quantum entanglement, a situation in which two quantum particles meet, interact, and go their separate ways, yet always remain mysteriously joined. In Quantum Mechanics: The Theoretical Minimum, Susskind and Friedman provide a story-like thought experiment for this spooky action: Charlie has two coins in his hands—a penny and a dime. He mixes them up and holds them out, one in each hand, to Alice and Bob, and gives one coin to each of them. No one looks at the coins and no one knows who has which. Then, Alice gets on the shuttle to Alpha Centauri while Bob stays in Palo Alto. Charlie has done his job and doesn’t matter anymore (sorry, Charlie). Before Alice’s big trip, Alice and Bob synchronize their clocks—they have done their relativity homework and accounted for time dilation and all that. They agree that Alice will look at her coin just a second or two before Bob looks at his. Everything proceeds smoothly, and when Alice gets to Alpha Centauri she indeed looks at her coin. Amazingly, the instant she looks at it, she knows exactly what coin Bob will see, even before he looks. Is this crazy? Have Alice and Bob succeeded in breaking relativity’s most fundamental rule, which states that information cannot go faster than the speed of light? Of course not. What would violate relativity would be for Alice’s observation to instantly tell Bob what to expect. Alice may know what coin Bob will see but she has no way to tell him—not without sending him a real message from Alpha Centauri, and that would take at least the four years required for light to make the trip.42

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Susskind and Friedman refer to this thought experiment as “classical entanglement.” They mean that it bears some resemblance to “quantum entanglement” but is still within the bounds of classical physics. The penny-and-dime outcome is not surprising—Alice and Bob have a fifty-fifty chance of holding a specific coin until they check, and common sense dictates that if Alice sees a dime, she knows immediately that Bob has the penny no matter how much distance or time separates the two. To represent entanglement more deeply, Susskind and Friedman reintroduce Charlie, who prepares two spinning particles in an entangled state. Without measuring their spin, he gives one to Alice and one to Bob. Remember that in the probabilistic world of quantum theory, neither particle has a definite spin until it is measured or observed. Nevertheless, if Alice measures her particle spin at any time on her trip to Alpha Centauri and determines that it is in the up direction along the z-axis (+1), she instantly knows Bob’s particle is in the down direction along that same axis (-1), no matter how far or long Alice has traveled. By “instantly,” we mean instantly—no delay needed for a message to be sent at the speed of light. With continued spin measurements for a sphere along the z-direction on separate trips, and comparisons once Alice and Bob return home: “Sometimes, Bob measures +1 and Alice measures -1. Other times, Alice measures +1 and Bob measures -1 [i.e., the outcome is completely uncertain and yet . . . ]. The product of the two measurements is always -1.”43 That is truly spooky action at a distance. A whole subfield of quantum physics has sprung up around entanglement. New theory emerging from quantum particle entanglement has become intimately entangled with much physics today—the theory of black holes, wormholes, the multiverse, and the unification of general relativity and quantum mechanics. What’s more, physics experiments using quantum entanglement are now almost routine. Still, Susskind and Friedman’s view of it probably reflects current thinking within the physics community: “What should be apparent is that quantum mechanics is a consistent calculus of probabilities for a certain kind of experiment involving a system and an apparatus. We use it, and it works, but when we try to ask questions about the underlying ‘reality,’ we get confused.”44

At the end of the nineteenth century, physicists looked back in pride at what Isaac Newton, Michael Faraday, James Clerk Maxwell, and J. J. Thomson had achieved. In the shadow of such giants, it is no wonder some might have felt there were no more interesting questions to answer. It is ironic that one of their number, the scientifically conservative Max Planck, inadvertently kick-started 84

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a quantum revolution whose maxim was that light is not just wave-like, but particle-like. While Planck had no intention of fomenting a revolution, foment one he did. Our interest, however, is less in his science than in how he persuaded his fellow physicists that he was right about his quantum equations. He did so partially through a thought experiment, a fiction so tightly constrained by real-world contingencies that just like a real experiment, it could do significant science. Thought experiment is also integral to another seminal scientific paper in quantum theory, Heisenberg’s on the uncertainty principle. This thought experiment not only helped establish the now-famous principle among fellow physicists, but redefined two central terms in physics: position and momentum. It also introduced a principle now known far beyond the limited readership of physics journals. While many quantum physicists have tried to convey their science to the general public, they face formidable rivals in the writings of Heisenberg, Einstein, and Schrödinger. You do not need to be a physicist to understand the thought experiments of these Nobel Prize winners, even though they first appeared in specialized physics journals. In fact, if there were a Nobel Prize in Scientific Communication, they would have won that, too. To offer such high praise is to take nothing from Feynman’s thought experiments meant for undergraduates. Nor do we mean to denigrate the extraordinary ingenuity of Gamow, Al-Khalili, Susskind and Friedman, and Ball in books meant for an educated lay audience with varying mathematical skills. Collectively, the thought experiments and accompanying visuals of all these physicists convincingly convey the alien nature of the quantum world—a world with unimaginably small particles in light rays, wave-particle duality, position-momentum uncertainty, superposition, entanglement, Schrödinger’s cat, and many worlds besides are own. Still, we must never forget the magnitude of the communicative task. Although the effects of the quantum world can be depicted with words and pictures, the quantum world itself ultimately eludes depiction that is not somehow misleading.

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In his 1949 Autobiographical Notes about his life in science, Albert Einstein reported that quantum theory “on the one hand, and the theory of relativity on the other, are both considered correct in a certain sense, although all efforts to fuse them into a single whole so far have not met with success.”1 The same can be said today, over seventy years later. Einstein himself had no interest in synthesizing these two theories since he firmly believed that the uncertainties of quantum mechanics would one day be usurped by a new deterministic theory more along the lines of general relativity. Most important, he spent the last decades of his life in a vain search for a unification theory that would merge gravity and the electromagnetic force without resorting to quantum mechanics. What is dramatically different from Einstein’s day is a firmly established unification theory—with a nondescript name (Standard Model)—that fuses three of the four known forces: electromagnetism and the strong and weak nuclear forces, but not gravity. Physicists formulated this model largely in the 1960s and 1970s,2 and they have captured the essence of this theory in the form of a table with rows and columns of information, similar to the periodic table of elements. The persuasiveness of this table rests, in part, on an implied analogy: what the periodic table is to chemistry, the Standard Model table of particles is to physics. And like the periodic table, the Standard Model table has within it predicted particles later confirmed by experiment. Despite its many successes and explanatory power, 86

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however, this table is known to be incomplete and imperfect. Physicists will be continuing to refine and possibly expand it for the foreseeable future. In addition to the Standard Model, there are in the rarefied air of the physics literature a number of highly speculative theories that add gravity to the Standard Model and/or unify quantum mechanics and general relativity. The most prominent such theory in the popular science literature is string theory, an impossibly complex mathematical construction with a simple-to-understand foundational analogy—the fundamental particles of nature are like strings, not points—and supporting visual representations. This theory has captured the science-interested public’s imagination, as is evident from numerous books and a NOVA television documentary.3 Not quite as well publicized in popular expositions is another highly speculative unification theory, loop quantum gravity, with its own foundational analogy—there is a quantum of space itself analogous to Planck’s quantum of energy—and accompanying image to capture its essence. Neither theory has the benefit of any arguments in its favor by comparisons of theoretical calculations to experimental results or even the prospect of such comparisons any time soon. How then to argue for the credibility of these theories? Their persuasiveness hinges in part, at least in the popular science literature, on the seductiveness of their analogies and visual representations. Extrapolating even further into the distant future, beyond the projected success with any current unification theory, some physicists even dream about a unification theory to end all unification theories, or a final theory of everything. Outside of pure accidents, nothing would be exempt from it, neither a galaxy, nor the beings that populate it, nor a humble piece of chalk. No visual representation or analogy has yet to capture the essence of this holy grail of physics. Instead, we will be examining an elaborate thought experiment arguing for its possibility, starting with a simple piece of chalk, visible to all, and drilling inward to its quantum particles, visible to none. This thought experiment has raised an additional question for physicists and philosophers of science. Even if some future Einstein or Einsteins were to create some mathematical formulation for a final theory of physics, what would that actually explain? As noted by philosopher Margaret Morrison, “Inferential practices grounded in the explanatory power of a theory often are simply inapplicable to the theory’s unifying power.”4

The Journey to the Standard Model Dmitri Mendeleev and the periodic table, Murray Gell-Mann and the eightfold way, a large cohort of physicists (Peter Higgs being one of many) and the Standard Model—in each case a conjectured natural order receives startling empirical confirmation. In each, what looks like a scientific table, what is a table, 87

THE MANY VOICES OF MODERN PHYSICS Figure 4.1. An early version of Mendeleev’s periodic table of elements. From D. Mendelejeff, “Ueber die Beziehungen der Eigenschaften zu den Atomgewichten der Elemente” (1869), 405–6.

is also a theory whose goal is unification: in the first case, of the elements, in the second and third of the subatomic particles, their constituents. In 1869 Zeitschrift für Physik published a translation of a short article: “On the relationship between the characteristics and the atomic weight of the elements.” It contained a table, the periodic table (figure 4.1), a table of rows and columns with repeating trends among the elements. To see what this periodicity means, let’s focus on the element silicon, in the third column, atomic weight 28. If we look just to the right, we find a question mark, the prediction of a yet undiscovered element Mendeleev called eka-silicon (eka being Sanskrit for “one of two or many”). Mendeleev predicted not only the existence of this element but also its specific gravity and its density compared to the density of water: 5.5. In 1886 the German chemist Clemens Winkler discovered the provisionally named eka-silicon and named it germanium in honor of his country. Its specific weight, he determined, was 5.469, matching Mendeleev’s prediction (and not far from the modern value of 5.32). Winkler was impressed by what Mendeleev had achieved. Donning the robes of a historian of science, he wrote: “Investigation of the properties of germanium becomes actually a touchstone for human ingenuity. It would be impossible to imagine a more striking proof of the doctrine of periodicity of the elements than that afforded by this embodiment of the hitherto hypothetical ‘eka-silicon’; this is in truth more than a mere verification of a daring hypothesis, it represents an enormous extension of the chemist’s field of view, a mighty stride into the realm of cognition.”5 It is very seldom that so flattering a hyperbole turns out to be the simple truth. And in time, the periodic table morphed into the visual representation routinely taught to students in chemistry class. 88

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Figure 4.2. Baryon decuplet triangle showing “strangeness” (s) and electric charge (q) for ten baryons (solid circles). The omega minus particle at the bottom of the triangle has a strangeness of −3 and charge of −1. From Wikimedia Commons, https://commons.wikimedia.org/wiki/ File:Baryon_decuplet.png.

We now jump ahead in time to the eightfold way, Murray Gell-Mann’s organizational scheme for subatomic particles known as hadrons, composites containing two or more fundamental particles called quarks. The basis for this organization is three fundamental properties of particles (electric charge, spin, and mass) and their “strangeness.” The latter concerns the rapidity of formation of certain particles during collisions and their decay afterwards. In 1962, at the Rochester Conference at CERN, Gell-Mann made a bold prediction—the existence of an omega minus particle (W-) with a mass of 1685 MeV (millions of electron volts), strangeness of –3, and a spin of 3/2.6 You can see this particle, a member of the eightfold way, at the bottom of the innovative triangular image in figure 4.2, with subatomic particles strategically positioned in rows and diagonal columns. Two years later in a bubble chamber apparatus at Brookhaven National Laboratory, the omega-minus particle was discovered (figure 4.3). An examination of fifty thousand photographs revealed two instances. Since the omega-minus lifetime is just a bit less than a one ten trillionth of a second, the Brookhaven physicists were lucky fifty thousand photographs were enough. Consistent with 89

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Figure 4.3. A bubble chamber photograph at Brookhaven. Left side shows image of particle tracks created by bubble chamber experiment while those on the right are the interpretation of those tracks, confirming formation and decay of the omega-minus particle, as predicted. From V. E. Barnes et al., “Observation of a Hyperon with Strangeness Minus Three” (1964), 205. Reprinted with permission of American Physical Society.

theory, the particle had a mass of 1672.45 ± 0.29 and a spin of 3/2, a clear indication that the eightfold way was not just an organizational scheme. It had, like the periodic table, a credible theory behind it. According to this theory—invented by Gell-Mann and independently by George Zweig—what were once thought to be fundamental particles, the proton and neutron, actually consist of three quarks each. What is more, quarks come in three flavors: up, down, and strange. The quarks and their flavors would later become key inhabitants of the Standard Model table. Gell-Mann’s theory was a giant step toward the Standard Model, a theory that also required the Higgs boson predicted by Peter Higgs and five other physicists in the mid-1960s. This elementary particle is associated with an invisible field that permeates the entire universe and bestows mass on Gell-Mann’s quarks and other particles that would otherwise be massless. Without the Higgs field, the building blocks of all physical things—atoms—could not exist. And without detection of the associated particle, the Standard Model had a big gap in 90

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it. From 1998 to 2008 a massive team of scientists, engineers, designers, and other workers thus built the Large Hadron Collider (better known as the LHC) on the Franco-Swiss border near Geneva, Switzerland, to hunt for the Higgs boson. In popular science physics books, the magnificent machines of physics like the LHC tend to get short shrift. Not so in theoretical physicist Lisa Randall’s Knocking on Heaven’s Door. Of her first visit to the completed LHC, Randall writes: “I was surprised at the sense of awe it inspired—this in spite of my having visited particle colliders and detectors many times before. Its scale was simply different.”7 She then presents us with a list of its arresting properties, amplified with quantitative comparisons and analogies. The first is the triumph over time. The LHC will be able to simulate events that occurred in the “first trillionth of a millisecond after the Big Bang,”8 the time when the Higgs field created mass. The second is the triumph over space, the investigation of the tiniest components of the universe: “Incredibly small sizes—on the order of a tenth of a thousandth of a trillionth of a millimeter . . . a factor of ten smaller in size than anything any experiment has ever looked at before.”9 Other superlatives concern energy: “Up to seven times the energy of the highest existing collider”; temperature, “even colder than outer space”; magnetic field, “100,000 times stronger than the Earth’s”; and cost, “the most expensive machine ever built” ($9 billion, with operating costs of $1 billion a year). Even more superlatives and comparisons follow, depicting for us the components within the LHC. Within three-inch-wide pipes in a twelve-foot-wide tunnel that traverses some seventeen miles in circumference, it takes “89 millionths of a second . . . for the accelerated highly energetic protons traveling at 99.9999991 percent of the speed of light to make it around.”10 Powerful magnets coax the protons to follow a circular orbit rather than their normal linear trajectory. Each of the 1,232 LHC magnets is fifty feet long and weighs thirty tons. Each magnet “contains coils of niobium-titanium superconducting cables, each of which contains stranded filaments a mere six microns thick—much narrower than a human hair. The LHC contains 1,200 tons of these remarkable filaments. If you unwrapped them, they would be long enough to encircle the orbit of Mars.”11 The cables in the magnets are cooled to 1.9 degrees above absolute zero, “even lower than the 2.7-degree cosmic microwave background temperature in outer space,” making the LHC ring “the coldest extended region in the universe.” With these magnets, the electrical current can reach 12,000 amperes, “40,000 times the current flowing through the lightbulb in your desk,” requiring enough electricity to power “a small city such as nearby Geneva.” None of Randall’s quantitative comparisons and analogies is hyperbolic. Her skillful presentation of these comparisons makes the LHC appear just as impressive as any physics theory. And the LHC worked as planned after a few hiccups. 91

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The Standard Model Table The architects of the LHC designed it primarily to detect a single particle in the Standard Model, the mass-giving Higgs boson. What is the place of this particle in the Standard Model? Randall does not just tell us; she shows us by arranging its force and substance particles in a table obviously modeled on the periodic table (figure 4.4). The force particles appear in the row at the bottom with the Higgs boson; the substance particles, in the rows and columns above it. According to Randall, the Standard Model as a whole compactly categorizes our current understanding of elementary particles and their interactions (summarized in [figure 4.4]). It includes particles like the up and down quarks and the electrons that sit at the core of familiar matter, but it also accommodates a number of other heavier particles that interact through the same forces, but which are not commonly found in nature—particles that we can study carefully only at high-energy collider experiments. Most of the Standard Model’s ingredients, such as the particles the LHC is currently studying, were rather thoroughly buried under the clever experimental and theoretical insights that revealed them in the latter half of the twentieth century.12

Scanning and matching within this table’s rows and columns we see depicted a decrease in mass from the third to first generation, the journey to stable matter. First-generation particles are especially important because two up quarks plus one down quark make a proton, while two down quarks plus one up quark constitute a neutron. Together with electrons, protons and neutrons constitute the building blocks of atoms. In turn, the chemical elements build by increasing the number of protons and neutrons in the nucleus and the electrons circling around it. The various lines in the table (dotted, dashed, and solid) link the substance particles in the dark squares with their respective force carriers in the grey squares. These links associate gluons with the strong force; W+, W-, and Z particles with the weak force; and the photon with the electromagnetic force. By following these lines, various principles within the Standard Model come to life. For example, following the dotted line along the right side of the table reveals that the photon associated with the electromagnetic force gives rise to electric charge for all of the substance particles except the three types of neutrinos (“neutral”), a key particle in the evolution of the early universe. Also, following the dashed lines from the gluon associated with the strong force reveals that 92

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Figure 4.4. The elements of the Standard Model of particle physics (with masses shown in units of either million or billion electron volts). Table includes information on the three key distinguishing properties of particles: mass, charge, and spin. From Lisa Randall, Knocking on Heaven’s Door (2011), 242. Copyright © 2011, 2012 by Lisa Randall. Used by permission of HarperCollins Publishers.

that force applies only to quarks, not leptons like the electron. For that reason, electrons do not get bound into the protons and neutrons of the atomic nucleus and instead can orbit it. Note that the Higgs boson, undiscovered at the time figure 4.4 was published, stands apart from the other particles. Its discovery in the LHC in 2012 has not changed its lonely status. The Higgs is “not just a new particle, but a 93

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new type of particle.”13 Even though no lines in Randall’s table connect it with the substance or force particles, it is central to the existence of most. Acting like a charge that permeates the entire universe, its associated field gives mass to the six quarks, three charged leptons (column on far right), and three weak-force bosons (bottom row). Randall’s little table does a big job. To devote a quarter hour to it is to have penetrated the nature of the universe to a level deeper than the periodic table—to have discovered the building blocks of the chemical elements. It is the interactions of the substance and force particles as captured in figure 4.4 that constitute the essence of the Standard Model, governed by an enormous equation we will not reproduce here.14 Given the incredible success of the Standard Model, some physicists have taken to making exaggerated statements about it. Robert Oerter, for example, calls the Standard Model “the theory of almost everything.”15 He claims that it “explains, at the deepest level, nearly all of the phenomena that rule our daily lives.” True, “at the deepest level,” that assertion is accurate. Yet, the theory by itself does not explain all that much about the earthbound macroscopic world we all live and die in. And conspicuously missing is any accounting for three actors important on a cosmic scale: approximately 80 percent of the matter in the universe (dark matter), a form of energy so powerful that it began accelerating the expansion of the universe about nine billion years after the big bang (dark energy), and gravitation. Only discovered over the last few decades, neither dark energy nor dark matter has been detected directly and little is known. Scientists inferred them from astronomical observation and theoretical calculations. At the quantum level, gravity, so central on Earth and in the cosmos, is too weak to be significant. Still, however weak, no complete theory can exclude it. We believe it best to stick to what the theory actually is—a theory of almost everything at the subatomic scale except for the effects of gravity, dark matter, and dark energy. That is no small feat.

The Supersymmetric Table The Standard Model table has a strong argument in its favor. Just as the periodic law predicted the existence of other elements to fill in gaps within the periodic table, the Standard Model of the 1960s and 1970s predicted the existence of new particles that could be fit into its table (top quark, weak force particles, the heaviest neutrino, and of course the Higgs boson), all later confirmed in experiments at particle colliders. Hence, physicists have the utmost confidence in the current contents of figure 4.4. Yet, on close inspection, a critical viewer might well exclaim: The Higgs boson does not really fit in this arrangement of 94

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particles. It seems to be just stuck in a convenient corner. And in sharp contrast to the periodic table of elements, the complicated relationships among the leptons and quarks and bosons do not appear to be part of any grand design that favors consistency in symmetry and pattern. Moreover, there is a key missing part in the model: the gravitational force and its corresponding hypothetical particle the graviton. This absence has as its cause the “hierarchy problem.” That is, why is the gravitational force so much weaker than the weakest other force (sixteen orders of magnitude)? Can the gravitational force fit into the table at all? How so? Randall informs her readers what one possible route to a solution might be, the “supersymmetric model,” an expansion of the Standard Model and its associated table: Since the 1970s, many physicists have considered the existence of supersymmetric theories so beautiful and surprising that they believe it has to exist in nature. They have furthermore calculated that forces should have the same strength at high energy in a supersymmetric model—improving on the near-convergence that happens in the Standard Model, allowing the possibility of unification. Many theorists also find supersymmetry to be the most compelling solution to the hierarchy problem, despite the difficulty in making all the details agree with what we know [our emphasis]. Supersymmetric models posit that every fundamental particle of the Standard Model—electrons, quarks, and so on—has a partner in the form of a particle with similar interactions but different quantum mechanical properties. If the world is supersymmetric, then there exist many unknown particles that could soon be found—a supersymmetric partner for every known particle. Supersymmetric models could help solve the hierarchy problem and, if so, would do it in a remarkable fashion. In an exactly supersymmetric model, the virtual contributions from particles and their superpartners cancel exactly. That is, if you add together all the quantum mechanical contributions from every particle in the supersymmetric model and tally their effect on the Higgs boson mass, you would find they all add up to zero. In a supersymmetric model, the Higgs boson would be massless or light [we now know its mass to be 125 GeV], even in the presence of quantum mechanical virtual corrections. In a true supersymmetric theory, the sum of the contributions of both types of particles exactly cancel. This sounds miraculous perhaps but is guaranteed because supersymmetry is a very special type of symmetry. It’s a symmetry of space and time—like the symmetries you are familiar with such as rotations and translations—but it extends them into the quantum space.16

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In Knocking on Heaven’s Door, Randall includes a supersymmetric version of figure 4.4 that is twice as large. The left half is basically the same as figure 4.4. In the right half, however, every substance particle now has a partner with a new but similar name and the quantum mechanical properties of a force carrier, while the force carriers have a symmetric particle with the quantum mechanical properties of a substance particle. The ordered arrangement of particles in the supersymmetric table results in a more periodic table–like table than figure 4.4. So one argument in its favor is its visual elegance. Another is mathematical, spelled out in the last paragraph in the quoted passage: the quantum mechanical contributions on the right side exactly cancel out those on the left, eliminating some serious problems related to the predicted mass of particles. A third argument, hinted at by Randall in the first paragraph of the quoted passage, is computational robustness: it predicts the merging of all three nongravitational forces into one at an energy level approaching that present in the immediate aftermath of the big bang, while the Standard Model does not.17 Yet, as mentioned by Randall, the crucial argument is lacking: many decades after its formulation, the supersymmetric model remains without any experimental support. All the supersymmetric particles added to the expanded table are hypothetical.18 While Randall conjectures that the supersymmetric model “could help solve” the hierarchy problem, her supersymmetric table does not provide any hint as to what that solution might be. The gravitational force and graviton are still nowhere to be found. The supersymmetric model’s main attractiveness is that it better unites the three nongravitational forces and might be a step in the right direction toward a model eventually uniting all four known forces. Our next unification theory takes that next step.

Beyond the Standard Model The pre-Socratic philosopher Thales said the first principle of the universe was water. Two other pre-Socratics disagreed: Anaximander said it was the infinite; Anaximenes, that it was air.19 Brian Greene thinks these ancient Greeks were wrong. The first principle is strings—minute, one-dimensional strings, so small, so elusive, that even a Large Hadron Collider half as big as the universe could not possibly detect them. String theory has this virtue: it is a supersymmetric theory of “everything”; that is, it is designed to unify, to encompass all the four forces: the strong force, the weak force, the electromagnetic force, and gravity. While Einstein failed in his decades-long struggle to unite electromagnetism and gravity, string theorists may one day succeed in their unification of the four forces plus the two best theories physics has, general relativity and quantum mechanics, theories at present more incompatible than chardonnay and roast beef. 96

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What attracts the general public to these bold fantasies of sophisticated mathematical physics? Greene is the P. T. Barnum of string theory, the star of a NOVA special, the author of the best-selling The Elegant Universe, an original contributor to string theory itself, and more. In that popular science book, Greene’s goal is no less than the normalization of string theory as a legitimate new addition to the history of physics and heir apparent to the crowning triumphs of twentieth-century physics: relativity theory and quantum mechanics. Greene relies heavily on analogies with everyday reality to make all these theories real in the minds of readers with little or no scientific or mathematical background. As an example of his deft melding of analogy with image, Greene compares the warping of space predicted by general relativity to a rubber sheet, the sun to a bowling ball whose mass distorts that sheet, and the resulting spatial distortion to the force of gravity.20 Three images accompany the written description: one of flat space by itself (a perfectly flat rubber sheet), one with the sun (bowling ball–like) resting on the flat sheet and stretching it, and one with Earth (tiny ball) in orbit around the bowling ball sun as it is stretching the sheet. The latter represents how the sun’s warping of space dictates Earth’s orbit. Having endorsed this analogy, this link between our world and abstruse theory, he backs away. There are important caveats, as Greene amplifies.21 First, the warping of space itself constitutes gravity. Second, the sun warps all of surrounding space, not just the sheet. Third, it warps both space and time. Spelling out these qualifications thus enhances our understanding of the analogy. In this section of Elegant Universe, Greene is imitating Richard Feynman in his QED: The Strange Theory of Light and Matter. He is a professor using “a powerful pedagogical device”22 to teach us well-established physics with words and pictures. When it comes to his exposition of the untested string theory, the bold and ingenious analogies remain, and the caveats mostly fade into the background: All properties of the microworld are within the realm of [string theory’s] explanatory power. To understand this, let’s first think about more familiar strings, such as those on a violin. Each such string can undergo a huge variety (in fact, infinite in number) of different vibrational patterns known as resonances. . . . These are the wave patterns whose peaks and troughs are evenly spaced and fit perfectly between the string’s two fixed endpoints. Our ears sense these different resonant vibrational patterns as different musical notes. The strings in string theory have similar properties. There are resonant vibrational patterns that the string can support by virtue of their evenly spaced peaks and troughs exactly fitting along its spatial extent. . . . Here’s the central fact: Just as the different vibrational patterns of a

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Figure 4.5. Artistic rendering of shapes of strings in string theory for several subatomic particles. From Shutterstock. violin string give rise to different musical notes, the different vibrational patterns of a fundamental string [see figure 4.5] give rise to different masses and force charges. As this is a crucial point, let’s say it again. According to string theory, the properties of an elementary “particle”—its mass and its various force charges—are determined by the precise resonant pattern of vibration that its internal string executes. It’s easiest to understand the association for a particle’s mass. The energy of a particular vibrational string pattern depends on the amplitude—the maximum displacement between peaks and troughs—and its wavelength— the separation between one peak and the next. The greater the amplitude and the shorter the wavelength, the greater the energy. This reflects what you would expect intuitively—more frantic vibrational patterns have more energy, while less frantic ones have less energy. . . . This is again familiar, as violin strings will vibrate more wildly, while those plucked more gingerly will vibrate more gently. Now, from special relativity we know the energy and mass are two sides of the same coin. Great energy means greater mass, and vice versa. Thus, according to string theory, the mass of an elementary

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UNIFICATION PHYSICS particle is determined by the energy of the vibrational pattern of its internal string. Heavier particles have internal strings that vibrate more energetically, while lighter particles have internal strings that vibrate less energetically. Since the mass of a particle determines its gravitational properties, we see that there is a direct association between the pattern of string vibration and a particle’s response to the gravitational force. Although the reasoning involved is somewhat more abstract, physicists have found that a similar alignment exists between other detailed aspects of a string’s pattern of vibration and its properties vis à vis other forces.23

Greene’s basic argument in string theory’s favor is simple but powerful: theorists have overcome the barriers to unification by substituting an analogy that had served physics well for more than a century—subatomic particles are like dimensionless points, with another—that the smallest particles in nature are like the strings of a violin. There are, of course, caveats to this comparison. No violin string or even other subatomic particle is anywhere near “a hundred billion (1020) times smaller than an atomic nucleus.”24 That subatomic particles are like dimensionless points is an inference from well-established theory; that they are one-dimensional strings (that is, length, but no width or thickness) is a conjecture. There is more. The violin vibrations do not create mass, but acoustic waves. Most important, there is a mathematical price to be paid for the conceptual simplicity of the string analogy. The theory requires the strings to vibrate in nine spatial dimensions—the three of our experience plus six extra ones. The new six are in the form of miniscule circular loops far beyond detection by current and maybe even future technology. To convince us of the possibility of six extra spatial dimensions, Greene starts with an analogy to a garden hose laid out in a straight line. Viewed from the top of a nearby tall building, it appears to be the same as a two-dimensional line drawn on a sheet of paper; at ground level, however, its three dimensions are plain as day. This analogy, you might object, is a far cry from the hidden six dimensions. But Greene is just getting started. To represent hidden six-dimensional space, he employs a single six-dimensional shape discovered by mathematicians, the Calabi-Yau manifold. Of necessity, he does so on the two-dimensional page displaying a flat two-dimensional grid tilted at an angle to imply a third dimension. There now appears in figure 4.6 a series of origami six-dimensional shapes sitting on a three-dimensional flat grid, a total of nine dimensions convincingly depicted on the two-dimensional page. Greene elaborates on their importance: “These dimensions are an integral and ubiquitous part of the spatial fabric; they exist everywhere. For instance, if you sweep your hand in a large arc, you are 99

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Figure 4.6. Visualization of nine dimensions. Six-dimensional Calabi-Yau manifolds placed on grid of familiar three dimensions (length, width, and height) for a total of nine. From Shutterstock.

moving not only through the three extended dimensions, but also through these curled-up dimensions.”25 The unwary reader may well be swept away with Greene’s powerful visualizations and his authoritative voice and may be led, mistakenly, to believe string theory is established science. But buried in a long paragraph far from Calabi-Yau spaces is Greene’s admission that “at the present time [1999] . . . we do not know if the fundamental characteristics of our universe . . . can be explained by string theory.”26 Overall, however, more than two decades after The Elegant Universe appeared, the theory remains incomplete, open to technical criticisms, and untested and perhaps even truly untestable.27 But the purpose of The Elegant Universe is not to focus on caveats or limitations to string theory; it is to sweep us off our feet by means of a tsunami: Greene’s persuasive analogies of strings as fundamental particles, visualizations of nine dimensions on the two-dimensional page, and much more. In contrast to Greene and string theory, Carlo Rovelli narrows the scope of unification to a central problem for the Standard Model, its marriage of quantum mechanics with gravity: loop quantum gravity theory. Its distinct advantage is that it does not require additional space-time dimensions beyond the normal 100

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four. Rovelli argues for the credibility of this theory, which replaces the analogy of strings with loops and, in a bold imaginative leap, applies quantization to the very fabric of space. Like energy and the quantum, in Rovelli’s universe, space is not continuous but divisible into tiny Planck-sized chunks that “are linked to each other, forming a network of relations which weaves the texture of space, like the rings of a finely woven immense chain mail.”28 That there are loops, “closed lines in space,” is a requirement of the mathematical foundations of the theory.29 We cannot see these loops because the Planck length is approximately 10 –35 meters, a length you might find a bit mysterious. Is it the diameter of the smallest observable particle? Nowhere near: “To give an idea of the smallness of scale we are discussing: if we enlarged a walnut shell until it had become as big as the whole observable universe, we still would not see the Planck length. Even after having been enormously magnified thus, it would still be a million times smaller than the actual walnut shell was before magnification. At the scale, space and time change their nature. They become something different; they become ‘quantum space and time,’ and understanding what this means is the problem.”30 By an analogy with a walnut shell, Rovelli gives Planck length what rhetoricians call presence. Rovelli frequently refers to loop quantum gravity, a phrase that captures the theory’s three main elements: gravity is the gravity of general relativity; quantum is the quantum of quantum theory; loop is the geometric shape that unites the two by means of the quantization of space itself. There is a communicative problem with the word loop, however: it summons up the image of a circular object like a ring or particle accelerator. To correct that impression in figure 4.7, Rovelli creates a visual for space at the Planck scale as applied to his loop analogy. The left side is a graph of interconnected nodes that serves as the framework for superimposing loop-like particles of space, shown by the image on the right. These are not in space, they constitute space. Each has a volume that “cannot be arbitrarily small. A minimum volume exists. No space smaller than this volume exists.” At this scale, space is “a fluctuating swarm of quanta of gravity that act upon one another, and together act upon things.”31 Just as energy proved to be discontinuous in Planck’s quantum theory, now it is at least theoretically true for space itself. In this theory, time does not exist. Classical physics assumed the existence of “absolute time.” Special and general relativity showed the arbitrariness of that assumption—time is relative to the observer and to gravitational fields. Just as quantum mechanics does away with the notion of precisely predicable motion over time in the microworld, loop quantum gravity dispenses with space-time in the Planck world: “There is no background ‘spacetime,’ forming the stage on 101

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Figure 4.7. Representation of interconnected quantum loops. From Carlo Rovelli, Reality Is Not What It Seems (2014), 165. Copyright © 2014 by Rafaello Cortina Editore SpA. Translation copyright © 2016 by Simon Carnell and Erica Segre. Used by permission of Riverhead, an imprint of Penguin Publishing Group.

which things move. There is no ‘time’ along which everything flows.”32 Time is the by-product of space at the Planck scale and the loop analogy. In his publications, Rovelli argues that, in contrast to string theory, one of the main attractions of loop quantum theory is that, in uniting general relativity and quantum theory, it applies them as they stand now, though suitably adjusted to achieve unification. There is thus no need for a radical departure from current theory, elementary particles that vibrate like strings, a gaggle of new supersymmetry particles, or any extra spatial dimensions. Despite these advantages in his argument, good scientist that he is, Rovelli also confesses that, like string theory, loop quantum gravity summons a speculative Alice in Wonderland world, without experimental support of any kind. His qualification of the theory here is particularly blunt and honest: “Needless to say, there are no experiments supporting this (or any other) quantum theory of gravity. All current theories of quantum gravity are in the realm of the theoretical attempts. But the situation is more serious than just this. Loop gravity, as well as all other quantum theories of gravity, has so far been incapable of producing a single clear-cut prediction that could in principle put the theory under cogent empirical test. This is bad and is a weakness of today’s fundamental theoretical physics.”33

Too Beautiful to be False? While lacking verifiability by some crucial experiment or set of experiments, one could legitimately argue that unification theories like string theory and loop quantum gravity are beautiful, in the minds of theoretical physicists anyway. 102

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What is the role of beauty in theoretical physics? In “Beauty and the Quest for Beauty in Science,” the Nobel Prize–winning astrophysicist Subrahmanyan Chandrasekhar mentions Hermann Weyl’s gauge theory of gravitation, an early attempt at unifying electromagnetism and gravitation. Weyl thought that while the theory was not true, it was too beautiful to abandon. As it turned out, his lack of confidence was partially misplaced; while the theory was physically untenable, part of it eventually found its way into the Standard Model. Still, when truth is at stake, beauty cannot be criterial. In Mysterium Cosmographicum, the seventeenth-century astronomer Johannes Kepler thought that he had revealed God’s geometric plan of the solar system, a symmetrical construction of Platonic solids surrounded by the orbit of Saturn. He turned out to be wrong on that point. What are the criteria for theoretical beauty in physics? Chandrasekhar suggests two: “The first is the criterion of Francis Bacon: ‘There is no excellent beauty that hath not some strangeness in the proportion!’ (Strangeness, in this context, has the meaning ‘exceptional to a degree that excites wonderment and surprise.’) The second criterion, as formulated by Heisenberg, is complementary to Bacon’s: ‘Beauty is the proper conformity of the parts to one another and to the whole.’” In Chandrasekhar’s view, Einstein’s general relativity is such a theory. Chandrasekhar had the same reaction to it that Gabriel Lamé had to the work of the great French mathematician Charles Hermite: on a la chair de poule. It gave him goosebumps.34 In A Beautiful Question: Finding Nature’s Deep Design, Nobel Prize winner Frank Wilczek finds that judged by these criteria the Standard Model is wanting: “It’s a kludge [a solution that works at the cost of elegance], for sure, and a harsh critic might call it a mess.” It is no periodic table governed by a clear overall organizing principle. Wilczek’s proposed solution is a supersymmetric extension of the Standard Model to include gravity, a solution that he expresses with tables resembling in format figure 4.4 and Randall’s supersymmetric table.35 As a replacement for the unsatisfactory term Standard Model or some slight variation, Wilczek named his solution Core Theory, meaning a theory about the origin of matter at the core of theoretical physics. Wilczek gives his unification theory, while still lacking evidence, the kind of presence Greene would give it, by means of an analogy with the world we can see and manipulate: Might the Artisan, once the Core was roughly hewn, have called it a good week’s work, and stopped right there? Before giving in to that disturbing thought let’s return to the lesson of the dodecahedron [a solid with twelve faces]. We saw in that case how beauty—and, in particular, symmetry—suggests a compelling

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THE MANY VOICES OF MODERN PHYSICS interpretation of what otherwise might seem a random jumble [of faces, seemingly unconnected]. Understanding the possible symmetries of the objects in space led us to realize that there are only a handful of Platonic solids [of which the dodecahedron is one], and that knowledge allowed us to infer an underlying dodecahedron from partial distorted evidence. . . . Might the Core’s piecemeal symmetry, and the apparently lopsided and disconnected objects it acts on, be pieces of a larger symmetry acting on a larger object whose connections have been hidden from view?36

The rhetorical question with which Wilczek ends this paragraph is in fact a real one whose answer is not yet forthcoming. In a positive assessment of the current status of string theory equally applicable to core theory, philosopher Richard Dawid confidently asserts that theoretical physics has entered a new epistemological stage in which “non-empirical theory assessment breaks new ground in replacing the old dichotomy between empirical confirmation and mere speculation by a continuum of degrees of credibility.”37 But in the absence of sound experimental verification, a seemingly unlikely outcome anytime soon, it is not only impossible to decide whether a particular unification theory is true, it is also impossible to choose between theories except on the somewhat shaky grounds of their internal coherence or coherence with other theories. So what will it take to make strings or quanta of space as real for us as atoms, electrons, protons, neutrons, and so forth?

The Final Theory Thought Experiment Physics terms come in many varieties: quark, a colorful name whimsically borrowed from James Joyce’s opaque masterpiece Finnegans Wake; dark matter, a term for matter that is not dark at all, just invisible; fermion, a particle named to honor Enrico Fermi; grand unified theory, a theory that unifies three of the four forces. Three out of four is not bad, but what to call a theory unifying all four forces? Theory of everything is the term that has stuck, with some vagueness as to its precise meaning. In a 1986 Nature article, John Ellis defined “theory of everything” as a candidate theory that “may unify all the fundamental interactions-—electromagnetism, strong and weak nuclear forces and gravity— and explain the number and couplings of all the particles.”38 He then argued that supersymmetric string theory might just fit the bill, “although it has some doubtful aspects.” As mentioned earlier, those “doubtful aspects” remain today, more than three decades later. In the popular science literature, one can easily find a stronger version of Ellis’s definition, either implied or stated: a set of equations that captures everything 104

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as part of a “final theory” spanning the microworld of quantum mechanics to the macroworld as described by relativity and classical physics, and “describing all phenomena that have been observed, or that ever will be observed.”39 These “phenomena” would encompass all microscopic and macroscopic phenomena in the cosmos, whether they be physical, chemical, geological, or biological, including mental processes. Is such a theory to end all theories truly possible? A prominent and undeniably compelling voice on the assent side is that of Nobel Prize winner Steven Weinberg, a gifted and opinionated popular science writer whether for books or literary magazines like the New York Review of Books. In an essay titled “On a Piece of Chalk” appearing in Dreams of a Final Theory, he borrows a strategy from the Victorian scientist and popularizer Thomas Huxley. Weinberg performs a thought experiment-like exercise that involves a piece of chalk. He repeatedly asks the rhetorical question why, according to current and past physics, it is white as he progresses from visible to invisible phenomena. Thanks to his way with words, a “final theory” comes vividly to life, as through the process of reduction, our sense of color is drilled down to the behavior of subatomic particles: Chalk is white. Why? One immediate answer is that it is white because it is not any other color. That is an answer that would have pleased Lear’s fool, but in fact it is not so far from the truth. Already in Huxley’s time it was known that each color of the rainbow is associated with light of a definite wavelength—longer waves for light toward the red end of the spectrum and shorter waves toward the blue or violet. White light was understood to be a jumble of many different wavelengths. When light strikes an opaque substance like chalk, only part of it is reflected; the rest of absorbed. A substance that is any definite color, like the greenish blue of many compounds of copper (e.g., the copper aluminum phosphates in turquoise) or the violet of compounds of chromium, has that color because the substance tends to absorb light strongly at certain wavelengths; the color that we see in the light that the substance reflects is the color associated with light of the wavelengths that are not strongly absorbed. For the calcium carbonate of which chalk is composed, it happens that light is especially strongly absorbed only at infrared and ultraviolet wavelengths that are invisible anyway. So light reflected from a piece of chalk has pretty much the same distribution of visible wavelengths as the light that illuminates it. This is what produces the sensation of whiteness, whether from clouds or snow or chalk. Why? Why do some substances strongly absorb visible light at particular wavelengths and others not? The answer turns out to be a matter of

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THE MANY VOICES OF MODERN PHYSICS the energies of atoms and of light. This began to be understood with the work of Albert Einstein and Niels Bohr in the first two decades of the century. As Einstein first realized in 1905, a ray of light consists of a stream of enormous numbers of particles, later called photons. Photons have no mass or electric charge, but each photon has a definite energy, inversely proportional to the light wavelength. Bohr proposed in 1913 that atoms and molecules exist only in certain definite states, stable configurations having certain definite energies. Although atoms are often likened to little solar systems, there is a crucial difference. In the solar system any planet could be given a little more or less energy by moving it a little farther from or closer to the sun, but the states of an atom are discrete—we cannot change the energies of atoms except by certain definite amounts. Normally an atom or molecule absorbs light, it jumps from a state of lower energy to one of higher energy (and vice versa when light is emitted). . . . Chalk is white because the molecules of which it is composed do not happen to have any state that is particularly easy to jump to by absorbing photons of any color of visible light.40

The answer to the next “why” in the thought experiment relies on quantum mechanics. Weinberg tells us that because the electrons in chalk atoms are tightly bound within their energy levels, they are not boosted to a higher energy level by absorption of the photons from visible light. The wavelength for the higher energy would correspond to some color other than white. We perceive the white in chalk or snow or clouds because no such quantum jump occurs. Weinberg then continues with a further quantum mechanical explanation that involves the Standard Model. It explains the interactions between the substance and force particles that govern the behavior of matter, including those quantum states that produce different colors. Weinberg is not done yet. He continues his rhetorical questioning by starting with the chemical constituents of chalk—calcium, carbon, and oxygen—and drilling down to the same end point, the particles of the Standard Model. He then repeats the same exercise with the biological constituents of chalk, calcium carbonate shells of long-gone tiny animals that dwelled in ancient seas. So, in Weinberg’s reductionist view, all sciences reduce to particle physics. He does caution, however, that “the final theory may be centuries away and may turn out to be totally different from anything we can now imagine.”41 Not all physicists agree with Weinberg’s reductionist thought experiment. Let’s start with a counter thought experiment from Eugene Wigner, a Nobel Prize– winning theoretical physicist who contributed as much to the understanding 106

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of quantum mechanics as Weinberg. You pick up the keys you just dropped fully expecting to pick them up undamaged. Why is this not true of a glass? The answer is in solid-state physics, not in the Standard Model, however much enhanced. Harvard physicist John C. Slater points to the contrast between the “few interesting properties” of atoms and the “wealth of phenomena,” the “unique diversity,” and the “unending possibilities” of their combination in massive numbers. Nobel Prize winner and solid-state physicist Philip Anderson asserts that the reductionist hypothesis does not by any means imply a “constructionist” one. The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science, much less to those of society . . . The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other.42

This caveat does not dismiss the Standard Model as useless, nor does it cast aside its renowned nineteenth-century predecessor, Mendeleev’s periodic law and the corresponding table unifying the known chemical elements. The caveat does assert that, although none of the above unification theories beyond the Standard Model is lacking in merit and ingenuity, none has achieved consensus, and none at this point in development will realize Weinberg’s dream of a final theory anytime soon. This caveat merely says that, yes, we are composed of elementary particles, but no, there is no final predictive theory in the offing to figure out how to get from quarks to us. It is similarly problematic to even develop a single theory for how three elements—calcium, a metal; carbon, a nonmetal; and oxygen, a gas—became the white cliffs of Dover.

A Theory of Absolutely Everything? As evidenced by Wigner and Anderson, not all physicists are reductionists. In The Fabric of Reality, maverick physicist David Deutsch sees the imagined theory of everything as not living up to its grandiose name. In the following passage, he defines exactly what he means by the term theory of everything, then explains how it differs in an important way from the “real Theory of Everything” imagined by reductionists like Weinberg: 107

THE MANY VOICES OF MODERN PHYSICS I must stress immediately that I am not referring merely to the “theory of everything” which some particle physicists hope they will soon discover. Their “theory of everything” would be a unified theory of all the basic forces known to physics, namely gravity, electromagnetism and nuclear forces. It would also describe all the types of subatomic particles that exist, their masses, spins, electric charges and other properties, and how they interact. Given a sufficiently precise description of the initial state of any isolated physical system, it would in principle predict the future behavior of the system. Where the exact behavior of a system was intrinsically unpredictable, it would describe all possible behaviors and predict their probabilities. In practice, the initial states of interesting systems often cannot be ascertained very accurately, and in any case the calculation of the predictions would be too complicated to be carried out in all but the simplest cases. Nevertheless, such a unified theory of particles and forces, together with a specification of the initial state of the universe at the Big Bang (the violent explosion with which the universe began), would in principle contain all the information necessary to predict everything that can be predicted. But prediction is not explanation. The hoped-for “theory of everything,” even if combined with a theory of the initial state, will at best provide only a tiny facet of a real Theory of Everything. It may predict everything (in principle). But it cannot be expected to explain much more than existing theories do, except for a few phenomena that are dominated by the nuances of subatomic interactions, such as collisions inside particle accelerators, and the exotic history of particle transmutations in the Big Bang. What motivates the use of the term “theory of everything” for such a narrow, albeit fascinating, piece of knowledge? It is, I think, another mistaken view of the nature of science, held disapprovingly by many critics of science and (alas) approvingly by many scientists, namely that science is essentially reductionist.43

As an alternative to a theory of everything in Weinberg’s sense, Deutsch proposes what he calls a “unified theory of the fabric of reality,” a theory where everything does not ultimately boil down to physics, a theory that would mainly explain, not predict. This theory of everything has four strands, only one of which concerns physics, the many branching worlds interpretation of quantum mechanics. This theory explains all the bizarre quantum phenomena discussed in chapter 3, including the superposition and entanglement featured in Erwin Schrödinger’s cat experiment.44 The second strand is Alan Turing’s theory of computation, a theory of many virtual worlds: there exists a universal Turing computing machine 108

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that can construct virtual realities whose repertoire encompasses “every physically possible environment.”45 The third strand is from biology, an evolutionary theory propounded by Richard Dawkins, where the genes are in essence the components of a super-complex computer program: “So life is the means—presumably a necessary means—by which the effects referred to in the Turing principle have been implemented in nature.”46 The fourth strand is from philosophy, the evolution of knowledge by a survival-of-the-fittest mechanism similar though different than Darwinian biological evolution, a matter of conjectures and refutations, the brainchild of philosopher Karl Popper. In Deutsch’s unified multidisciplinary theory, it is as a consequence of this four-headed mechanism that we humans can come to understand the fabric of reality. In Deutsch’s estimation, his theory will not ever predict or explain everything but could, with much further development into the distant future, explain everything that can be predicted. About quantum mechanics and computer theory, Deutsch is an international expert; only a fool (or another expert) would argue with him. But in matters of philosophy of science and evolutionary biology, fields outside his disciple, we feel safe in quibbling with him on several points, especially as his theory seems to have had little traction after more than fifteen years since publication. Here are two examples. First, for the philosophy of knowledge strand, Deutsch seems to be under the impression that Thomas Kuhn does not believe in scientific progress, that he believes that a shift in scientific world views, of paradigms, represents a sharp break with the past, the abandonment of a wholly mistaken world view. In his book on Copernicus, however, Kuhn shows us how deeply embedded the great astronomer was in the science in which he was trained.47 Moreover, in his book on blackbody radiation, Kuhn shows us how deeply Max Planck was embedded in the nineteenth-century physics in which he was trained, how alien Planck felt in the wholly new world of Einstein, Heisenberg, and Schrödinger’s making, a revolution that a nonrevolutionary had initiated.48 Second, for the evolutionary biology strand, Deutsch’s main guide is Richard Dawkins, an impressive theorist, and an even more impressive popularizer. But Deutsch is under the mistaken impression that Dawkins’s selfish-gene theory of evolution is now Charles Darwin’s theory. Only Dawkins has, finally, got Darwin right. Along with Dawkins, he is also under the misapprehension that Stephen Jay Gould and Niles Eldredge proposed punctuated equilibrium to “[solve] some allegedly overlooked problem”49 in evolutionary theory. But their target was not evolutionary theory—it was Darwin’s gradualism, still supported by Dawkins, the forlorn hope that in every case there were intermediary fossils between apparent evolutionary jumps, and that in some cases at least, these 109

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would be found. Very few ever were. It was Gould and Eldredge who insisted, plausibly, that at times the pace of evolution increased, that the evolutionary clocked ticked faster than usual. No theory of Deutsch’s scope, no unification theory, can be built on such a sandy foundation.

Few would maintain that the Standard Model established in the 1970s has been anything other than a resounding success, especially after the detection of the Higgs boson in the Large Hadron Collider. The picture that emerges from books and articles discussing this theory is of a periodic-like table of fundamental particles whose interactions produce all the chemical elements and takes into account three of the four forces that control our universe. The persuasiveness of this table rests on the experimental detection of particles predicted by it and the analogy between it and the periodic table. What’s more, though obviously imperfect and incomplete now, this table at some unspecified time in the future might be expanded and refined to realize a theory unifying all four forces in a table more closely resembling the periodic table of elements in terms of symmetry and elegance. In the later twentieth century, various physicists have advocated for different unification theories that surpass the current Standard Model in ambition. Brian Greene has been the leading exponent for the much-ballyhooed string theory, a supersymmetric theory based on a vibrating string analogy that unifies gravity with the three nongravitational forces, as well as general relativity and quantum mechanics. In our view, Greene is unsurpassed as a science communicator. Yet, while his arguments, analogies, visuals, and thought experiments make a highly compelling case that nine spatial dimensions and string-like fundamental particles might actually exist, string theory remains without a shred of experimental evidence, and after nearly a half century since its initial formulation, some within the physics community are questioning whether obtaining truly convincing evidence is even possible. Also lacking experimental evidence, with none in sight in the foreseeable future, is Carlo Rovelli’s loop quantum gravity theory, a theory that unifies general relativity and quantum theory based on the quantization of space itself and an analogy of it to interconnected loops. About the more ambitious unification theories in physics than his, the radical Rovelli is somewhat conservative: “The philosophy underlying loop gravity is that we are not near the end of physics, we better not dream of a final theory of everything, and we better solve one problem at the time, which is hard enough.”50 In light of the slow experimental progress on unification theories beyond the Standard Model, Steven Weinberg’s vividly imagined final theory seems 110

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little more than a dream or wishful thinking at this time, certainly nothing to be expected in our or our children’s lifetimes. What’s more, David Deutsch questions whether we would really learn all that much more about the universe even if a final physics theory were to be confirmed. For him, explanations of reality should be at least as important as any quantitative predictions for observed phenomena possible with a final theory, so he has proposed a multidisciplinary unified theory that weaves together a physics strand with strands for computation, life, and thought. His theory is the product of a brilliant and imaginative thinker but is also untestable, and at least two of the non-physics strands have some questionable aspects. Obviously, much work lies ahead for future generations of physicists working on unification theories and communicating them persuasively to diverse audiences.

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5 COSMIC CONJECTURES

The subject of this chapter might be considered the grandest thought experiment ever conceived. Start with a blank slate: no time, no space, and no matter. Next, formulate a set of conjectures. The universe is infinite in time, or not. The universe is infinite in space, or not. The universe is expanding, or only appearing to do so. The universe is flat spatially throughout, or curved. The universe was born out of another universe, or nothing, or almost nothing. There is only one universe or many. Now, work out the origin and evolution of this hypothetical universe by using some combination of established and speculative physics theories. Accept the resulting narrative, no matter how strange or apparently ridiculous. Key to carrying out such a thought experiment is conjecture—that is, an initial assumption or set of assumptions based on little or no supporting evidence. It is to Isaac Newton that we owe the first conjecture by a major scientist concerning the state and progress of the universe after its creation, a series initiated solely by God’s will: The most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being. And if the fixed stars are the centers of similar systems, they will all be constructed according to a similar design and subject to the dominion of One, especially since the light of the fixed stars is of the same nature as

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COSMIC CONJECTURE the light of the sun, and all the systems send light into all the others. And so that the systems of the fixed stars will not fall upon one another as a result of their gravity, he has placed them at immense distances from one another.1

For believers like Newton, a divine being as the creator of the universe was beyond questioning.2 By contrast, whatever their religious beliefs, modern physicists who tell us what happened from the moment of creation to the present, and sometimes beyond that as well, tell us coherent stories compatible with the available astronomical evidence, conjectures extrapolated from existing theory, mathematics, and certain assumptions about the universe. What they say is interesting and ingenious. On occasion, of course, new evidence reveals some of their conjectures as fictions in part or whole. This was the case, for example, when contra to Isaac Newton’s and Albert Einstein’s different versions of a static universe, the universe was discovered actually to be expanding. The failure of earlier cosmological conjectures has not deterred others from conjecturing further and far more boldly, with the hope that some sort of supporting astronomical evidence might come to the rescue at a later time. Today, readers of popular science books about the universe have an abundance of cosmological narratives to choose from with ever bolder conjectures. The universe is a product of an enormous one-time-only spatial inflation in the tiniest of times immediately after the big bang. The universe has no boundary in time. The universe is expanding, then contracting, then renewing itself. There are more universes than the one we inhabit—possibly countless more. All of these narratives are plausible; none is contradicted by the available evidence. But that they are all plausible is just the conundrum. Beyond the standard big bang universe, there is at present no smoking-gun evidence that permits anyone to definitively choose one in preference to the others. Of course, as with classic novels like Anna Karenina or To the Lighthouse, we readers of popular science need not ever choose between them, though cosmological physicists themselves cannot subsist in that happy state of indecision. This chapter examines the conjectures, narratives, and supporting arguments behind major cosmological theories, starting with Einstein’s and ending with one for a universe of universes.

The Static Spherical Universe After completing his revolutionary papers on general relativity, Einstein applied his new theory to a reigning theory about the universe: the conjecture was that the universe was infinite in space and time and filled with stars more or less homogeneously distributed throughout on an astronomical scale. But as Einstein 113

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notes in Relativity (having been revised in 1918 with the addition of a concluding part on cosmology), Newton’s gravitational theory predicts that such a universe would have to be a dense core of stars gradually diminishing in intensity from the center, not a homogeneous arrangement of stars everywhere. The observable universe would thus be analogous, in Einstein’s poetic phrase, to “a finite island in the infinite ocean of empty space.”3 Over a vast span of time, Einstein argued, individual stars within the island universe would be continually floating into the ocean of empty space. The island universe would thus become “impoverished” over time as stars continually vanish into empty space, never to be replaced or to interact with another star. But if time is infinite, shouldn’t that scenario have already happened? Einstein circumvented that reductio ad absurdum by conjecturing that the universe was infinite temporally but finite spatially, being without any edges or borders, like a round balloon but with matter distributed more or less uniformly over the surface. This picture of the universe could remain static and unchanging on a large scale throughout time. In a seminal paper published in 1917, “Cosmological Considerations in the General Theory of Relativity,” Einstein makes the case for his treatment of the distribution of matter in space by means of an analogy with geodesists, scientists who measure and monitor the size and shape of the Earth by making a simplifying geometric assumption: According to the general theory of relativity the metrical character (curvature) of the four-dimensional space-time continuum is defined at every point [in the universe] by the matter at that point and the state of that matter. Therefore, on account of the lack of uniformity in the distribution of matter, the metrical structure of this continuum must necessarily be extremely complicated. But if we are concerned with the structure only on a large scale, we may represent matter to ourselves as being uniformly distributed over enormous spaces, so that its density of distribution is a variable function which varies extremely slowly. Thus our procedure will somewhat resemble that of the geodesists who, by means of an ellipsoid, approximate to the shape of the earth’s surface, which on a small scale is extremely complicated.4

Einstein’s simplifying assumption is that the universe as a whole is perfectly spherical, yet like Earth, on a small scale anyway, “extremely complicated.” In the cosmological part of Relativity, Einstein pictures that universe vividly for us by means of a thought experiment. We are to imagine the universe as a sphere populated by two-dimensional beings carrying flat measuring rods: 114

COSMIC CONJECTURE The flat beings with their measuring-rods and other objects fit exactly on this surface and they are unable to leave it. Their whole universe of observation extends exclusively over the surface of the sphere. Are these beings able to regard the geometry of their universe as being plane geometry and their rods withal as the realization of “distance”? They cannot do this. For if they attempt to realize a straight line [extending as far as possible in this two-dimensional universe], they will obtain a curve, which we “three-dimensional beings” designate as a circle, i.e. a self-contained line of definite finite length, which can be measured up by means of a measuring-rod . . . The great charm from this consideration lies in the recognition of the fact that the universe of these beings is finite yet has no limits.”5

On a flat two-dimensional map, we can easily trace a nice Euclidean straight line between, say, Chicago and Paris. But if we try to do so on a three-dimensional globe, we cannot. The shortest distance must follow a curved path. And if we fly on straight past Paris and continue without stopping, eventually, we draw a complete circle. Einstein’s geodesic analogy here is that our universe is like the spherical Earth. Neither has a definitive end or beginning point—“no limits,” in Einstein’s phraseology. There was a technical catch in the geodesic analogy, however. In applying the curved structure of space to his general relativity equations, Einstein found that he could not mathematically derive a satisfactory solution without adding a hypothetical term or fudge factor, what came to be known as the cosmological constant. This term embodies the repulsive force needed to maintain a static universe and exactly counteract the contraction and collapse of the universe that would otherwise occur due to the attractive force of gravity. In “Cosmological Considerations in the General Theory of Relativity,” Einstein added this constant to his governing equation for general relativity. In Einstein’s words from a 1946 appendix added to Relativity, this term “was not required by the theory as such nor did it seem natural from a theoretical point of view.”6 Later, after the discovery of the expanding universe as a result of Edwin Hubble’s astronomical measurements in 1929, Einstein reportedly admitted that adding this term was his “biggest blunder.”7 There was another more important catch to the geodesic assumption, as stated in Einstein’s 1917 paper: “Whether, from the standpoint of present astronomical knowledge, it is tenable, will not here be discussed.”8 Nor does he even propose a means for verifying it. With respect to the tenability of Einstein’s conjecture of a static universe, the verdict of history is that even from a theoretical point of view, as contemporary cosmologists Paul Steinhardt and Neil Turok bluntly put 115

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it, “This situation is contrived and unstable: unless the balance between forces is perfect, the universe either collapses or blows up.”9 While Einstein’s conjecture may have had a relatively short shelf life due to the discovery of the expanding universe, the cosmological constant has had a robust afterlife in subsequent narratives, as has the geodesic analogy and the notion that the fabric of space itself is key to understanding the universe.

The Never-Changing but Expanding Universe In Relativity, Einstein remarks that one of the unsatisfactory consequences of Newton’s theory is that the light from the stars and stars themselves would be “perpetually passing out into infinite space, never to return, and without ever again coming into interaction with other objects of nature.”10 At essentially the same time as the big bang narrative was taking shape by fits and starts to explain Edwin Hubble’s astronomical measurements suggesting a spatially expanding universe, a trio of imaginative physicists—Fred Hoyle, Hermann Bondi, and Thomas Gold—proposed a brilliant and plausible alternative solution: the spontaneous creation of atomic matter to replace the stars constantly exiting the observable universe, a kind of perpetual motion machine. While expansion is assumed, a starting point in time is not. In this conjecture, the universe remains the same at any time or place, on a cosmic scale anyway, throughout eternity, yet from anywhere in the universe, the stars appear to be always speeding apart as though projectiles from an explosion, in keeping with Hubble’s data. If this were the case, as Einstein commented above, one would think all the stars would vanish from each other’s sight in time. The trio’s work-around was that new atomic particles are constantly being created out of nowhere throughout the universe and eventually gathering together to form new stars and galaxies to replace the disappearing ones. Hoyle analogized this constantly creating yet steady state universe as river-like: “One can have unchanging situations that are dynamic, as for instance a smoothly flowing river.”11 This river-like universe would have no beginning and presumably never stop flowing. In The Nature of the Universe, Hoyle makes a spirited defense for his “steady state” theory over the competing “big bang” theory to explain the apparent mirage of expansion: The most obvious question to ask about continuous creation is this: Where does the created matter come from? At one time created atoms do not exist, at a later time they do. The creation arises from a field, which you must think of as generated by the matter that exists already. We are well used to the idea of matter giving rise to a gravitational field. Now we must think of

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COSMIC CONJECTURE it also giving rise to a creation field. Matter that already exists causes new matter to appear. Matter chases its own tail. This may seem a very strange idea and I agree that it is, but in science it does not matter how strange an idea may seem so long as it works—that is to say, so long as the idea can be expressed in a concise form, and so long as its consequences are found to be in agreement with observation. Some people have argued that continuous creation introduces a new assumption into science—and a very startling assumption at that. Now I do not agree that continuous creation is an additional assumption. It is certainly a new hypothesis, but it only replaces a hypothesis that lies concealed in the older theories, which assume, as I have said before, that the whole of matter in the Universe was created in one big bang at a particular time in the remote past. On scientific grounds this big bang assumption is much less palatable of the two. For it is an irrational process that cannot be described in scientific terms. Continuous creation, on the other hand, can be represented by mathematical equations whose consequences can be worked out and compared with observation. On philosophical grounds, too, I cannot see any good reason for preferring the big bang idea. Indeed, it seems to me in the philosophical sense to be a distinctly unsatisfactory notion, since it puts the basic assumption out of sight where it can never be challenged by a direct appeal to observation. Perhaps you may think the whole creation of the Universe could be avoided in some way. But this is not so. To avoid the issue of creation, it would be necessary for all the material of the Universe to be infinitely old, and this it cannot be for a very practical reason. For if this were so, there could be no hydrogen left in the Universe. As I think I demonstrated when I talked about the insides of stars, hydrogen is being steadily converted into helium throughout the Universe, and this conversion is a one-way process—that is to say, hydrogen cannot be produced in any appreciable quantity through the breakdown of the other elements. How comes it, then, that the Universe consists almost entirely of hydrogen? If matter were infinitely old this would be quite impossible. So we see that the Universe being what it is, the creation issue simply cannot be dodged. And I think that of all the various possibilities that have been suggested, continuous creation is the most satisfactory.12

Hoyle’s main argument for favoring his conjecture over the big bang universe is that, instead of a whole universe, it only requires matter in the form of hydrogen atoms, or some hydrogen-producing precursor, to appear out of nowhere at a rate high enough to replace the lost matter. To account for the magical 117

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spontaneous creation of matter, in a 1948 scientific paper Hoyle swapped the cosmological constant term (λgμν) in Einstein’s governing equation for general relativity with a “creation tensor” (C μν).13 In the second quoted paragraph, Hoyle dismisses any alternative theory in which the universe is static spatially and with no beginning of time (as in Einstein’s theory) on the technical grounds that hydrogen, the key element in star formation, could not possibly exist in such great abundance today. In 1957 Hoyle greatly extended the steady state theory in a coauthored paper on the formation of the elements in the stars that unquestionably merited a Nobel Prize for him and the three other authors,14 though the Norwegian Nobel Committee never saw it that way. In Hoyle’s expanded steady state conjecture,15 while hydrogen atoms spontaneously appear throughout the universe to form new stars, the star cores constantly forge helium by the fusion of hydrogen, then they convert the helium into carbon and the elements in the periodic table through iron by chemical reactions at very high temperatures. Many millions of years later, reactions due to the violent explosion of dying stars, or supernova, yield the heavier elements through uranium, and these dispersed elements accumulate in the gaseous clouds around newly formed stars, from which planets and other solid bodies form. In the end, while neither the creation tensor nor the conjecture regarding spontaneously created hydrogen passed the test of time, Hoyle and his colleagues’ basic narrative on the forging of elements in the stars has proved enduring.

The Expanding Balloon Universe Following Einstein’s lead in applying general relativity to cosmology in the early 1930s, theoretical physicist and Catholic priest Georges Lemaître explained Hubble’s finding that the velocity of galaxies increases with their distance away from Earth: it was possibly due to the universe expanding spatially over time, starting with a primordial atom whose mass equals that of the entire universe.16 In the late 1930s and 1940s, a trio of physicists—George Gamow, Ralph Alpher, and Robert Herman—added many rich details to the expansion narrative based on theoretical calculations from astronomical data. Hoyle later dismissively characterized their narrative as the “big bang,” which he found impossible to believe in without a plausible starting mechanism and solution for the hydrogen-abundance problem. What does it mean for space to expand starting with a big bang? An oft-repeated analogy modifies Einstein’s static sphere to an expanding balloon dotted on the surface with spots representing two-dimensional galaxies. Gamow communicated this analogy in a popular science book from 1953: 118

COSMIC CONJECTURE If the expansion of the space of the universe is uniform in all directions, an observer located in any one of the galaxies will see all other galaxies running away from him at velocities proportional to their distances from the observer. This can be easily demonstrated by gluing a number of pieces of paper (cut in the shape of galaxies, if desired) to the surface of a rubber balloon and blowing up the balloon to larger and larger size . . . An observer located in any one of these model galaxies will see that all the others run away from him and he may be inclined to believe (incorrectly) that he is at the center of the expansion.17

And here is Stephen Hawking’s slightly more compact version from 1988: “The situation is rather like a balloon with a number of spots painted on it being steadily blown up. As the balloon expands, the distance between any two spots increases, but there is no spot that can be said to be the center of the expansion. Moreover, the farther apart the spots are, the faster they will be moving apart.”18 Smoking-gun evidence for this analogy arrived in 1964, when Arno Penzias and Robert Wilson measured the cosmic microwave background, the remnant heat from the big bang spread more or less uniformly throughout the universe (further detailed in chapter 8). They received a Nobel Prize in Physics for that discovery in 1978. The year prior, the big bang universe had grabbed the attention of the reading public with the appearance of Steven Weinberg’s best-selling The First Three Minutes. As Weinberg notes, the expression big bang is only a metaphor and deeply deceptive. Weinberg amplifies by contrasting it with an ordinary earthly explosion: “In the beginning there was an explosion. Not an explosion like those familiar on earth, starting from a definite center and spreading out to engulf more and more of the circumambient air, but an explosion which occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle.”19 Also very much unlike any explosive force, Weinberg’s conjecture is that this cosmic explosion begins at infinite temperature and density, both of which fall with time in accord with established physics theory. The centerpiece of Weinberg’s book is a chapter on what happened from just after the big bang through the first three minutes. The scenario begins at t = 1/100 second, the time when physics theory of that day first kicks in with any assurance. Rather than any sort of visual representation of change over time, Weinberg relies on a cinematic screenplay: We are now prepared to follow the course of cosmic evolution through its first three minutes. Events move much more swiftly at first than later, so it

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THE MANY VOICES OF MODERN PHYSICS would not be useful to show pictures spaced at equal time intervals, like an ordinary movie. Instead, I will adjust the speed of our film to the falling temperature of the universe, stopping the camera to take a picture each time that the temperature drops by a factor of about three. Unfortunately, I cannot start the film at zero time and infinite temperature. Above a threshold temperature of fifteen hundred thousand million degrees Kelvin (1.5 × 1012 °K), the universe would contain large numbers of particles known as pi mesons, which weigh about one-seventh as much as a nuclear particle . . . Unlike the electrons, positrons [antiparticle to the electron], muons, and neutrinos [see figure 4.4], the pi mesons interact very strongly with each other and with nuclear particles—in fact, the continual exchange of pi mesons among nuclear particles is responsible for most of the attractive force which holds atomic nuclei together. The presence of large numbers of such strongly interacting particles makes it extraordinarily difficult to calculate the behavior of matter at super-high temperatures, so to avoid such difficult mathematical problems I will start the story in this chapter at about one-hundredth of a second after the beginning, when the temperature had cooled to a mere hundred thousand million degrees Kelvin, safely below the threshold temperatures for pi mesons, muons, and all heavier particles . . . With these understandings, let us now start the film. first frame. The temperature of the universe is 100,000 million degrees Kelvin (1011 °K). The universe is simpler and easier to describe than it ever will be again. It is filled with an undifferentiated sop of matter [particles mentioned above] and radiation [photons], each particle of which collides very rapidly with the other particles. Thus, despite its rapid expansion, the universe is in a state of nearly perfect equilibrium. The contents of the universe are therefore dictated by the rules of statistical mechanics, and do not depend at all on what went before the first frame. . . . The abundant particles are those whose threshold temperatures are below 1011 °K; these are the electron and its antiparticle, the positron, and of course the massless particles, the photon, neutrinos, and antineutrinos. . . . The universe is so dense that even the neutrinos, which can travel for years through lead bricks without being scattered, are kept in thermal equilibrium with the electrons, positrons, and photons by rapid collisions with them and with each other.20

Weinberg’s screenplay runs five frames and covers a little past the first three minutes, then jumps ahead to a sixth frame at about thirty-five minutes. The 120

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narrative makes for an action picture to end all actions pictures: unimaginably vast armies of different subatomic particles collide and scatter or annihilate each other, pair off, vanish, appear out of pure energy, and even change identities while the temperature and energy density drop precipitously from mountainous heights and space itself expands. Weinberg’s main characters in the drama are the subatomic particles, with the first few elements (mainly hydrogen and helium) only forming after hundreds of thousands of years more of expansion and cooling. The location for all this action resembles the inside of a physics experiment, not anything remotely like the universe we know today. The skeptical reader may legitimately wonder how Weinberg or any physicist could possibly know so much fine detail about the first three minutes some fourteen billion years in the past. Building on the earlier conjectures of physicists like Lemaître and Gamow, Weinberg makes several credible assumptions, takes into account the recent astronomical observations, and cranks out the physical consequences in accord with mostly textbook physics like statistical mechanics and particle physics. Voilà, a plausible scenario regarding the first three minutes after the big bang and beyond that captured the public’s imagination.

The Inflationary Expanding Universe At the time Weinberg’s The First Three Minutes was published in 1977, the standard narrative for the big bang theory offered no satisfactory explanation for the actual big bang or its cause, only what came afterward based on an educated guess about the initial state. It left open the question on how our entire universe could have sprung out of apparent nothingness in terms of space and time. Three decades earlier, Gamow had conjected that it “could have originated (if one let’s one imagination fly beyond any limit) as the result of hypothetical universal collapse preceding the expansion.”21 Extrapolating beyond that conjecture, we assume Gamow envisioned a universe undergoing endless cycles of expansion and collapse. But that origin story was a guess no more credible than a divine creator being. In the late 1970s and following decades, Alan Guth and other physicists devised an ingenious conjecture that relies on the spontaneous appearance of the equivalent of an ounce of starter matter whose diameter is “more than a billion times smaller than a proton”22—that is, a single thing of almost nothing. In Guth’s scenario, this spontaneously created matter, immediately after the big bang, doubled in size some one hundred times in an unimaginably “brief interval of time” powered by a conjectured repulsive force Guth calls a false vacuum, something akin to the repulsive force behind Einstein’s cosmological constant. Guth explains this analogy in his popular science book The Inflationary Universe: 121

THE MANY VOICES OF MODERN PHYSICS Curiously, the gravitational effect of the false vacuum is identical to the effect of Einstein’s cosmological constant. . . . Recall that Einstein introduced this term so that the repulsive force could prevent his static model of the universe from collapsing under the normal attractive force of gravity. There is, however, an important difference between the cosmological constant and the false vacuum: while the cosmological constant is a permanent term in the universal equations of gravity, the false vacuum is an ephemeral state that exerts its influence for only a brief moment in the early history of the universe. A short calculation shows that the gravitational repulsion causes the universe to expand exponentially. That is, the expansion is described by a doubling time, which for typical grand unified theory numbers is about 10 –37 seconds. In this brief interval of time, all distances in the universe are stretched to double their original size. In two doubling times, the universe would double again, bring it to four times its original size. After three doubling times it would be eight times its original size, and so on. As has been known since ancient times, such an exponential progression leads rapidly to stupendous numbers.23

Guth’s inflationary period accounts for all of a millionth of a trillionth of a trillionth second in the early universe, during which it would have expanded by some one hundred trillion trillion times significantly faster than the speed of light, then slowed to a much lower rate. Motivating this cosmic conjecture is a seemingly ludicrous and far-fetched analogy proposed by physicist Edward Tryon in 1973. In quantum theory, particles can spontaneously and randomly appear out of nowhere while others disappear with no net gain or loss in mass or energy. By analogy, the starter material for an entire universe could have appeared by a quantum fluctuation.24 A serious problem with the standard big bang theory was that, given the violent start to the universe, the early universe should have been in a tremendously chaotic state during its initial expansion: space would be warped and contorted; temperature and density would have fluctuated wildly throughout the ever expanding space. Yet, astronomical measurements had proved that the temperature throughout the universe was incredibly uniform at three hundred thousand years of age, a variation of a mere one part to one hundred thousand in all directions.25 On the face of it, that does not seem possible—something equivalent to the temperature of an entire ocean being essentially the same no matter where you measured it at any point from the surface to the lowest depth, and from any side across to the adjacent side. 122

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In Guth’s conjecture, a “false vacuum” appears as a result of a quantum fluctuation. Because of its short-lived repulsive force, the universe undergoes the above super expansion, which smooths out the temperature variations everywhere in the universe. And almost as soon as this expansion starts, it ceases forever throughout our universe, its smoothing task complete. Then, the repulsive-gravity material decays into ordinary subatomic particles, and the cosmological narrative returns to that of the standard big bang theory with its far lower expansion rate. From there Guth’s cosmic narrative more or less follows the standard big bang narrative. On the face of it, Guth’s now-you-see-it, now-you-don’t false vacuum may seem more deus ex machina than plausible scientific explanation. Although limiting his hedging to the occasional “if inflation is right, then . . .” through much of The Inflationary Universe, toward the end, Guth does quote approvingly a cautionary pronouncement by fellow physicist Frank Wilczek (1997): “I think it is fair to say that while the general idea of an inflationary universe is extremely attractive, the specific models so far put forward do not inspire confidence in detail.”26 But in a brief chapter that immediately follows, Guth seems to qualify Wilczek’s qualification. There, he reports that in 1992 the Cosmic Background Explorer (COBE) satellite had taken extensive astronomical measurements of the slight temperature variations in the cosmic microwave background radiation, and the results had shown superb agreement with the predictions of inflationary theory. He even includes a graph showing the very impressive-looking comparison between measurement and prediction. These results were even presented to the public with great fanfare at a press conference. Carried away somewhat with the excitement at that time, Hawking called it the “discovery of the century, if not all time.” Yet, with over four decades of continued refinement backed by even more supportive astronomical measurements, agreement between predictions and measurements has not yet been judged by the physics community as sufficient proof of the theory, though definitely a promising sign. As Guth noted in a 2014 interview: “The temperature nonuniformities in the cosmic microwave background were first measured in 1992 by the COBE satellite, and have since been measured with greater and greater precision by a long and spectacular series of ground-based, balloon-based, and satellite experiments. They have agreed very well with the predictions of inflation. These results, however, have not generally been seen as proof of inflation, in part because it is not clear that inflation is the only possible way that these fluctuations could have been produced.”27 With further astronomical measurements of the microwave background now planned, Guth and several other contributing physicists may someday soon be able to claim vindication of inflationary theory, or not. For now, Guth’s theory 123

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has altered the shape behind the governing cosmological analogy away from an expanding balloon to more of an expanding church bell shape.

Picturing the Big-Bell Expanding Universe Timelines display key events in chronological order, normally on a numbered horizontal or vertical line or strip. They can span relatively short periods, such as the horrific events on 9/11 or the four years of the Civil War, or extremely long periods, like the origin and evolution of species or even the universe. Figure 5.1 shows a popular timeline for the universe from beginning to the present time, with Guth’s quantum fluctuation and inflationary universe at the start.28 It has only two dimensions. One is key events in cosmic evolution during the last 13.77 billion years; the other is the shape of the spatial expansion during the time that they occurred. It is obviously not balloon-like, but more like a large church bell on its side. The balloon analogy has proven extraordinarily fecund for picturing the effects of spatial expansion on the distance between stars and galaxies. But here, the balloon analogy must be jettisoned to be able to accommodate Guth’s super expansion at the universe’s birth. This big-bell picture comes with an origin narrative based on the current favored conjectures, established theories, and many astronomical measurements. According to this narrative,29 the universe we inhabit sprang into existence about fourteen billion years ago at a temperature and density so high that no analogy or comparison will suffice to describe them adequately. This “infernoverse” formed for reasons still uncertain, but possibly a quantum fluctuation followed by appearance of a repulsive force causing space to expand faster than the speed of light for 10 –30 seconds or thereabout. With continued spatial expansion at a much slower pace after the miraculous start, the density and temperature fell accordingly as a function of time. Over the next 375,000–400,000 years, the universe remained so dense and hot that photons, subatomic particles, and nuclei could not travel far without colliding and interacting with other particles. The most complex chemical structures were nuclei, combinations of protons and neutrons comprising three quarks each. That changed at around 375,000 years, as free electrons and protons combined to form the first hydrogen atoms. Some helium and lithium atoms also emerged as free electrons joined with nuclei. That first 400,000 years pose a communicative challenge for science writers to picture with words or images, since the time span bears no resemblance whatsoever to the following many billions of years, when the much more easily depicted stars and galaxies formed and prospered. Physicist Katie Mack is up to the challenge, in the form of an extended analogy comparing this astronomical period to a journey from the center of the sun: 124

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Figure 5.1. Timeline for origin and evolution of the inflationary universe from the big bang to the present. Original in color. Image credit: NASA.

I sometimes imagine experiencing this phase of the early universe like a journey from the center of the Sun outward, but instead of moving through space, you’re moving through time. You start in the center of the Sun, when the heat and density are so high that atomic nuclei are fusing together to make new elements. The solar interior is opaque with light, with photons continually bouncing off electrons and protons so violently that it can take hundreds of thousands of years of constant scattering for a photon to reach the surface. Eventually, as you move outward, the plasma becomes less dense and light is able to travel farther between scatterings. At the surface, it can stream freely out into space. In a similar way, a journey through time from the first few minutes of the universe to about 380,000 years later takes the entire cosmos from that hot dense plasma to a cooling gas of protons and electrons that can finally come together to make neutral atoms [no electric charge], allowing light to travel freely between them instead of constantly bouncing off the charged particles. We call the end of this fireball stage of the early universe the “surface of last scattering,” because it’s a kind of surface in time at which light goes from being trapped in plasma to traveling long distances across the cosmos.30

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Figure 5.2. Another timeline of the inflationary universe emphasizing particle and antiparticle formation, annihilation, and combination within first few minutes of the universe. Original in color. Image credit: Particle Data Group at Lawrence Berkeley National Laboratory. Reprinted with permission of Lawrence Berkeley National Laboratory.

That transition stage in the early universe marks the start of the cosmic microwave background (labeled “afterglow light pattern” in figure 5.1) detected by Penzias and Wilson in 1964. The narrative behind figure 5.1 continues. Over about four hundred million years of “Dark Ages,” the primordial hydrogen and helium atoms condensed into stars and lit up the universe. At the same time, the nuclear furnaces at the center of the stars manufactured the elements up to iron, and much later, the remaining natural elements formed and dispersed throughout the universe with the explosion of massive stars at the end of their lifetimes. Stars agglomerated into the first galaxies at one billion years. After about nine billion years and ever since, a second wave of accelerated expansion began, this time powered by the repulsive effects of a newly conjectured form of energy that repulses matter 126

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(“dark energy”), countering the attractive effects of gravity. (Not to be confused with the repulsive effects of Guth’s false vacuum during the early universe.) Taking advantage of the features of a data map and time series, figure 5.2 presents a more complete picture of the big-bell expanding universe compared with figure 5.1.31 This “space-time-story graphic” visually represents not only the bell-shape spatial expansion in figure 5.1 but also the evolution of the universe from Standard Model particles (quark, gluon, electron, meson, etc.) to stars and galaxies and black holes. In addition, it plots data for three key variables along the bell side. From them, readers can track the change in temperature and energy (indicative of the universe’s mass, since E = mc2) as a function of cosmic time. In visual impact, we believe figure 5.2 rivals Charles Joseph Minard’s famous spatiotemporal graph depicting Napoleon Bonaparte’s retreat from Russia in 1812, one of graphics expert Edward Tufte’s favorite examples illustrating “how multivariate complexity can be subtly integrated into graphical architecture.”32 Note that time had to be purposely distorted in figure 5.2. About half the graph represents the first one hundred seconds of the universe, and the units of measure suddenly change at the midpoint from seconds to years. Even within that one hundred seconds, the bulk of the graph represents the first second, the period covered by the latest unification theories during which a single force presumably separated into the four separate ones (weak, strong, electromagnetic, gravitational) and the key subatomic particles formed. The graph also focuses on the first one hundred seconds because that is the time of most interest to the image’s creators, scientists from the Particle Data Group at Lawrence Berkeley National Laboratory in Berkeley, California.

Picturing the Big Brane Universe The inflationary period represented in figures 5.1 and 5.2 involves a supercharged expansion of the universe by a million million million million million times in the first millionth of a trillionth of a trillionth of a second. Then, it stopped with little trace. Even though Guth’s inflationary universe narrative seems to be the favorite at present, within certain quarters skepticism runs deep.33 The picture could be all wrong. A leading competitor that explains the present data just as well is a cyclic universe that expands and contracts, starting afresh every trillion years. While in 1948 Gamow only hinted at the possibility of such a universe, Paul Steinhardt and Neil Turok recently worked out a scientifically plausible argument for one. In a 2014 interview for Scientific American, Steinhardt summarizes his problem with Guth’s hyperinflation and launches into an argument for his and Turok’s alternative narrative: 127

THE MANY VOICES OF MODERN PHYSICS Since 1983, it has become clear that inflation is very flexible (parameters can be adjusted to give any result) and generically leads to a multiverse consisting of patches in which any outcome is possible. Imagine a scientific theory that was designed to explain and predict but ends up allowing literally any conceivable possibility without any rule about what is more likely. What good is it? It rules out nothing and can never be put to a real test. . . . The cyclic model emerged when my collaborators and I asked the question: is there any way of explaining the smoothness and flatness of the universe and small ripples in density without inflation? The answer was yes: the key is to have a universe in which the big bang is replaced by a big bounce. In this picture, the present period of expansion and cooling is preceded before the bounce by an epoch of contraction, and the important events that shape the large-scale structure of the universe (smoothing, flattening and generating fluctuations) occur before the bounce during a period of slow contraction. There is no high-energy inflation phase—the universe goes straight from the bounce into a period of slow expansion and cooling. Inflation is not needed to smooth and flatten the universe. Consequently, there is no multiverse. The bounces can repeat at regular intervals resulting in a cyclic universe. In some versions, the theory is geodesically complete (existing infinitely into the past), unlike inflation, which requires a beginning and special initial conditions. The cyclic theory makes one generic model-independent prediction: no detectable primordial gravitational waves [generated in the aftermath of the big bang]. Hence, if BICEP2 [an astronomical experiment called Background Imaging of Cosmic Extragalactic Polarization] had been correct [BICEP2 scientists errantly had announced the detection of these gravitational waves in 2014] or if primordial gravitational waves are observed in future experiments, all cyclic models based on smoothing via slow contraction will be entirely ruled out. Therefore, yes, the cyclic theory is definitely falsifiable!34

Steinhardt’s counterargument is that if Guth’s “false vacuum” spawned our universe, who is to say the same mechanism did not give birth to countless others. Why would that only happen once? Why not an infinite number of times? And since certain parameters in the governing equations are arbitrarily adjustable, inflationary theory is not falsifiable, falsifiability being Karl Popper’s essential criterion for separating science from nonscience. By contrast, 128

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Figure 5.3. Stages of evolution for cyclic universe composed of parallel colliding branes. From Paul J. Steinhardt and Neil Turok, Endless Universe (2008), 158–59. Reprinted with permission of Orion Publishing through PLSclear. For an animated version of this picture, see http://physics. princeton.edu/~steinh/brane3.html.

Steinhardt maintains, his theory created with Turok is “definitely falsifiable.” If an inflationary period had indeed roiled space-time, it should have created “primordial gravitational waves” in the fabric of space-time, ripples that should be detectable with astronomical technology. If primordial ripples, then no cyclic theory. In the popular science book Endless Universe, Steinhardt and Turok present their cyclic universe. Actually, it requires two universes: ours and a parallel one to explain ours. Figure 5.3 visualizes it as a space-time story graphic divided into six epochs.35 The first four are periods of expansion: the big bang itself, then separate epochs dominated by radiation (photons, other subatomic particles, and nuclei), matter (atoms), and dark energy. In the last two epochs, the universe contracts and prepares for the birth of a newly recycled universe. The plausibility of Steinhardt and Turok’s picture obviously rests on their conjecture of an apparently undetectable parallel universe to ours. Also important is their imagined transformation mechanism from the last to first epoch, their alternative to the inflationary narrative: 129

THE MANY VOICES OF MODERN PHYSICS Unlike the inflationary picture, the cyclic model does not include a moment when the temperature and density become infinite. Instead, the big bang is an event that can, in principle, be fully described using the laws of physics. Before the bang [upper right image in figure 5.3], space is flattened and filled with a smooth distribution of energy resulting from the decay of dark energy. At the bang, some of this energy is transformed into smoothly distributed matter and radiation at a very high temperature, high enough to evaporate ordinary matter into its constituent quarks and electrons and to produce many other exotic particles through high-energy collisions. But from before to after the bang, the fabric of space remains intact, the energy density is always finite, and time proceeds smoothly.36

This six-epoch narrative lasting about a trillion years has the decided advantage of a before and after the bang so that the universe does not miraculously pop up out of “empty” space due to some quantum fluctuation. It also dispenses entirely with Guth’s once-in-a-lifetime, fleeting inflationary period. Steinhardt and Turok’s visual realization of these epochs in no way resembles other visual representations showing the universe starting as a point and expanding over many billions of years. The physics behind this visualization is based on a refinement to string theory, called M-theory. According to that theory, the one-dimensional strings that constitute subatomic particles can be extended to universe-sized three-dimensional membranes, called “branes” for short. Steinhardt and Turok posit a universe-size big brane that exists separately from but parallel to the brane we inhabit, where the two parallel branes attract and repel each other in an elaborate dance to the music of time (figure 5.3). Each brane has three infinite spatial dimensions that are separate yet connected by an additional spatial dimension (the “bulk”) and thus invisible to each other. The inflationary and cyclic narratives are both founded on bold conjectures, both captured by persuasive visual representations, both under constant revision and refinement, both battling for the attention and approval of the physics community. The former has two inflationary periods created by different mechanisms, a false vacuum and dark energy. The latter has two branes separated by an extra spatial dimension based on an unproven and incomplete theory (string theory) that has yet to receive anything approaching verification. On the other hand, it is falsifiable, circumvents the problem of a beginning or end of time, and explains the existing astronomical data as plausibly as the inflationary narrative.37 The above pictures of the universe may be favored within different corners of the physics community at the moment, but there are still other plausible alternatives out there, including one from the most famous physicist since Einstein. 130

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Picturing the Imaginary Time Universe Stephen Hawking’s A Brief History of Time is indeed “brief,” as the title proclaims, but not really a brief history of time, as it covers many other modern physics topics as well. Still, time does figure prominently at times; in particular, it is front and center in Hawking’s no-time-boundary theory for the origin and evolution of our universe, created with James Hartle in the early 1980s. At the root of this theory is a bold conjecture: if space might have more than three dimensions, why should we not consider the alternative of two time dimensions instead? With his characteristic good humor, Hawking argues for a radical redefinition of time: In the classical theory of gravity, which is based on real space-time, there are only two possible ways the universe can behave: either it has existed for an infinite time, or else it had a beginning at a singularity at some finite time in the past. In the quantum theory of gravity [unifying quantum mechanics and relativity], on the other hand, a third possibility arises. Because one is using Euclidean space-times, in which the time direction is on the same footing as directions in space, it is possible for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge. Space-time would be like the surface of the earth, only with two more dimensions. The surface of the earth is finite in extent but it doesn’t have a boundary or edge: if you sail off into the sunset, you don’t fall off the edge or run into a singularity. (I know, because I have been round the world!) If Euclidean space-time stretches back to infinite imaginary time, or else starts at a singularity in imaginary time, we have the same problem as in the classical theory of specifying the initial state of the universe: God may know how the universe began, but we cannot give any particular reason for thinking it began one way rather than another. On the other hand, the quantum theory of gravity has opened up a new possibility, in which there would be no boundary to space-time and so there would be no need to specify the behavior at the boundary. There would be no singularities at which the laws of science broke down, and no edge of space-time at which one would have to appeal to God or some new law to set the boundary conditions for space-time. One could say: “The boundary condition of the universe is that it has no boundary.” The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE.38

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Whereas the standard big bang universe has a boundary—a starting time at t = 0 from which our universe springs forth for no apparent reason—Hawking proposes a universe with “no boundary of space-time.” How is that possible? Hawking’s answer has two intertwined narratives, each with a different kind of time, real or imaginary. In the real time narrative, there is a t = 0 at which our universe spontaneously appeared at a singularity, a point of infinite space-time curvature and density, conditions that also exist in black holes. After that, some version of the standard narrative consistent with the expanding balloon analogy holds sway. This real-time narrative also has no mandatory end to the universe. Under the attractive force of gravity, all the matter in the world contracts to a singularity and t = 0 again. And the whole process could start over under the right conditions. Nothing is really new here. Hawking also proposes a concurrent narrative, a conjectured imaginary time universe that is mathematically tied to the real time universe. “Imaginary” here does not connote a complete fabrication or fairy tale, but use of an “imaginary number,” an extremely valuable mathematical construct in physics in which a real time is multiplied by an imaginary unit equal to the square root of –1 (abbreviated as i). Because i2 = 1, this magical mathematical construct has proved extremely fecund to physicists and mathematicians, allowing them to circumvent mathematical dead ends. Hawking spares us the mathematics for converting the real into the imaginary time universe, or vice versa. However, he does offer an analogy, comparing an Earth-like sphere to the imaginary time universe in picture form (figure 5.4). He borrowed this picture from Einstein’s no-space-boundary universe, characterized by a sphere of finite size without boundaries or edges, mentioned at the beginning of the chapter. Imaginary time follows a longitudinal path from the North to South Pole, while the size of the universe follows a latitudinal path, expanding from the North Pole to the equator, then contracting from the equator to the South Pole. Central to this analogy is that imaginary time has a north and south pole, but no absolute boundaries or edges or singularities. With his no-boundary conjecture, Hawking theoretically manages to have his cake and eat it too. The big bang remains, yet imaginary time has no absolute beginning or end, and thus no need for the laws of physics or time to spontaneously spring forth at the big bang or to vanish at the big crunch. Hawking’s no-boundary universe in no way contravenes Guth’s inflationary universe. In contrast to the latter, however, the former was at the time of publication, and remains so today, purely the product of Hawking’s and Hartle’s fertile imaginations and complex calculations with no apparent means of rigorously verifying it. As Hawking cautions in A Brief History of Time, “This idea that time and space should be 132

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Figure 5.4. Space-time in Hawking’s no-boundary universe. From Stephen Hawking, A Brief History of Time (1996), 143. Reprinted with permission of Bantam Books. Illustration by Ron Miller, copyright ©1988 by Ron Miller.

finite ‘without boundary’ is just a proposal,” an intriguing conjecture that still has avid followers in the physics community but no astronomical evidence.39

Analogies for the Multiverse There is reported to be a couple hundred billion galaxies in our universe and many orders of magnitude more stars and planets. Is there anything in our universe about which one could claim it to be the one and only, nothing else remotely similar? So one might wonder, by analogy, why should there be only one universe or just two or just three or . . . an infinite number? That is a question tackled by Brian Greene, the modern master of scientific narrative and analogy, in The Hidden Reality. One of Greene’s nine (!) versions of possible multiple universes is the “inflationary multiverse,” an extension of Guth’s inflationary conjecture for our universe. 133

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The main argument is that if a quantum fluctuation followed by inflation started a universe once, then it must have surely done so in the creation of other universes as well. Who knows how many times? Filling this conjectured multiverse is a fertile “inflaton field,” in which new universes emerge under the right conditions: Collectively, these insights show that inflationary cosmology leads to a vastly new picture of reality’s expanse, one that can be grasped most easily with a simple visual aid. Think of the universe as a gigantic block of Swiss cheese, with the cheesy parts being regions where the inflaton field’s value is high and the holes being regions where it’s low. That is, the holes are regions, like ours, that have transitioned out of the superfast expansion and, in the process, converted the inflaton field’s energy into a bath of particles, which over time may coalesce into galaxies, stars, and planets. In this language, we’ve found that the cosmic cheese acquires more and more holes because quantum processes knock the inflaton’s value downward at a random assortment of locations. At the same time, the cheesy parts stretch ever larger because they’re subject to inflationary expansion driven by the high inflaton field value they harbor. Taken together, the two processes yield an ever-expanding block of cosmic cheese riddled with an ever-growing number of holes. In the more standard language of cosmology, each hole is called a bubble universe (or a pocket universe). Each is an opening tucked within the superfast stretching cosmic expanse. Don’t let the descriptive but diminutive-sounding “bubble universe” fool you. Our universe is gigantic. That it may be a single region embedded within an even larger cosmic structure—a single bubble in an enormous block of cosmic cheese—speaks to the fantastic expanse, in the inflationary paradigm, of the cosmos as a whole. And this goes for the other bubbles too. Each would be as much a universe—a real, gigantic, dynamic expanse—as ours.40

Greene’s passage presents a multifaceted analogy: the inflationary multiverse is like a block of Swiss cheese, the holes in the cheese are like individual big bang universes that have evolved past the inflationary phase, and the cheesy parts are like a high-intensity inflaton field in “empty” space. In theory, there could even be an infinite number of universes within this cheese-like multiverse. That gives rise to a possibility that sounds more like science fantasy. Greene explains with his usual novelistic flair: In the far reaches of an infinite cosmos, there’s a galaxy that looks just like the Milky Way, with a solar system that’s the spitting image of ours, with

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COSMIC CONJECTURE a planet that’s a dead ringer for earth, with a house that’s indistinguishable from yours, inhabited by someone who looks just like you, who is right now reading this very book and imagining you, in a distant galaxy, just reaching the end of this sentence. And there’s not just one such copy. In an infinite universe, there are infinitely many. In some, your doppelganger is now reading this sentence, along with you. In others, he or she has skipped ahead, or feels in need of a snack and has put the book down. In others still, he or she has, well, a less than felicitous disposition and is someone you’d rather not meet in a dark alley.41

That description is true for any multiverse with an infinite number of universes, not just the inflationary one, of course. The conjecture of an infinite number of anything has all sorts of strange consequences, as rendered in a famous short story written by the Argentine writer Jorge Luis Borges, “The Library of Babel.” In this literary equivalent to a thought experiment, Borges transforms a mathematical construct, infinity, into a fictional world—the ultimate library—a world analogous to the infinite multiverse. The story begins more like a math problem than a story: “The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries.”42 Each hexagonal room has bookcases covering four walls. Each book in those cases is filled with a random assortment of twenty-two letters, plus comma, period, and space. Also random is the arrangement of the books on the shelves. No two books are identical. While most books are nonsense or nonsense with short snatches of sense, it is extrapolated that the library must have someplace on its infinite shelves every book ever written, every book that could be written, and every possible permutation on any given book, including its translation into all languages. The Library of Babel books must also include predictions of everything that will happen in the future, biographies of every being that has existed or will exist, and so on. While this library is a true marvel, it drives scholars mad because they cannot decipher the texts in most of the books they open or get a handle on what book is where. The infinite multiverse, the boldest astrophysics conjecture of all, bears some resemblance. But then, as physicist and historian of science David Kaiser observes, one of the many lessons from the history of science is that “neither ‘bizarre’ nor ‘absurd’ imply incorrect.”43

In the past hundred years, cosmic conjectures and the picture of the universe have undergone constant major revisions. In his model for a static universe, Albert Einstein assumed the universe was eternal and analogized it as an enormous 135

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static sphere with no beginning or end spatially. After that analogy faltered in the face of astronomical data, one team of theorists proposed the universe as akin to an expanding balloon in which the galaxies constantly speed apart after a “big bang” that is like an ordinary explosion on Earth, but an explosion of space itself. An opposing theory sought to negate the expanding balloon analogy and big bang metaphor with an alternative theory of an expanding universe in a steady state. An expanding universe without beginning or end does seem bizarre and absurd at first glance. According to this theory, however, the stars rush apart as though the universe were expanding while hydrogen atoms or some precursor spontaneously appears in great enough abundance throughout the universe to eventually gather together and make new stars. While expanding, this universe thus never really changes on a cosmic scale as newly created stars constantly replace the ones escaping the confines of the observable universe. That theory went by the wayside after the astronomical detection of the cosmic microwave background supporting big bang expansion. To the expanding balloon analogy, Alan Guth contributed a fleeting period of ultrafast expansion at the start to explain how the universe could be so uniform looking and flat on a cosmic scale after a big bang. Guth changed the cosmic picture—to a big bang universe that expands spatially in the shape of a church bell on its side. Moving from left to right in the bell we see the appearance of subatomic particles, nuclei, atoms, stars, black holes, galaxies, and clusters of galaxies. The picture also shows hyperinflation at the origin due to a false vacuum, then a bump in the rate of expansion nine billion years later due to dark energy. But there are also other pictures based on different conjectures, including cyclic, no-boundary, and multiple universes. It would appear that an existential question hoovers over the present astrophysics community: What form of firm observational or experimental evidence would validate the boldest cosmic conjectures and resulting narratives and pictures with a degree of certainty relatively few cosmological experts would question? Could we reach a point where such consensus is not possible because of built-in limitations to astronomical observation and experiment? In the absence of such, will consensus have to give way to comparing theoretical predictions with supercomputer simulations abetted by artificial intelligence?

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6 QUANTUM MAGIC

In a 1962 essay titled “What Is a Thing?” philosopher Martin Heidegger spelled out two principal ways of thinking about a “thing.” One is an ordinary thing, like a table or chair. The other is a thing as seen through the eyes of science: “The English physicist and astronomer [Arthur] Eddington once said of his table that every thing of this kind—the table, the chair, etc.—has a double. Table number one is the table known since his childhood; table number two is the ‘scientific table.’ This scientific table, that is, the table which science defines in its thingness, consists, according to the atomic physics of today, not of wood but mostly of empty space; in this emptiness electrical charges are distributed here and there, which are rushing back and forth at great velocity.”1 Speaking of things in a lecture on physics for college students, Richard Feynman says that “all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.”2 Feynman then goes on to work his magic with words to transform an ordinary thing, water, into a scientific thing. His is a thought experiment with analogies worthy of Albert Einstein or Werner Heisenberg: To illustrate the power of the atomic idea, suppose that we have a drop of water a quarter of an inch on the side. If we look at it very closely we see

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Figure 6.1. Feynman’s picture of water magnified a billion times. From Richard P. Feynman, Robert B. Leighton, and Matthew Sands, The Feynman Lectures on Physics, vol. 1 (1965), 2. Copyright © 2011. Reprinted with permission of Basic Books. nothing but water—smooth, continuous water. Even if we magnify it with the best optical microscope available—roughly two thousand times—then the water drop will be roughly forty feet across, about as big as a large room, and if we looked rather closely, we would still see relatively smooth water—but here and there small football-shaped things swimming back and forth. Very interesting. These are paramecia. You may stop at this point and get so curious about the paramecia with their wiggling cilia and twisting bodies that you go no further, except perhaps to magnify the paramecia still more and see inside. This, of course, is a subject for biology, but for the present we pass on and look still more closely at the water material itself, magnifying it two thousand times again. Now the drop of water extends about fifteen miles across, and if we look very closely at it we see a kind of teeming, something which no longer has a smooth appearance—it looks something like a crowd at a football game as seen from a very great distance. In order to see what this teeming is about, we will magnify it another two hundred and fifty times and we will see something similar to what is shown in [figure 6.1]. This is a picture of water magnified a billion

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QUANTUM MAGIC times, but idealized in several ways. In the first place, the particles are drawn in a simple manner with sharp edges, which is inaccurate. Secondly, for simplicity, they are sketched almost schematically in a two-dimensional arrangement, but of course they are moving around in three dimensions. Notice that there are two kinds of “blobs” or circles to represent the atoms of oxygen (black) and hydrogen (white), and that each oxygen has two hydrogens tied to it. (Each little group of an oxygen with its two hydrogens is called a molecule.) The picture is idealized further in that the real particles in nature are continually jiggling and bouncing, turning and twisting around one another. You will have to imagine this as a dynamic rather than a static picture. Another thing that cannot be illustrated in a drawing is the fact that the particles are “stuck together”—that they attract each other, this one pulled by that one, etc. The whole group is “glued together,” so to speak. On the other hand, the particles do not squeeze through each other. If you try to squeeze two of them too close together, they repel.3

Feynman’s paragraph defines water down to the atomic scale; he does not reach deeper to the quantum level, where very different rules apply. Ordinary things in motion possess very definite properties, like spin, speed, and position. But quantum things do not until someone measures them. In ordinary things, two negatively charged particles (electrons) repel each other. In quantum things, they can attract. An ordinary thing cannot seem to be in two states at the same time. Quantum things can. An ordinary thing is frozen and not a liquid at absolute zero degrees, a point of unsurpassable cold in which all heat is gone and normal activity ceases—even colder than the farthest reaches of outer space. But quantum things can be. One ordinary thing cannot influence another a great distance away and do so at a speed greater than light. But quantum things can, or at least appear to do so. And while the atoms in ordinary things have nuclei, quantum things can dispense with them. Sometimes these quantum effects are of interest only to physicists; other times they raise a practical question as well: Now that we discovered it, how can it find a niche in the marketplace? Earlier chapters dealt with how the communication of bleeding edge theories has transformed our understanding of time, space, mass, velocity, acceleration, particles, waves, gravity, light, and the universe. This chapter concerns materials made possible from insights gained with quantum mechanics. These quantum materials have transformed our picture of what a thing is, could be, and can do. In contrast to Heidegger’s wood table, they start out life as a new thing first discovered and defined by scientists. It is only by definition that a newly discovered thing can become something with a name, and something with a 139

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name can become a scientific thing, which one day might make the leap to an ordinary thing.

Redefining Metal What is a metal? In physics, its distinguishing property is that it can conduct electricity well, and some individual metals and combinations of metals (alloys) are better at it than others, as known since the early eighteenth century. In 1911 the Dutch experimentalist Heike Kamerlingh Onnes found that, at a temperature of near absolute zero—the complete absence of heat and colder than outer space—some metals pose no resistance to the movement of electrons through them. These superconductors are perfect conductors of electricity but only at that ultralow temperature. In one of the few popular science books devoted to superconductivity, physicist Stephen Blundell defines for us what a perfect conductor is by means of a simple thought experiment: To appreciate how bizarre superconductivity is, imagine making a coil of superconducting wire and somehow passing an electrical current around it. Never mind for a moment how you would do this, we will get to that later. What you find is that the electrical current would keep going round and round the coil forever. Once started, the current keeps going. Batteries are not included for this experiment because you wouldn’t need them. You can retreat to a safe distance and watch the extraordinary sight of a current going round and round, all by itself, with no power sources driving it.4

The catch here, of course, is that you have to expend considerable energy to maintain the wire at near to absolute zero. Over the several decades following Onnes’s discovery, physicists sought in vain to devise a theory for the mechanism explaining why metals and alloys acquire the above magical power at near absolute zero. As explained by Blundell, the quantum mechanical solution at the electron level arrived in 1957 in the form of a scientific paper by John Bardeen, Leon Cooper, and Robert Schrieffer (subsequently referred to within the scientific community as BCS). The key was understanding the movement of the superconductor’s electrons, which violate the dictum that like charges repel each other: The initial breakthrough was Cooper’s. The full problem of many interacting electrons seemed to be too complicated so, instead, he focused down on just two electrons, interacting with each other, with all the other electrons “frozen” in place in a so-called “Fermi sea.” In 1956, using the methods

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QUANTUM MAGIC of field theory [explaining natural phenomena in terms of interactions between matter and fields], Cooper was able to show that an arbitrarily small attraction between electrons can make it cost less energy for the two electrons to pair up together, rather than float as singletons in the Fermi sea. He therefore showed that the electron pair, now called a Cooper pair, is a stable entity. Cooper had shown that as long as there is some way for a weak attractive interaction to occur, even if it is extremely tiny, . . . pairing of electrons will inevitably occur. This still left unsolved the problem of what the attractive interaction might be. What causes two electrons to pair up when conventional wisdom has it that “like charges repel” and there should therefore be a Coulomb repulsion between them? Bardeen, Cooper, and Schrieffer realized that the solution might be associated with what is called the electron–phonon interaction, that is the interaction between electrons and the vibrations in the crystal lattice [symmetrical arrangement of atoms]. Lattice vibrations are known as “phonons” because it turns out to be helpful to think of a lattice vibration as a kind of particle and physicists tend to give particles names ending in “-on.” As mentioned earlier [not excerpted here], the electron–phonon interaction had already been studied by [Herbert] Fröhlich, and also by Bardeen and [David] Pines. Might phonons, these vibrations of the crystal lattice, play a role in electron pairing and overcoming the Coulomb repulsion? Electrons are not only repelled by each other but are attracted to the positively charged ions in the metal, and therefore an electron will distort the ions around it by pulling them slightly towards it. The heavier ions take longer to respond than the fast, nimble electron whizzes around and so the distortion persists for a little while after the electron has left. This persisting distortion is essentially a little region of positive change and it can result in a second electron being attracted to the first electron and its surrounding distortion of positively charged ions, as shown in [figure 6.2].5

Like much popular science writing, Blundell relies on defining technical terms that if not explained would leave the general reader completely adrift: Fermi sea, Cooper pair, phonon, Coulomb repulsion, and phonon-electron interaction. He also throws in a three-tier figure to visualize for us the movement of an electron pair through the crystal structure in a superconducting metal (figure 6.2). In the top image, we see a perfectly symmetrical crystal structure of positively charged ions (spheres with plus sign) in a superconductor. The two images below are snapshots of two electrons (spheres with negative signs) joined to form a Cooper pair. In the middle image, the first electron has just passed between 141

THE MANY VOICES OF MODERN PHYSICS Figure 6.2. Copper pair (dark circles with arrows on top) of electrons moving through metallic crystal structure. From Stephen Blundell, Superconductivity (2009), 57. Reprinted with permission of Oxford Publishing through PLSclear.

positively charged ions and distorted the symmetrical arrangement of four of the ions due to a phonon-electron interaction as defined by Blundell. In the bottom image, the second electron of the pair has been attracted to the same quartet of positively charged ions and speeds toward them. If there had been another image, we would have seen the positively charged ions recoiling back to their original positions, thereby opening up space for the second electron of the pair to zip through unimpeded. Not conveyed in figure 6.2 is that at near absolute zero, a seemingly miraculous phase transition occurs in superconducting materials, and an enormous number of Cooper pairs join together and move “as if each was part of a larger, inseparable whole,” which is mathematically captured by what is now called the BCS wave function—a brand new quantum property to join company with wave-particle duality, Heisenberg uncertainty, superposition, and entanglement. This property only manifests itself for metals at ultracold temperatures.6 At a few degrees above absolute zero, the superconductivity vanishes, and electrical resistance occurs because the electrons do not easily move through the metal atomic structure any longer: they repel each other, bump into the positively charged ions, lose energy, and give off heat. Superconducting things are not just scientific curiosities but essential components in the powerful magnets used for particle accelerators and nuclear resonance imaging machines in hospitals. Superconductivity changed the picture of what a metal is and can do. The scientific thing called “metal” was never the same after 1911.

Redefining Gas What is a gas? In our everyday lives, it is the air we breathe, the helium that keeps balloons inflated, the vapor from boiled water. In classical physics, it is a collection of atoms without the confined volume of a liquid or the fixed shape 142

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of a solid. In a container, gaseous atoms normally have a wide range of energies and speeds, their values on average decreasing with lower temperature. In 1924 Satyendra Nath Bose and Albert Einstein predicted that upon cooling of a gas inside a container to slightly above absolute zero, one will find that all the atoms in the gas move ever more slowly until they condense into a single quantum state, a Bose-Einstein condensate. Malcolm Browne defined this term for the general reader in a 1995 New York Times article: A Bose-Einstein condensate is a gas of atoms that have been so chilled [near absolute zero] that their normal motion is virtually halted. In this almost stationary condition, the wavelengths of individual atoms—the dimensions that define the regions in which they may be found—grow to relatively enormous size, overlapping each other and merging into a kind of super atom. This merged atom, despite growing to a range of sizes typical of those of bacteria, obeys the rules of quantum mechanics, the physics of the ultra-small.7

Good science writer that he is, Browne conveys what makes this “super atom” super by a simple but vivid analogy: it is a single atom as big as bacteria. It took some seventy years after Bose and Einstein’s prediction before experimentalists Eric Cornell, Carl Wieman, and Wolfgang Ketterle assembled such a superatom: two-thousand rubidium atoms acting as one. Three years after their success, they won a Nobel Prize in Physics. Even though contemporary Nobel Prize lectures are typically aimed at those with a firm understanding of the science, Cornell and Wieman broke away from the unfortunate norm and told general readers what a Bose-Einstein condensate is as well as what they do and why it is important: In June 1995 our research group at the Joint Institute for Laboratory Astrophysics (now called JILA) in Boulder, Colo., succeeded in creating a minuscule but marvelous droplet. By cooling 2,000 rubidium atoms to a temperature less than 100 billionths of a degree above absolute zero (100 billionths of a degree kelvin), we caused the atoms to lose for a full 10 seconds their individual identities and behave as though they were a single “super-atom.” The atoms’ physical properties, such as their motions, became identical to one another. This Bose-Einstein condensate (BEC), the first observed in a gas, can be thought of as the matter counterpart of the laser—except that in the condensate it is atoms, rather than photons, that dance in perfect unison.

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THE MANY VOICES OF MODERN PHYSICS Our short-lived, gelid sample was the experimental realization of a theoretical construct that has intrigued scientists ever since it was predicted some 73 years ago by the work of physicists Albert Einstein and Satyendra Nath Bose. At ordinary temperatures, the atoms of a gas are scattered throughout the container holding them. Some have high energies (high speeds); others have low ones. Expanding on Bose’s work, Einstein showed that if a sample of atoms were cooled sufficiently, a large fraction of them would settle into the single lowest possible energy state in the container. In mathematical terms, their individual wave equations—which describe such physical characteristics of an atom as its position and velocity—would in effect merge, and each atom would become indistinguishable from any other. Progress in creating Bose-Einstein condensates has sparked great interest in the physics community and has even generated coverage in the mainstream press. At first, some of the attention derived from the drama inherent in the decades-long quest to prove Einstein’s theory. But most of the fascination now stems from the fact that the condensate offers a macroscopic window into the strange world of quantum mechanics, the theory of matter based on the observation that elementary particles, such as electrons, have wave properties. Quantum mechanics, which encompasses the famous Heisenberg uncertainty principle, uses these wavelike properties to describe the structure and interactions of matter. We can rarely observe the effects of quantum mechanics in the behavior of a macroscopic amount of material. In ordinary, so-called bulk matter, the incoherent contributions of the uncountably large number of constituent particles obscure the wave nature of quantum mechanics, and we can only infer its effects. But in Bose condensation, the wave nature of each atom is precisely in phase with that of every other. Quantum-mechanical waves extend across the sample of condensate and can be observed with the naked eye. The submicroscopic thus becomes macroscopic.8

Cornell and Wieman’s minuscule but marvelous droplet is like a condensate—not in the usual sense of a gas condensing into a liquid such as steam into water, but in another sense, that of many atoms in a gas condensing into a thing that behaves quantum mechanically like a single atom.9 They support their definition of this new quantum thing with another scientific analogy: what the laser is to photons, the Bose-Einstein condensate is to atoms. In the former, photons behave as one; in the latter, atoms of rubidium do. Why is this new form of condensation important to physics? As Cornell and Wieman note, one reason is historical—two legendary physicists, Einstein 144

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and Bose, had predicted its existence. A more important reason is that it offers a “macroscopic window into the strange world of quantum mechanics.”10 Might this phenomenon be important to our lives? When the New York Times science writer asked the standard utility question, Wieman answered with the standard evasive response: “Asking that question at this point is like asking Columbus when he stepped ashore in the new world what the prospects were for finding iron ore. We’re just at the very beginning. Who would have guessed when the laser was invented in the 1950s that it would play the enormous role it now does?”11

Redefining Liquid What is a liquid? For one thing, it has a property scientists call viscosity. As we stroke and kick our way through a swimming pool, we experience this property directly as resistance to our forward movement. If we pour water or molasses out of a bottle, we find a difference in the rate of escape. Physicists tell us that a quantum liquid can completely lack such viscosity. In 1908 the discoverer of superconductivity in metals, Heike Kamerlingh Onnes, made a second unexpected discovery: helium gas turns into a liquid at four degrees above absolute zero and remains in that state no matter how low the temperature. In 1938 other scientists found that an isotope of helium in liquid form, helium-4, loses its resistance to flow at about two degrees above absolute zero, a quantum mechanical effect analogous to the superconductivity of solids. It was a Nobel Prize breakthrough. In a 2018 issue of Nature, the scientific journal that had first revealed this discovery to the world, physicist William Halperin celebrates its eightieth anniversary, the year 1938 marking the start of a chain reaction that leads first to the discovery of superfluidity, then to a theory that explains both superfluidity and superconductivity by a similar mechanism: In the early twentieth century, scientists discovered the non-intuitive phenomena of superconductivity and superfluidity, in which electrons and atoms, respectively, flow without resistance over great distances. Superfluidity was beautifully demonstrated 80 years ago in two papers published in Nature by [John] Allen and [Donald] Misener [Nature 141 (1938): 75, and [Pyotr] Kapitza [Nature 141 (1938): 74]. The authors observed the flow of liquid helium-4 through extremely narrow channels and showed that the substance becomes a superfluid at very low temperatures. The studies presaged the firm understanding of the relationship between superfluidity and superconductivity that now exists, and which provides the foundation for investigating unconventional superconductors and superfluid phases. Allen and Misener observed the flow of liquid helium-4 through long,

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Figure 6.3. Experimental evidence for superfluidity. P. Kapitza, “Viscosity of Liquid Helium below the λ-Point,” (1938), 77. Reprinted with permission of Springer Nature.

thin tubes, and found that the fluid’s viscosity became immeasurably low at temperatures below 2.17 kelvin [zero degrees kelvin is the same as absolute zero]. Kapitza obtained similar results by measuring the flow through a small gap between two glass disks [figure 6.3]. With foresight, Kapitza noted a possible connection to superconductivity, for which a complete theory was eventually realized in 1957 by Bardeen, Cooper and Schrieffer [Physical Review 108 (1957): 1175–1204]. Shortly after the two Nature papers were published, an explanation for the superfluidity of liquid helium-4 was offered: Bose–Einstein condensation, the process whereby many particles known as bosons “condense” into a single quantum state. . . . At sufficiently low temperatures, helium-4 atoms undergo Bose–Einstein condensation and become a superfluid. Similarly, in the BCS theory of superconductivity, electrons that have a suitably attractive interaction can combine into charged composite bosons called Cooper pairs, which condense to form a superconductor.12

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The mechanism behind a superfluid is thus discovered to be analogous to that for a Bose-Einstein condensation and superconductor. To show rather than just tell us what it means for a fluid to lack viscosity, Halperin draws on Pyotr Kapitza’s famous 1938 experiment involving a glass tube of liquid helium-4 in a bath of ordinary liquid helium at four degrees above absolute zero (figure 6.3). At the bottom of the tube are two glass disks separated by a narrow gap. As the temperature falls below four degrees above absolute zero, the height of the helium-4 remains steady. Once superfluidity kicks in at 2.17 degrees above, however, the height rapidly drops as the helium-4 joins the helium bath by escaping through the narrow gap. At this temperature, the helium-4 becomes a collection of atoms governed by the quantum mechanical wave function. It has zero viscosity, a quantum effect visible to the naked eye. Subsequent experiments turned up other helium-4 magic. It will drip through molecular-sized holes in the bottom of a beaker and drain out; it will flow spontaneously from colder to hotter regions while all normal fluids flow in the opposite direction; it will creep up and over the sides of an open stationary container until empty, remain motionless if a container of it is spun, and swirl around ad infinitum after a stationary container of it has been stirred.13 Along with Bose-Einstein condensation and superconductivity, superfluidity is important as one of a trio of related quantum effects that have altered our view of liquid, gas, and metal. Since no one has yet found a significant everyday application for superfluids, however, they remain largely scientific things, far from the world of individual experience. One specialized market niche for the superfluid helium-4 is as the cooling fluid for the superconducting magnets in the Large Hadron Collider, where it creates a twenty-seven-kilometer stretch in a circular beamline colder than outer space and housed in an underground subway-like tunnel.

Redefining No Small Thing The Nobel Prize–winning theoretical physicist Richard Feynman had a knack for making prescient statements. In 1960 he wrote: “Atoms on a small scale behave like nothing on a large scale, for they satisfy the laws of quantum mechanics. So, as we go down and fiddle around with the atoms down there, we are working with different laws, and we can expect to do different things.”14 In the decades since, thanks in no small measure to extraordinary advances in analytical methods at the nanoscale (there are a billion nanometers in a meter), scientists have created many new things by fiddling around with the atoms. Especially interesting are super small objects composed of carbon atoms. These do not require the ultracold temperatures of the Bose-Einstein condensate, superconductor, or 147

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superfluid—an important factor for any widespread practical application. One of these super small things netted the 1996 Nobel Prize in Chemistry for Robert Curl, Harold Kroto, and Richard Smalley. Their prize was for the discovery of a new family of pure carbon structures, fullerenes, named after the iconoclastic architect Buckminster Fuller. They christened one of these structures buckminsterfullerene (nicknamed “buckyball”), the most striking fullerene esthetically with a highly unusual soccer-ball architecture constructed out of sixty carbon atoms. This enormous single molecular structure of the same element forms naturally in outer space and soot, can be relatively easily fabricated in the lab, and also comes in structures larger than sixty atoms. More important, it has inspired the discovery of different nanoscale carbon geometries, in particular, tubular (nanotubes) and two-dimensional plane (graphene). It has changed scientists’ idea of what a pure carbon structure can be aside from diamond and graphite. To communicate the idiosyncratic behavior of carbon, Professor Smalley represents it metaphorically as if it were a living thing. It is a “genius” with a “birthright.” Though it has “a talent,” we are still its masters, for it can be “tricked.” And it radiates “great beauty,” even compared with diamond. This is not rhetoric, a device in aid of popularization. If it were, Smalley would not be using as much jargon as he does, terms barely comprehensible by any outsider. This in what carbon really means to him, an insight into Smalley, and into science, no scientific paper would ever reveal: Instead, the discovery that garnered the Nobel Prize was the realization that carbon makes the truncated icosahedral [twenty-sided] molecule, and larger geodesic cages [those with curved surfaces], all by itself. Carbon has wired within it, as part of its birthright ever since the beginning of this universe, the genius for spontaneously assembling into fullerenes. We now realize that all you need to do to generate billions of billions of these objects of such wonderful symmetry is just to make a vapor of carbon atoms and to let them condense in helium. Now we are still in the process of discovering all of the other consequences of the genius that is wired into carbon atoms. It isn’t just a talent to make balls. It can also make tubes such as the short section shown in [figure 6.4]. Nearly all of us have long been familiar with the earlier known forms of pure carbon: diamond and graphite. Diamond, for all its great beauty, is not nearly as interesting as the hexagonal plane of graphite. It is not nearly as interesting because we live in a three-dimensional (3D) space, and in diamond each atom is surrounded in all three directions in space by a full

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Figure 6.4. Four perfect crystalline forms of carbon: diamond, buckyball (C60), graphite, and a short length of a fullerene (10,10) nanotube. This figure is a part of Richard Smalley’s Nobel Prize lecture. Copyright © The Nobel Foundation 2018. coordination. Consequently, it is very difficult for an atom inside the diamond lattice to be confronted with anything else in this 3D world because all directions are already taken up. In contrast, the carbon atoms in a single hexagonal sheet of graphite (a “graphene” sheet) are completely naked above and below. In a 3D world this is not easy. I do not think we ever really thought enough about how special this is. Here you have one atom in the periodic table, which can be so satisfied with just three nearest neighbors in two dimensions, that it is largely immune to further bonding. Even if you offer it another atom to bond with from above the sheet—even a single bare carbon atom, for that matter—the only result is a mild chemisorption [forming a chemical bond at a surface] that with a little heat is easily undone, leaving the graphene sheet intact. Carbon has this genius of making a chemically stable two-dimensional, one-atom-thick membrane [a very strong sheet even though so thin] in a three-dimensional world. And that, I believe, is going to be very important in the future of chemistry and technology in general. What we have discovered is that if you just form a vapor of carbon atoms and let them condense slowly while keeping the temperature high

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THE MANY VOICES OF MODERN PHYSICS enough so that as the intermediate species grow they can do what it is in their nature to do, there is a path where the bulk of all the reactive kinetics [agents of change] follow that goes to make spheroidal fullerenes. Now it turns out that in addition to this most symmetric of all possible molecules, C60, and the other fullerene balls, it is possible by adding a few percent of other atoms (nickel and cobalt) to trick the carbon into making tubes. Of all possible tubes there is one tube that is special. It is the tube shown in [figure 6.4], the (10,10) tube. We are beginning to understand that what causes this tube to be the most favorite of all tubes is also wired within the instruction set of what it means to be a carbon atom. The propensity for bonding that causes C60 to be the end point of 30–40% of all the reactive kinetics, leads as well to this (10,10) tube.15

Figure 6.4 is not just a depiction; it is also an argument demonstrating the “genius” of carbon at the nanometer scale. Smalley starts with an everyday thing: diamond. His image does not show the multifaceted gem of everyday experience, but the symmetrical molecular structure of science, a tetrahedral arrangement of carbon atoms extending in all three directions. Adjacent to the diamond of science is the structure of a single buckyball molecule in the shape of a soccer ball. To the far right is the nanotube, a structure of hexagons with semispherical buckyball caps at both ends. The final structural form of pure carbon, graphite, comes in stacked sheets of hexagons. A single sheet of graphite, “graphene,” has width and length, and is only a single atom thick yet stronger than steel, more pliable than rubber, and a stellar conductor of heat and electricity. This essentially two-dimensional material landed Andre Geim and his colleagues the 2010 Nobel Prize in Physics. Smalley mentions that nanotubes and graphene are “going to be very important in the future of chemistry and technology in general.” Later in his Nobel Prize lecture, he elaborates on that claim: “I believe that in the future of chemistry we are likely to see a vast new set of metallic fullerene molecules . . . available from chemical supply houses. Imagine what the impact could be. Essentially, every technology you have ever heard of where electrons move from here to there [batteries, transistors, etc.] has the potential to be revolutionized by the availability of molecular wires made up of carbon. Organic chemists will start building devices. Molecular electronics could become reality.”16 Scientists around the world are now racing to realize the many possible applications of nanotubes and graphene.17 While buckyballs are still without much significant practical use, they are playing a role in advancing quantum physics. Experiments have demonstrated that these sixty-atom molecules exhibit both 150

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wave and particle behavior, just like electrons and neutrons, making them the most massive object about which scientists have detected this quantum behavior. While not a macroscopic object, these scientific things have inched forward our knowledge of the question, “Can the fundamental concepts of quantum physics apply to everyday ‘classical’ objects as well as those in the atomic and subatomic regime?”18

Redefining Atom What is an atom? As every high school student should know, the atom consists of a nucleus orbited by electrons. The positively charged protons in the nucleus help keep the negatively charged electrons in orbit, since opposites attract. With current quantum materials and techniques, scientists are able to corral a small collection of electrons into an atom-like thing without a nucleus. Initially, they named this new thing “artificial atom” or “quantum dot.”19 The catchy term quantum dot eventually won the day. In a 1996 Nature review article, Raymond Ashoori defines what this new thing is and explains its connection to quantum mechanics: The puzzle of atomic spectra was a prime motivation for the development of quantum mechanics. Niels Bohr unraveled the mystery by determining that the wavelike nature of electrons allowed them to occupy only discrete orbits within an atom, with well-defined energies. Starting about 10 years ago [in the mid-1980s], advances in semiconductor technology [used in digital devices and discussed in the next chapter] allowed the fabrication of structures so small that their discrete quantum level structure was resolvable. In the past few years, powerful new spectroscopic probes have revealed a wealth of new physics in these “artificial atoms.” Essentially, artificial atoms are small boxes about 100 nm [nanometers] on a side, contained in a semiconductor, and holding a number of electrons that may be varied at will. As in real atoms, electrons are attracted to a central location. In a natural atom, this central location is a positively charged nucleus; in an artificial atom, electrons are typically trapped in a bowl-like parabolic potential well in which electrons tend to fall in towards the bottom of the bowl. One can consider the artificial atom as a tiny laboratory in which quantum mechanics and the effects of electron-electron interactions can be studied.20

To achieve his communicative aims, Ashoori reaches beyond the denotive to the metaphorical. Artificial atoms are not atoms, though they share some 151

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behavioral traits. They do not contain bowls, though they behave as if they do. They are not scientific laboratories, though they can be used to perform experiments that are not possible with real atoms. In The Quantum Dot, Richard Turton gives us an example of the possible real-world uses of this particular quantum weirdness, the link between the size of a nanoscale material and its color. His is a sound argument that deliberately leads to a true, but apparently ludicrous, conclusion, pulling a quantum rabbit out of a cadmium selenide hat: The quantum world is a strange and deceiving place. Many of the predictions of quantum theory appear to be contrary to our intuitive perceptions. This is because the world that we experience is generally immune to the miniscule fluctuations which occur on the quantum scale. It is only when we consider extreme physical conditions that these rules become important. A typical case occurs when we drastically reduce the dimensions of an object [to the nanoscale]. A vivid example of such an effect has been demonstrated within the past decade. It is now possible to create tiny crystals of the material cadmium selenide which contain less than a thousand atoms. Each one measures a few millionths of a millimeter across. (In comparison, the diameter of a dust particle is typically measured in thousandths of a millimeter.) The peculiar feature of these crystals is that, although they all have precisely the same composition, they exhibit quite different properties. In particular, the larger crystals are found to be red in color, smaller ones orange, and the very tiniest (containing barely a hundred atoms) are yellow. We arrive at the seemingly ludicrous conclusion that the color of an object depends upon its size. Strange as it may seem, this is indeed the case in the quantum world.21

In the scientific journal Nature, borrowing the typical language of product marketing, Alexander Efros calls quantum dots “one of the biggest nanotechnology success stories so far.”22 It does now seem likely that this material could one day become a hidden part of everyday technology, in things like television sets and other visual displays, light-emitting diodes (LEDs), medical imaging devices, and solar cells. Time will tell whether that assessment is right or hype.

Redefining Computer What is a computer? The word started off meaning any person that computes, then morphed to any automated machine that computes. Current computing machines all run with bits of information, zeros and ones corresponding to the 152

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electrical states off or on, the smallest increment of data on a digital computer. Bits are the neurons of computer technology. In the 1980s, scientists and engineers began to wonder if computers could be built with quantum materials, such as the superconductors, Bose-Einstein condensates, or quantum dots discussed earlier, which do not behave anything at all like ordinary materials. This oddity makes them candidates for use in a new kind of computing, quantum computing. Many credit physicist David Deutsch as the seer of quantum computation. In The Beginning of Infinity, he first defines qubit, then describes its astonishing computational power: In a typical quantum computation, individual bits of information are represented in physical objects known as “qubits”—quantum bits . . . with two essential features. First, each qubit has a variable that can take one of two discrete values [as a consequence of the quantum property called superposition], and, second, special measures are taken to protect the qubits from entanglement [that is, to isolate them from interacting with the complex systems in their environment]—such as cooling them to temperatures close to absolute zero. A typical algorithm using quantum parallelism begins by causing the information-carrying variables in some of the qubits to acquire both their values simultaneously. Consequently, regarding those qubits as a register representing (say) a number, the number of separate instances of the register as a whole is exponentially large: two to the power of the number of qubits. . . . In such computations, a quantum computer with only a few hundred qubits could perform far more computations in parallel than there are atoms in the visible universe. At the time of writing, quantum computers with about ten qubits have been constructed. “Scaling” the technology to larger numbers is a tremendous challenge for quantum technology, but it is gradually being met.23

In conveying quantum mechanical behavior for computation, in our view, Deutsch does not clearly define, for the general reader anyway, what a qubit actually is beyond “quantum bits.” In her profile of Deutsch in the New Yorker, Rivka Galchen deftly amplifies the connection between the qubit and the two pillars of quantum strangeness: superposition and entanglement. In the following passage, she shows a willingness to turn particles into people endlessly chatting away, anthropomorphism being a standard move of popularization. But her allusion to Schrödinger’s cat hints at another insight: she has a reasonably firm grasp of her elusive subject for a nonphysicist, projecting an authoritative voice to readers that she can be believed when she relates what seems 153

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incredible even to some seasoned scientists: A classical computer—any computer we know today—transforms an input into an output through nothing more than the manipulation of binary bits, units of information that can be either zero or one. A quantum computer is in many ways like a regular computer, but instead of bits it uses qubits. Each qubit (pronounced “Q-bit”) can be zero or one, like a bit, but a qubit can also be zero and one—the quantum-mechanical quirk known as superposition. It is the state that the cat in the classic example of Schrödinger’s closed box is stuck in: dead and alive at the same time. If one reads quantum-mechanical equations literally, superposition is ontological, not epistemological; it’s not that we don’t know which state the cat is in, but that the cat really is in both states at once. Superposition is like Freud’s description of true ambivalence: not feeling unsure but feeling opposing extremes of conviction at once. And, just as ambivalence holds more information than any single emotion, a qubit holds more information than a bit. What quantum mechanics calls entanglement also contributes to the singular powers of qubits. Entangled particles have a kind of E.S.P.: regardless of distance, they can instantly share information that an observer cannot even perceive is there. Input into a quantum computer can thus be dispersed among entangled qubits, which lets the processing of that information be spread out as well: tell one particle something, and it can instantly spread the word among all the other particles with which it’s entangled. . . . When one turns to a quantum computer for an “answer,” that answer, from having been held in that strange entangled way, among many particles, needs then to surface in just one, ordinary, unentangled place. That transition from entanglement to non-entanglement is sometimes termed “collapse.” Once the system has collapsed, the information it holds is no longer a dream or a secret or a strange cat at once alive and dead; the answer is then just an ordinary thing we can read off a screen.24

Contributing to Galchen’s distinctive voice in her article is her many deft literary moves. One example is her above analogy: ambivalence (as defined by Sigmund Freud) is to a single emotion as a qubit is to a bit. Another example is her comparison of entangled qubits to someone with extrasensory perception. In conveying the computational power of the quantum, Deutsch mentions that it increases by a power of two per qubit, the number two representing the simultaneous zero and one allowed by superposition. To put that power in context, he calculates that a mere few hundred entangled qubits “could perform far more computations in parallel than there are atoms in the visible universe.” 154

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How is that possible? Deutsch does not explain. But in an entirely different context (his theory for hyperinflation of the early universe), theoretical physicist Alan Guth has provided a simple thought experiment to visualize the power of two to the nth power.25 Before us is an imaginary chessboard with squares of ever-increasing size to accommodate increasingly large accumulations of sand. We place a grain on a square, then double the number on each adjacent square until the last one. Square ten contains a small pile of 512 grains. But square nineteen would have a rather large pile of 262,144 grains, with a peak about the length of a pencil. By square fifty-five, the pile would have expanded to more than eighteen quadrillion grains, with a peak height equivalent to the Empire State Building. Finally, the last pile would have more than nine quintillion grains, a mountain of grains covering the entire island of Manhattan. Continuing to the equivalent of several hundred squares beyond the chessboard, we arrive at an astoundingly number, one exceeding the atoms in the visible universe. Such doubling power seems within reach with qubits26 and should eventually lead to far superior quantum mechanical computations for scientific research and a far deeper understanding of the mysteries of quantum mechanics. In fact, Galchen reports that Deutsch is betting that a quantum computer could one day allow testing of the seemingly untestable many-worlds interpretation propounded by Hugh Everett (discussed in chapter 3). This “ontologically extravagant proposition,” Galchen’s charming phrase, offers a fairly simple explanation for all quantum phenomena at the expense of common sense: the need for many branching worlds besides our own. For example, Schrödinger’s cat is alive in one world, and dead in a separate branching world. All the quantum things described so far are observable by the naked eye or with current high-powered microscopes. The next one is not.

Defining a Wholly Theoretical Thing What is a magnet? For one thing, it is a material with a north and south pole, which generates a field that attracts metallic objects. Break a magnet in half and the two poles will always remain two. There is, however, a hypothetical quantum particle with a single magnetic pole, north or south. Having learned about the truly strange quantum behavior of other scientific things, we can be forgiven for thinking this property is under-whelming. We would be wrong, as Guth explains. Monopoles are not mythical beasts like unicorns. Instead, like the whereabouts of Amelia Earhart, they are a mystery that must have a solution. It is one that will be of intense theoretical interest. Guth defines this wholly theoretical thing in frameworks of personal experience and the 155

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history of science: Although I knew nothing about grand unified theories [in 1974], I have spent several years while I was at Columbia working on magnetic monopoles, hypothetical particles that produce a special kind of magnetic field. The magnetic field of ordinary magnets is caused by the motion of the electrons in the material, and all such magnets have both a north and a south pole of equal strength. . . . The lines of the magnetic field, which could be followed by placing compasses near the magnet, extend from north pole to the south. By holding one bar magnet in each hand, one could verify that two north poles repel, while a north and south pole attract. If a bar magnet is broken in two, one does not obtain separate north and south magnets; each piece has its own north and south pole. . . . A monopole, as its name suggests, is an isolated pole, either north or south. The magnetic field of the monopole points directly outward from the monopole, just like the electric field of a spherical charge or the gravitational field of a spherical mass. . . . Like the unicorn, the monopole has continued to fascinate the human mind despite the absence of confirmed observations. The monopole, however, has a much better chance of actually existing. As early as 1894 the French physicist Pierre Curie emphasized that the equations make only one distinction between electric and magnetic fields: electric charges exist [electrons and positrons], but magnetic charges (i.e., monopoles) apparently do not. If magnetic monopoles were to be discovered, a perfect symmetry would be established between electricity and magnetism. Driven by the beauty of the symmetry, the British physicist Paul Adrien Maurice Dirac tried to extend the theory of magnetic monopoles to the realm of quantum theory. In 1931 he showed not only that monopoles are consistent with quantum theory, but also that quantum theory gives a unique prediction for the strength of their magnetic charge. Interest in magnetic monopoles was rekindled in 1974, when Gerard ‘t Hooft in the Netherlands and Alexander Polyakov in the Soviet Union independently discovered that some types of modern particle theories imply the existence of magnetic monopoles, even though no one had previously suspected it.27

For Guth, since electrical fields have an associated particle (the negatively charged electron) and the electron has an antiparticle (the positively charged positron), it is logical to conclude that magnetic fields have a corresponding particle-antiparticle pair with opposite magnetic charges. The symmetry seems too good not to be true. Monopoles must exist. But where are they? No one has been able to detect them experimentally. It certainly has not been for want of 156

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trying.28 In his final sentence, Guth notes that modern particle theories predict the existence of magnetic monopoles. More important to Guth, as he explains in a later chapter, his inflationary theory for the universe predicts that monopoles were created during the big bang and are the particle hypothetically responsible for the inflation (see chapter 5). Fellow particle physicist Dan Hooper has elaborated on initial estimates of their probable numbers. His argument shows, apparently, that they cannot exist: “The first estimates of how many magnetic monopoles had been created in the Big Bang, and how many should remain today, were made in the 1970s. Although the answer to this question varies somewhat from theory to theory, all GUTs [grand unified theories linking the three nongravitational forces] predict that magnetic monopoles should be roughly as plentiful as protons in our Universe. Each monopole, however, would contain a million times more energy than a proton, implying a combined energy density much greater than is observed. Obviously, monopoles in such enormous quantities cannot exist.”29 But wait. Whatever GUT theories may predict, Hooper reports there is a clear explanation for the connection between the unicorn-like ontological status of monopoles and Guth’s theory. He employs analogy to make his point, in particular, the balloon analogy appropriated from popular science texts on cosmic expansion: Once a period of inflation is initiated, the size of the Universe begins to double nearly once every 10 –32 seconds [unimaginably fast]. It is easy to see that at this rate, it would take almost no time at all for a universe to grow from an extremely compact and densely filled state into an enormous volume of space. In most models the period of inflation lasts just 10 –30 seconds, after which the Universe’s expansion rate returns to a steady and much slower progression. Nevertheless, during that brief period, inflation theory predicts, the Universe grew larger by at least a factor of 1025, and possibly much more. As the universe inflated, the number of monopoles present in a given volume became diluted by the enormous increase in the volume of space. If you take a small balloon, put a collection of dots on the surface with a marker, and then inflate it to a much larger size, the number of dots per square inch of the balloon’s surface becomes much smaller. Similarly, even if an enormous number of monopoles existed in the early Universe, their density is reduced so dramatically during inflation that we would most likely not observe one in our Universe.30

There is no hiding from the fact here that a highly speculative theory supports 157

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the existence of a highly speculative particle. Yet the magnetic monopole is that most useful of scientific things to science: a predicted thing consistent with existing physics theory that, if ever observed, would provide strong support for a highly speculative theory. The jury is out. The search continues.

Philosopher Martin Heidegger titled one of his famous essays as a question, “What Is a Thing?”31 His answer defined two senses of the term: ordinary and scientific. The scientific things we just discussed are anything but ordinary. By various modes of communication about them, scientists and science writers have redefined our conceptions of what a solid, liquid, and gas is and can do. In metallic form near absolute zero, they lose all resistance to the movement of electrons. In a supercondensed form near absolute zero, they behave quantum mechanically like a single superatom, even when in a collection of millions of atoms. In gaseous form, they can transition into liquid form at near absolute zero and flow through solid barriers unimpeded and up the sides of a bowl. In solid form at room temperature, they can have essentially two dimensions— length and width—so they are only one atom thick. They also come in the shape of large artificial atoms with electrons not bound to a nucleus. In one of the aforementioned materials, they might some day become part of a quantum supercomputer that can “perform far more computations in parallel than there are atoms in the visible universe.”32 There are also wonder materials that exist so far only in theory. In magnetic form, for example, they have a north but no south pole and might constitute one of the starter ingredients of our universe. In “What Is a Thing?” Heidegger asks an interesting philosophical question about the humble table. Which is the “true” table—the ordinary one or the scientific one? His answer is that there must be a third type, “according to which number one and number two are true in their way and represent a variation of this truth.” Heidegger’s is not a truth physics will ever discover.

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And from my pillow, looking forth by light Of moon or favoring stars, I could behold The antechapel where the statue stood Of Newton, with his prism and silent face, The marble index of a mind forever Voyaging through strange seas of thought, alone. —William Wordsworth, The Prelude

Thus far we have dwelt mainly on the most conspicuous theorists, physicists such as Satyendra Nath Bose, Albert Einstein, Werner Heisenberg, George Gamow, Stephen Hawking, Erwin Schrödinger, Alan Guth, and David Deutsch, physicists who, like William’s Wordsworth’s Newton, possess “a mind forever voyaging through strange seas of thought, alone.” This description does not suit at least one distinguished theorist, John Bardeen, whose Nobel Prize was awarded for the discovery of the transistor effect, an effect made possible by a quantum material, the semiconductor. This achievement, as his Nobel lecture makes clear, was also dependent on cooperative colleagues, a legion of chemists, metallurgists, and technicians without whom Bardeen’s walk across the Oslo stage would not have been possible. In the presentation speech for the 1956 Nobel Prize in Physics, Norwegian Nobel Committee member Erik G. Rudberg described, with an extended and convoluted analogy, the physics behind that year’s award to Bardeen, along with 159

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Walter Brattain and William Shockley. His analogy compares the process of electrical rectification (conversion of alternating into direct current) to typical elements in a child’s adventure yarn: The description must now borrow a picture from the classical books of adventure. To place a negative electrode against a semiconductor with negative carriers [electrons]—this is like bringing a ship up to a quay in the Orient, with the yellow flag of the plague hoisted. The place becomes deserted by its carriers. Unloading—current—is blocked. But exchange that negative flag of pestilence for a positive sign [opposite sign to negative carriers] and the carriers will return, the contact becoming conducting. Electrically this is called rectification. In those seafaring tales it was perhaps possible to induce the carriers to return, without striking the flag, merely by throwing some gold coins on the quay, thus positively destroying the insulation. It is possible to destroy the blockade in the semiconductor in a similar fashion by throwing in some positive holes around which the negative carriers will gather. This is transistor action.1

This transistor action was made possible by a material whose main physical properties were known since the early nineteenth century: the semiconductor. The transistor itself is simply a blend of different types of semiconductors to which are attached electrical terminals through which current flows in and out. This miraculous device can do three crucial jobs without any moving mechanical parts. It can “rectify” to direct current the alternating current distributed to buildings from power plants. But even more important, it can both amplify current and switch current on and off. In his presentation speech for the Nobel Prize, Rudberg lists a few applications for the transistor at the time: better amplification in hearing aids, computing machines without vacuum tubes, and switches for telephone stations. With the advantage of the passage of time, we can add to that impressive list transistor radios, more compact televisions and computer screens with better picture resolution, and the microprocessors in personal computers, laptops, smartphones, and global positioning systems. In terms of impact on the life of just about everyone on the planet, no scientific thing comes close. Given this, it seems unfortunate that the list of popular science books on the topic by distinguished physicists or any other scientists is so paltry. Luckily, there is an excellent book by two historians and many articles by physicists and other writers in many genres. There are also a slew of online videos about semiconductors and transistors, which include instructive animated visuals on how they work.2 160

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We begin with how semiconductors function. What are the properties that have made them so important to the history of technology and ubiquitous in our society? From there we proceed to Bardeen and Brattain’s discovery of the transistor effect and its embodiment in ingenious designs of transistor created by them, Shockley, and other scientists. We close with Shockley’s Nobel Prize lecture, emphasizing the transistor’s commercial possibilities and heralding the transformation of this scientific thing into a key component within a host of ordinary things.

Semiconductors 101 The most important ingredient in the transistor is the semiconductor—a close cousin to the conductor and insulator. In brief, conductors (such as metal) pass electric current with relatively little resistance, while insulators (such as wood) block electric current. Semiconductors (such as silicon and germanium) are somewhere in between an insulator and conductor: they can both block and conduct electricity. By simply inserting different impurities (dopant atoms) into the pure material, they can behave more like an insulator or more like a conductor. Of course, there is much more to the semiconductor story than that. Here, scientists Les Johnson and Joseph Meany explain the chemistry, at the atomic scale, behind the doping of a silicon semiconductor: In chemistry, the name relevant to the discussion of doping is the “Octet Rule.” According to the Octet Rule, an atom is stable when it has eight electrons in its outer shell. Think of an atom’s shell as its skin. Each layer of skin can have only a certain number of electrons. If an atom has fewer electrons in its outer shell than are allowed for that layer, then it can readily share electrons with neighboring atoms to fill its shell. Once it does this, it is not likely to further react with other elements and is considered stable. This is the basis of chemistry. Silicon has four electrons in its outer shell and readily shares electrons with other silicon atoms that surround it, forming a symmetrical-appearing lattice [figure 7.1]. Each silicon atom is sharing spaces in its outermost shell with other silicon atoms, satisfying the Octet Rule, making them all content, and without unpaired electrons—causing silicon to be a nonconductor [insulator]. To make it a semiconductor, scientists insert into the lattice either an atom [dopant] that has five electrons in its outer shell or an atom that has three outer electrons. When an atom with five electrons is added, four of the five electrons bond with its neighboring silicon atoms, satisfying the Octet Rule, but this leaves one unpaired electron that is then free to

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Figure 7.1. Bonding of atoms in silicon semiconductor with different dopants. (Left, solid box) n-type dopant; note the extra electron forced into the lattice. (Right, dashed box) p-type dopant; note the hole where an electron is expected. From Les Johnson and Joseph E. Meany, Graphene (2018), 152. Reproduced by arrangement with Globe Pequot.

move around. The free electron allows the new lattice to conduct electrical current, albeit poorly. This is called a negative or n-type semiconductor. Had the scientists doped it with an atom containing only three electrons instead of five, then only three of the neighboring silicon atoms would satisfy the Octet Rule and one would not. The unfulfilled silicon atom, the one that has no electron to fill its outer shell [the “hole”], then behaves like it is charge positive, attracting any free electrons roaming around to fill its shell. This type of semiconductor is called a positive, or p-type semiconductor.3

This passage defines the two types of semiconductor (n-type and p-type) as well as the two most important ingredients (excess electrons and positively charged “holes”). But the above description tells us nothing about the property that makes semiconductors work, the movement of the excess electrons and the holes among billions of silicon atoms. For that you need some basics on solid-state physics theory, in particular, energy band theory. The Nobel Prize– winning physicist Walter Brattain summarizes this topic in a popular science 162

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article for tech-savvy readers. In it, he defines two energy bands, valence and conduction, as well as the energy gap between them: In terms of solid-state theory, the individual atomic energy levels of the atoms in the [semiconductor] crystal become energy bands, and can best be described in terms of quantum mechanics. Two types of bands are available: the valence-bond band and the conduction band. In metals, these bands overlap. In insulators, they are separated by a forbidden energy gap of several electron volts. Electrons cannot be excited sufficiently thermally or by light to raise them into the conduction band; thus the material is a good insulator. In a semiconductor, the band gap is small [about one electron volt]. This gap is small enough to allow the electrons to be easily excited thermally from the valence to the conduction band [see figure 7.2]. As the temperature increases, so does the number of electrons reaching the conduction band. The electrons in the conduction band produce a current when an electric field is set up between the ends of the material. But this is not the only way that current is carried. As electrons from the valence band become excited thermally, they leave behind a vacancy. This vacancy, or hole, leaves a net positive charge at the point in the [crystal] lattice formerly occupied by the electron. It is now possible for another electron from the valence band to “jump” over and fill the hole. This, however, leaves a hole elsewhere in the band. The application of the electric field causes this hole to “move” in the opposite direction of the electrons, behaving as a positive charge carrier with the same effective mass and magnitude of charge as an electron. Thus, by exciting an electron into the conduction band, one obtains a pair of oppositely charged carriers.4

Compare the above two straightforward passages with the earlier highly metaphorical but foggy one by Rudberg: highly literary analogy is not always the best path to clarity in science. Worth noting with regard to the Brattain passage is that the simple application of heat, light, or an input current or voltage can provide the needed push to hoist the excess electrons or holes from the valence band, across the band gap, and into the conduction band. Also note that the valence and conduction “bands” are not actual physical bands within the semiconductor material, but visual bands that only appear when energy levels are plotted in a graph. Many have illustrated these energy bands with a similar-looking diagram. Figure 7.2 is but one example. 163

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Figure 7.2. Band gap diagram for metal (conductor), semiconductor, and insulator. From Jordan Hanania, Kailyn Stenhouse, and Jason Donev, “Band Gap,” Energy Education, November 13, 2015, https://energyeducation.ca/encyclopedia/Band_gap#cite_note-3..

The semiconductor material itself is a crystal—that is, a lattice of atoms arranged in a way that, in the words of Shockley, “is practically homogeneous and perfect” from the mechanical point of view. The aforementioned excess electrons, holes, and dopant atoms besmirch that perfection. But their density “is so low that if one were to traverse a row of atoms [many millions] from end to end in the crystal one would, on the average, strike only about ten imperfections. Thus the crystal structure itself is only slightly altered by the presence of the imperfections. From the electrical point of view, on the other hand, the imperfections have profound effects.”5 In the 1930s, physicist Alan Wilson and others created the foundation for energy band theory based on quantum mechanical principles. At the time the theory was not developed nearly enough for anyone to immediately fabricate a device made out of semiconductors for signal rectification, amplification, or switching. That demanded a continuing dialogue over many years between theoretical explanations and experiments until one explanation at last prevailed, as manifested by demonstrations of actual working devices, sometimes witnessed by fellow researchers and managers. Historian of science Ernest Braun summarizes the nature of the achievement: “The history of semiconductor physics is not one of grand heroic theories, but one of painstaking intelligent labor. Not strokes of genius producing lofty edifices, but great ingenuity and endless undulation 164

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of hope and despair. Not sweeping generalizations, but careful judgment of the border between perseverance and obstinacy.”6 Having defined key terms and established what a semiconductor is and can do from different chemistry and physics perspectives, we now turn to the first working transistors.

Historical Accounts of Transistor Precursor Scientists are human beings. They like to win prizes for their work. They like to see their names in the media for their accomplishments. They like recognition by their peers through hordes of citations. They like patents that result in commercial products. They especially like to see their names in history books for some groundbreaking discovery. While scientific articles establish priority for a discovery that may be important to science, historical accounts bring to light whether or not it actually was. They also recount circumstantial details about discoveries that cannot be found in any scientific articles. In Crystal Fire: The Invention of the Transistor and the Birth of the Information Age, historians Michael Riordan and Lillian Hoddeson relate an anecdote that dramatizes the first inkling that doped crystalline silicon had magical properties that might be rigged up to replace the vacuum tube. This latter device for controlling electric current at the time was central to long-distance telephone networks—of special interest to the sponsor of the research, Bell Telephone Laboratories. Riordan and Hoddeson dramatize one historic afternoon at Bell Labs in early 1940 thusly: On the afternoon of March 6, 1940, [Joseph] Becker and [Walter] Brattain took an urgent call from [Mervin] Kelly, who asked them to come to his office immediately. When Becker objected that they were right in the midst of a measurement, Kelly became adamant. “Drop it,” he snapped, “and come on up here.” A few anxious minutes later they reached Kelly’s office, where they found several other group leaders and two men from Bell’s radio department. One of them was Ralph Bown, then director of radio research, and the other was Russell Ohl, an elfin bespectacled Pennsylvania Dutchman, who often had a merry twinkle in his eye. He certainly did that day. On the table in front of Ohl was a simple electrical apparatus: a voltmeter and wires hooked up to a coal-black rod of material almost an inch long. It was a piece of silicon, a common element whose behavior Ohl had been studying for five years; two metal leads were attached to it, one at

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THE MANY VOICES OF MODERN PHYSICS either end. He picked up a flashlight, switched it on, and pointed its light beam directly upon the dusky rod. Suddenly, the voltmeter’s needle sprang up to almost half a volt. Dumbfounded, Brattain shook his head in disbelief. It was an enormous effect— more than ten times greater than anything he and Becker had ever observed with any other kinds of photocells. Copper oxide and selenium rectifiers, often used at the time in exposure meters, would generate tiny voltages in room light. But nothing like this mysterious silicon rod. “We were completely flabbergasted at Ohl’s demonstration,” Brattain later confided to an old Bell Labs colleague.7

The authors purposely novelize this important moment in the history of science and technology with circumstantial details. Time is “urgent.” Kelly “snapped.” Ohl is “an elfin bespectacled Pennsylvania Dutchman, who often had a merry twinkle in his eye.” The semiconductor is “a piece of silicon, a common element whose behavior Ohl had been studying for five years.” When the voltmeter “sprang up” to almost half a volt, Brattain was “dumbfounded” and “shook his head in disbelief.” Brattain expressed his astonishment “to an old Bell Labs colleague.” This is Brattain’s more prosaic account, in the typical understated prose in keeping with the scientific ethos: Early in 1940, Mervin Kelly, Director of Research for Bell Laboratories, called Joseph Becker and me to his office. He wanted us to view a demonstration using silicon, a then little understood semiconductor, being given by Russell Ohl, a staff member. Ohl showed us a small black rectangular block with two metal contacts. When light from a flashlight illuminated a narrow region near the middle of this piece of silicon, a photoelectromotive force (emf) of about 0.5V [volts] developed. This was hard to believe! In the first place, the contacts were not being illuminated and the photo emf was ten or more times larger than any we had ever seen. Moreover, the silicon was black and opaque to visible light. In fact, I did not believe what I saw until Ohl gave me a piece to work with in my own laboratory.8

Here Ohl is merely “a staff member” at Bell Telephone Laboratories. The silicon is “a then little understood semiconductor.” As a result of shining a light on this material, “a photoelectromotive force (emf) of about 0.5V developed,” and Brattain found it “hard to believe” without shaking his head, at least as far as we know from this account. After the demonstration, Brattain does not mention 166

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confiding to a colleague his astonishment, but doing what any good scientist would do: he checked the effect out himself with a device in his own laboratory. What is the point of this incident? Why is it important to the history of science and technology? This was the first inkling of the photovoltaic effect of a semiconductor: that the exposure of a doped silicon semiconductor to light from an ordinary flashlight can generate measurable electricity, as evidenced by a sizable jump in a voltmeter. As Riordan and Hoddeson go on to explain later in Crystal Fire, Brattain soon understood why this effect had happened.9 The silicon rod had some part that was p-type, and another part that was n-type. Upon shining of the light on this semiconductor hybrid, the incoming photons interacted with the silicon atoms and released electrons energetic enough to jump from the valence to the conduction band, which caused the voltmeter to shoot up half a volt. In Brattain’s article, his conclusion about the significance of the aforementioned incident was simply that “this was the first p-n junction,” the precursor to the first transistor that could be activated by an applied voltage instead of light. Before that development could happen, Bell Labs metallurgists would produce an exceptionally pure germanium to test, a first cousin to silicon. Like silicon, germanium is an intrinsic semiconductor, useless as a conductor until “doped” with a small quantity of phosphorus—one atom per million. As a result, an intrinsic became an extrinsic semiconductor capable of extreme amplification.

Presenting the First Transistor to Peers It was Brattain and Bardeen who in 1947 created a device that amplified a small electric current in a germanium semiconductor, making in effect the first transistor at Bell Labs. Brattain and Bardeen published their discovery in back-to-back letters in Physical Review, a standard move for establishing scientific priority. The first letter was primarily experimental; the second, theoretical. We should not be misled into confusing their discovery—the reason for their Nobel Prize—with the actual device on which the discovery was demonstrated, the point-contact transistor. While scientific discoveries are credited to their discoverers, their discoverers do not own them: they are new knowledge that belongs to everybody. In their first Physical Review letter, Brattain and Bardeen open with an extremely brief verbal description of their new invention, complemented by a visual representation: A three-element electronic device which utilizes a newly discovered principle involving a semiconductor as the basic element is described. It may be employed as an amplifier, oscillator, and for other purposes for which

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Figure 7.3. Schematic of semiconductor triode (first point-contact transistor). From J. Bardeen and W. H. Brattain, “The Transistor” (1948), 230. Reprinted with permission of the American Physical Society.

vacuum tubes are ordinarily used. The device consists of three electrodes placed on a block of germanium as shown schematically in [figure 7.3]. Two, called the emitter and collector, are of the point-contact rectifier type and are placed in close proximity (separation ~.005 to .025 cm) on the upper surface. The third is a large area low resistance contact on the base.10 .

The paragraph tells us that their new relatively simple invention has a mere three components—emitter, collector, and base. Yet, it can replace vacuum tubes. Most everyone at the time would have known that large and fragile vacuum tubes were essential parts in radios, televisions, telephone systems, and computers. Replacing them with something better would have been a major technological breakthrough. Figure 7.3 presents the engineering behind the breakthrough. It is a type of visual beloved of electrical engineers and scientists: the circuit diagram. This schematic is essentially a subway map where the electrical components are different stations and the direction of current is the route from one station to the next. Some components are named. Others are symbolized. These valuable maps not only communicate the essence of the invention but also can serve as an aide for knowledgeable scientists to reproduce it. They are also interesting for what is left out. Figure 7.3, for example, bears no resemblance to the physical device itself: in reality, the emitter and collector are separated on the germanium surface by a distance only measurable with a microscope (five to twenty-five millionths of a meter, about the size of bacteria). This figure also does not visualize the important subatomic arrangement or movement of excess electrons and holes within the semiconductor material. Later diagrams by others would integrate that important feature into this type of visual, however.11 168

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Brattain and Bardeen’s next paragraphs spell out in some detail the physics behind the invention. This is what truly makes the authors’ paper of interest to the physics community and worthy of publication in Physical Review: The germanium is prepared in the same way as that used for high back-voltage rectifiers. In this form it is an N-type. . . . Of critical importance for the operation of the device is the nature of the current in the forward direction. We believe, for reasons discussed in the accompanying letter, that there is a thin layer next to the surface of P-type (defect) conductivity. As a result, the current in the forward direction with respect to the block is composed in large part of holes, i.e., of carriers of sign opposite to those normally in excess in the body of the block. When the two point contacts are placed close together on the surface and d.c. bias [direct current deliberately made to flow] potentials are applied, there is a mutual influence which makes it possible to use the device to amplify a.c. [alternating current, forward and back] signals. A circuit by which this may be accomplished is shown in [figure 7.3]. There is a small forward (positive) bias on the emitter, which causes a current of a few milliamperes to flow into the surface. A reverse (negative) bias is applied to the collector, large enough to make the collector current of the same order or greater than the emitter current. The sign of the collector bias is such as to attract the holes which flow from the emitter so that a large part of the emitter current flows to and enters the collector. While the collector has a high impedance for flow of electrons into the semi-conductor, there is little impediment to the flow of holes into the point. If now the emitter current is varied by a signal voltage, there will be a corresponding variation in collector current. . . . Using the circuit of [figure 7.3], power gains of over 20 db [that is, a factor of over one hundred] have been obtained.12

Key to why Bardeen and Brattain’s point-contact transistor works is the formation of a p-n junction that amplifies current, as discovered earlier by Ohl. Because of this junction, upon turning on a small current, positively charged “holes” in the outer shell of the semiconductor atoms flow in great number into the collector. The result is that the weak current entering the semiconductor on the top left in figure 7.3 transforms into a strong current exiting on the top right, with a power gain of over a hundred times. In a demonstration Bardeen and Brattain conducted at Bell Labs, through a microphone (indicated by “Signal” in the circuit diagram), the speaker’s amplified voice could be heard “with no noticeable change in quality.”13 169

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For Bardeen and Brattain, their communicative emphasis is not themselves (the personal pronoun we only appears once) or their device’s possibly lucrative applications from the demonstrated power gain, which would be of interest to the average citizen and extreme interest to Bell Labs management, but the science. In particular, the signal amplification is possible due to the movement of excess holes within the semiconductor under an applied current. That is the story the two authors want to tell. The gist of that story is well within the power of most diligent readers to grasp, even though conveyed in a highly specialized physics journal. Given the need to establish priority for such an important invention, it might strike us as odd that six months passed between the discovery just before Christmas 1947, and publication the following June. The delay was caused by Bell Lab’s need to touch base with the US military, given the possible military implications of the discovery, plus the length of the patent process application and the debate over whether to publicize at all.14 It should also strike us as odd that their co-Nobel Prize winner’s name, William Shockley, appears neither on the paper nor on the patent. This was the consequence of a serious misjudgment on his part. In the later and crucial stages of the process of discovery, even though Bardeen and Brattain’s manager, Shockley absented himself to work alone on projects he deemed more promising.15 This misjudgment, however, was enormously productive, for unless he came up with something as worthy as their transistor effect by himself, he would not walk across the stage in Oslo with the two men he supervised. He succeeded magnificently. He invented the junction transistor.

Picturing the Bipolar Junction Transistor Shockley decided to follow up immediately on the success of Bardeen and Brattain and pursue his idea of a transistor composed of a germanium semiconductor with a p-type sandwiched between two n-types. This n-p-n transistor had a better theoretical base, and unlike the point-contact transistor, impressive commercial possibilities for mass manufacturing. Because it had to be Shockley’s alone, however, Bardeen and Brattain had to be excluded from its development, even though they were on his team at Bell Labs. They complained about being snubbed, but to no avail. Director of research at Bell Labs Mervin Kelly was sympathetic but unresponsive, mesmerized by the tantalizing prospect of a commercially viable product. Shockley delivered in 1949. He theorized correctly that a three-semiconductor structure “would exhibit the behavior of hole and electron diffusion in rather impressive ways.” Just as important, he was dead on-target when he asserted that transistor action involved the bulk in its entirety, not just 170

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Figure 7.4. Schematic of junction transistor. From William Shockley, “Transistor Physics” (1954), 70. Reprinted with permission of American Scientist.

regions close to the surface, as Bardeen and Brattain had suggested. In his case, theory did not stay theory—it led to practice. The junction transistor was born and with it a new era in commercial electronics. In a 1954 article in American Scientist, a general interest magazine akin to Scientific American, Shockley explains his triumph with the bipolar junction transistor based on a germanium semiconductor: The means by which the junction transistor carries out its amplification is indicated in [figure 7.4]. The upper part of the figure represents the situation under a condition of thermal equilibrium. When voltages are applied[,] the collector junction, shown at the right, is biased in the reverse direction, and the potential energy diagram from the point of view of electrons is as shown in the lower part of the figure. This energy potential is such that large numbers of electrons tend to be drawn from the emitter region at the left toward the collector region. However, in order to travel from one region to the other they must travel over the potential barrier of the p-type region [represented wider than it is to display its contents; it is

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THE MANY VOICES OF MODERN PHYSICS actually very, very narrow]. The situation is similar to that which occurs when there is a water reservoir behind a dam. If unchecked, water will flow from a reservoir at high altitude to a lower level; but if the sluice gates in the dam are opened and closed, the flow of water through a power house may be varied. The operation in a junction transistor, corresponding to opening the sluice gates, consists of applying a potential between the emitter and the base layer. . . . As a result of these features the junction transistor has a large gain of both current and voltage and may have a power gain as high as 100,000fold or 50 db [decibels]. Also the junction transistors are quiet in the electrical sense and produce little noise; types have now been made which compete quite favorably with vacuum tubes from the point of view of noise [unwanted signal disturbance]. 16

The above passage makes vivid the mechanism behind Shockley’s discovery with an analogy—comparing it to the opening of sluice gates on a reservoir dam—and a visual in the form of a circuit diagram that embodies the analogy (figure 7.4). In contrast to Bardeen and Brattain’s circuit diagram (figure 7.3), Shockley’s visualizes the microscopic movement of electrons and holes within the semiconducting block. The n-type semiconductor on the left is the emitter, and the one on the right is the collector. The p-type semiconductor in the middle is the base. In the topmost diagram, the excess electrons (minus signs) in the emitter do not have sufficient energy to pass by the holes in the base (plus signs) and into the collector. The positively charged holes and negatively charged electrons are in equilibrium. As shown in the bottom diagram, however, a small current applied to the p-type emitter causes holes to form near to the n-p junction for the emitter. This situation changes everything: lowering the energy barrier between the emitter and collector, opening the floodgates for electrons in the emitter to advance beyond the p-n junction and rush past the base into the collector, and boosting the output current by as much as “100,000-fold or 50 db,” far surpassing the twenty-decibel boost reported by Bardeen and Brattain. The image at the lower right represents the science behind the floodgate analogy. Subsequent visuals by others have represented transistor action with holes and excess electrons in a similar way to figure 7.4.

Resurrecting the Inventors of the First Silicon-Based Transistor In the first footnote to their Physical Review article on the point-contact transistor, Bardeen and Brattain note that “while the effect has been found with both silicon and germanium, we describe only the use of the latter.”17 It was not Shockley, nor 172

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Bardeen and Brattain, but physical chemist Morris Tanenbaum who later made the first junction transistor based on silicon. Historian and physicist Michael Riordan interviewed Tanenbaum in 2008, about a half century after the work was done. The following passage reproduces his response to an interview question about the effort at Bell Labs to develop it, an effort he led in the mid-1950s. This and other communications about the first silicon transistor retrospectively elevated the names of Tanenbaum and others into the historical record: Germanium [as a semiconductor] had some problems. First of all, its energy gap [between valence and conduction bands] wasn’t as large as one would have liked it to be, and so it couldn’t operate very much above room temperature without cooling. The other problem was that it was highly surface sensitive. There was something called the “friendly effect,” that if you had a germanium transistor in an ordinary room, and waved your hand at it, and watched on the oscilloscope, the curves would wave back to you. So germanium transistors had to be carefully encapsulated, either in metal or ceramic or something, to control the atmosphere. Silicon was thought to be of interest because of its higher energy gap primarily, but it’s very chemically reactive. It was difficult to purify. A lot of diodes [semiconductors with two terminals attached] were made from silicon. There were some attempts to make grown-junction [silicon] transistors, I think by Gerald Pearson, but he could never get a useful transistor using the usual double-doping kind of techniques. After a period of time, and I’m only surmising here, the net result was that Bill Shockley said, “Let’s really settle this silicon thing once and for all. Let’s establish a group dedicated to seeing if we can make a silicon transistor.” I was invited to join that group along with Ernie Buehler, who was a super technician and crystal grower. I guess Bruce Hannay supervised us, although I reported directly to Morgan Sparks, who reported to Bill Shockley in that group. We struggled with trying to grow junction transistors and discovered that it was just not possible to control the doping in such a way. We knew that we were going to have to grow NPNs or PNPs with very thin base layer. By double doping [where single dopant induces two charge carriers], we could get down to about a thousandth of an inch width in the base layer, but that still didn’t give us enough; the injected carriers would disappear, would die before they reached the collector, and so it was clear that we had to get narrower junctions, and Ernie Buehler proposed that he try “rate growing.” It turns out that depending upon how fast [the rate] you pull a crystal from the melt containing impurities, the amount of impurity that gets

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THE MANY VOICES OF MODERN PHYSICS incorporated in the grown crystal varies with the rate at which you grow the crystal. Since you can make fairly rapid changes in the temperature [of the melt] and affect the growth rate, Ernie said maybe we can get thinner junctions, thinner base layers by rate growing. So he prepared some crystals of that sort and we made our first silicon transistor. I think it was the world’s first silicon transistor from a rate-grown crystal.18

In this passage we get some insider insights into the team approach at Bell Labs at the time as well as the importance of the art of material fabrication to science in general, expressed in the informal and sometimes colorful language of the oral interview, a marked contrast from the restrained and opaque language of the typical scientific article or even a general interest article like that quoted from Shockley. Note that Tanenbaum’s reply focuses on the strictly technical advantages of the fabrication of silicon over germanium semiconductors at the time. Contrast those with the broader reasons the silicon semiconductor won the day over germanium in the marketplace, as enumerated by Frederick Seitz and Norman Einspruch in Electronic Genie: “First, it is plentiful in nature; supply was not a problem. Second, silicon devices can operate over a wider temperature range than can germanium devices. Third, silicon can be produced in very pure form if one takes the precaution to use very pure reagents in its preparation. Fourth, Gordon K. Teal eventually demonstrated that excellent single crystals could be produced in commercial quantities. Finally, silicon oxide proved to be a fine, stable electrical conductor that could also serve as a good chemical barrier.”19 Sadly for Tanenbaum, he only communicated his invention in his laboratory notebook and a single paper in the middle-of-the-road Journal of Applied Physics— no Physical Review article, profitable patent, press conference, or prizes for him. This is partially because Bell Labs was not interested in backing this line of investigation at the time, favoring instead the germanium semiconductor. But Tanenbaum can console himself with the knowledge that his contribution has made it into historical accounts, and he went on from there to a storied career in science.20

Patenting the MOSFET Transistor Alfred Nobel’s will stipulates that interest from his investments be distributed “annually as prizes to those who, during the preceding year, have conferred the greatest benefit to humankind.”21 Physics is one of the categories in which the prize is to be given for the previous year’s “most important discovery or invention.” These stipulations have been consistently set aside. As one egregious example, Yoichiro Nambu was awarded the 2008 Nobel Prize in Physics when he was eighty-five years old for work done forty-five years before; moreover, 174

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his discovery of the mechanism of spontaneous broken symmetry in subatomic physics, however impressive, is of no benefit whatsoever to humankind. In awarding the Nobel Prizes in Physics, there seems a bias against technology invention. This is unsurprising.22 The Nobel Prize committee tends to be highly weighted toward theoretical physics professors. The nomination process is also seriously skewed: researchers from organizations like Texas Instruments are typically excluded in favor of elite universities like Harvard or the University of Chicago. While a Texas Instruments employee, Jack Kilby, did win the 2000 Nobel Prize in Physics for the integrated circuit, Bell Lab’s Mohamed Atalla and Dawon Kahng did not, despite the fact that they invented the device that truly made the integrated circuit and the electronics revolution possible—namely, the metal–oxide–semiconductor field-effect transistor (MOSFET). The violation of the intent of Nobel’s will highlights the difference between discovery—revealing something that has always existed, and invention—creating something that has never before existed. We might say, of course, that Bardeen and Brattain invented the point-contact transistor and that Shockley invented the junction transistor. After all, both were devices and both were patented. But for Bardeen and Brattain, the point-contact transistor was a demonstration of a theoretical principle: the transistor effect. It was for that they won the Nobel Prize. Most important for Shockley’s inclusion with Bardeen and Brattain, the junction transistor was a demonstration of another theoretical principle: the role of electrons and positively charged holes throughout the semiconductor bulk, not just in a surface layer, for current rectification, amplification, and switching. For the Nobel Prize committee, its commercial possibilities were of secondary importance. But MOSFET was not about demonstrating a principle; it was about achieving commercial success. It was not about taking credit for a discovery; it was about creating and marketing a product. As a condition of their employment and for the consideration of one dollar, Atalla and Kahng signed over their rights to MOSFET to Bell Labs. MOSFET thus became a valuable property owned in accordance with the US Constitution: “To promote the progress of science and useful arts, by securing for limited times to . . . Inventors the exclusive right to their respective . . . discoveries.” You can’t own a theory; you can only get credit for being its discoverer. You do so by publishing it in a scientific journal. While Bardeen, Brattain, and Shockley published in Physical Review, in 1960 Atalla and Kahng announced their invention at a conference at what is now Carnegie Mellon University.23 You will look in vain for any prestigious journal publication of their remarkable achievement. What was at stake was not credit, but ownership. The vehicle for this is the patent, a genre designed not to be read and understood by anyone but 175

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patent examiners, lawyers, and the inventors—it is written at times in what is probably the most bizarre form of English ever created. While scientific articles tell a story in which their discoveries are a development of previous achievements, a patent application presents an invention as a break with the past, something entirely new. While the operation of the device is described, the purpose is not to teach others how it works, but to warn them away from duplicating it. The vocabulary is deliberately idiosyncratic: interesting means “entirely new”; said as an adjective refers to a claim that has already been made. 24 Written by a Bell Labs attorney based on input from the inventor Atalla, the MOSFET patent describes a semiconductor device made of a silicon wafer with oxide coating. The coating is a special ingredient, as it allows the wafer “to achieve desirable changes in signals” upon application of a voltage.25 The heart of the patent is a technically dense and detailed passage defining the device in a way that clearly differentiates it from other similar devices, at least as judged by a subject matter expert: The device 80 of FIG. 5 [figure 7.5] is structurally similar to the device of FIG. 4 [not reproduced here]. However, inclusion of an additional PN junction 81 substantially parallel to the single junction 83 as depicted in FIG. 4 results in an NPN configuration corresponding to regions 84, 85 and 86 as shown. Additionally, individual ohmic contacts are provided to each of the two N regions 84 and 86. For the particular arrangement of conductivity type regions 84, 85, and 86 shown, a bias of positive to negative polarity is applied by way of a battery B connected between contact 87 to the oxide coating 88 and contact 90 respectively. Contact 87 extends across the extensions through the oxide of the planes of the two PN junctions 81 and 83. If, for example, junction 81 is biased in the forward direction and junction 83 is biased in the reverse direction by the application of an appropriate voltage from a battery B connected between ohmic contacts 89 and 90, a positive bias at the oxide will induce a region of negative charge 91 which will provide a low impedance path at a predetermined value of bias applied across the oxide layer. The device can be returned to its high impedance state by removing the bias or, alternatively, by application of a negative voltage at the oxide depending on design parameters. The operation of the device as a switch is evident from the above description. However, the device may be used alternately as an amplifier.26

Aside from the substitution of silicon for germanium semiconductors, the device shown in figure 7.5 is similar in many respects to the junction transistor 176

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Figure 7.5. A model of MOSFET. From M. M. Atalla, “Semiconductor Devices Having Dielectric Coatings” (1965).

invented by Shockley much earlier. The main difference is parts 87 and 88, a metal over a p-type semiconductor on top of a silicon oxide insulator spanning the n-p-n type semiconductors below (84, 85, 86). Parts 87 and 88 (the “gate”) make the device truly different from its predecessors and truly patentable and one of the most important technological inventions ever. The first paragraph above tells us why. If we apply a negative voltage to 87 above a certain threshold value, positively charged holes gather near the top of the p-type semiconductor due to an attractive force (opposites attract) and then flow between the two n-type semiconductors. And if we apply a positive voltage to 87, then excess electrons congregate and flow between the n-type semiconductors through the p-type. In both cases, with a fairly minimal increase in voltage, we get a major boost in current. This current can be easily turned on and off by varying the voltage above or below the threshold value. By taking advantage of this switching mechanism, later researchers were able to exploit the efficient conversion of electrical signals into the ones and zeros of computer code, marrying a physics technology with a mathematical system, binary code. 177

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Note that figure 7.5 is not to scale, just as in our earlier circuit diagrams. For example, the gate is only one hundred angstroms thick; there are some forty million gates to an inch. Also note that the patent is careful to say that the diagram and accompanying text do not reflect a complete description of the inventor’s idea, but merely one possible depiction of this idea: No effort has been made to exhaust the possible embodiments of the invention. It will be understood that the embodiment described is merely illustrative of the preferred form of the invention and various modifications may be made therein without departing from the Scope and spirit of this invention.27

It is not a specific device that is being patented, but the idea of the device.

There Is No I in Team At this point, our focus shifts from technology to its commercial exploitation. After the junction transistor, Shockley transformed himself into an entrepreneur, founding Shockley Semiconductor, the first step toward Silicon Valley. While the semiconductor industry grew exponentially, however, it did so without Shockley. His domineering management style fomented a rebellion of eight of his most talented researchers. They left to found Fairchild Semiconductor, the mother and father of Apple, Hewlett-Packard, and Intel, the home as well of Gordon Moore—author of Moore’s law, the empirical observation that the number of transistors in an integrated circuit will double every two years. In order to do so, transistors had to get smaller and smaller: a revolution in miniature in which enormous numbers of MOSFETs are embedded on tiny chips of semiconductor material. In keeping with Moore’s law, record-setting microprocessors skyrocketed from a mere 592 million transistors per chip in 2004 to 39.54 billion in 2019.28 In his lecture accepting the 1956 Nobel Prize in Physics for his role in the discovery of the transistor effect, Bardeen had to fill a difficult role: a team player and towering figure whose biography is accurately titled True Genius. Yet there is nary an I in his Nobel Prize lecture. Instead, we are given an accurate picture of the collaborative nature of his research, one instance of the ethos that characterized all work at Bell Labs. In Bardeen’s Nobel Prize lecture, as in Brattain’s, the science, not the scientist, stars. Neither of these scientists dwells for long on the practical applications of their discovery. This contrasts somewhat with Shockley’s Nobel Prize lecture. At the beginning, his emphasis is solving not fundamental science problems, but problems motivated by “practical considerations,” such as 178

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“telephone switching problems,” problems consistent with Alfred Nobel’s will. At the end, he quotes himself in the role of a prophet and venture capitalist: In closing this lecture, I would like to refer to a paragraph written in my book in 1950 [Electrons and Holes in Semiconductors]. I am pleased to see that the predictions of the paragraph appear to have been borne out to a considerable extent and I feel that it is now as applicable as it was then: It may be appropriate to speculate at this point about the future of transistor electronics. Those who have worked intensively in the field share the author’s feeling of great optimism regarding the ultimate potentialities. It appears to most of the workers that an area has been opened up comparable to the entire area of vacuum and gas-discharge electronics. Already several structures have been developed and many others have been explored to the extent of demonstrating their ultimate practicality, and still other ideas have been produced which have yet to be subjected to adequate experimental tests. It seems likely that many inventions unforeseen at present will be made based on the principles of carrier injection, the field effect, the Suhl effect [of a magnetic field on a semiconductor], and the properties of rectifying junctions. It is quite probable that other new physical principles will also be utilized to practical ends as the art develops. It is my hope to contribute to the fulfilment of the predictions of this paragraph through my new organization in California.29

By all accounts Shockley was a difficult and opinionated man with a towering ego. When the eight key scientists left his company in disgust, Shockley predicted they would fail. Instead, they were the pioneers that contributed to the fulfilment of Shockley’s prophecy quoted above and made Silicon Valley what it is today.30 It is no wonder that in the years before their Nobel Prize lectures, Bardeen and Shockley were not on speaking terms; it is not for nothing that his biography is titled Broken Genius.

Scientists and science writers have defined for us a newly invented scientific thing—the transistor—in many different kinds of communications: scientific articles, patents, historical accounts, memoirs, Nobel Prize lectures, and popular science articles. This scientific thing is now an essential cog in many ordinary things essential to modern life. In these publications, the writers carry out several tasks, providing a multifaceted view of the transistor from the atomic and 179

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subatomic level to the microscopic electronic components. The tasks include defining what the transistor building blocks are and how they function electronically; presenting the basic science behind why transistors do what they do; establishing who invented what, when, and how; and commenting on how these then newly discovered devices might be turned to practical ends. In keeping with the scientific ethos, whether the scientists emphasize the last item, even though it is the main motivation behind the research, depends on the context and the author. This chapter may leave the reader with the mistaken impression that the story of the transistor is only about a few brilliant scientists, some with giant egos, working night and day to invent something new and possibly useful to society. Another story is quietly conveyed in a short phrase immediately after the authors’ names in Physical Review and other publications that first communicated the science behind the inventions: “Bell Telephone Laboratories, Murray Hill, New Jersey.” Long since renamed and downsized, the once mighty Bell Labs was an organization that invested in pure science in the hope that an accompanying technological advance would lead to an improved bottom line, a hope that discoveries of pure science, which belong to everyone, could on occasion be turned into inventions that belonged only to Bell Labs. It served as a model industrial scientific organization for many decades.

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At first glance, it may seem perverse to view astronomy through the lens of economics. Its discoveries lack market value; moreover, the world, not the discoverer, owns them. Despite these caveats, discovery and value are inextricably intertwined. With success, the discoverers’ reputation is enhanced, along with the reputation of their institution and their nation; their value has increased. Moreover, the communication of a discovery is economic at its core, relying on publishers, those who work for a for-profit like Springer; those that are subsidized by subscriber fees, like the American Physical Society; or those that thrive on institutional patronage, like arXiv. In addition, because publication is only the last step that acknowledges a discovery, it would be wrong to exclude from our consideration the outlays that make that discovery possible. This chapter touches on the many different sources of economics behind astronomical discovery: the ducal patronage that supported Galileo Galilei, the royal patronage that supported William and Caroline Herschel, the philanthropy that supported Edwin Hubble’s extragalactic discoveries at the Mount Wilson Observatory, the industrial patronage of Bell Labs that supported Arno Penzias and Robert Wilson’s accidental discovery with a radio telescope, the federal patronage that supported the Hubble space telescope, and, finally, the international patronage that supported the Cassini-Huygens exploratory spacecraft to Saturn and the miles-long machines that detected gravitational waves. 181

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As we shall see, the need for such patronage requires scientists and science advocates to, on occasion, write in different genres with diverse aims: to solicit funds to conduct research or build an expensive machine to do the research, to acknowledge the source of those funds publicly, and to reinforce the value of such investments with success stories.

Galileo and the Grand Duke We briefly depart here from modern physics to the birth of physics in the early seventeenth century and, arguably, the most important instrument for physics discoveries ever invented, the telescope, still of crucial importance today. Galileo Galilei did not invent the refracting telescope: a telescope with two lenses, concave and convex, one on each side of a tube. Nor did he merely improve it. In making his improvements, he behaved not like a craftsman, but like a scientist: to discover the solution of a known and designated problem is a labor of much greater ingenuity than to solve a problem which has not been thought of and defined, for luck may play a large role in the latter while the former is entirely a work of reasoning. Indeed, we know that the Hollander [Hans Lippershey] who was first to invent the telescope was a simple maker of ordinary spectacles who in casually handling pieces of glass of various sorts happened to look through two at once, one convex and the other concave, and placed at different distances from the eye. In this way he observed the resulting effect, and thus discovered the instrument. But I, incited by the news, discovered the same by means of reasoning.1

This is not to say that his goal in The Starry Messenger (1610) was simply to represent celestial objects objectively, the task of an astronomer from the generation after Galileo, Johannes Hevelius. He objected that Galileo’s depiction of our moon distorted the crater at the lower edge of the terminus, the border between light and dark, representing it as far larger than it actually was. Was Galileo at fault? We have firm evidence that he could depict what he actually saw, a fact that allows us to infer that the crater might have been deliberately enlarged—a visual designed to show that Aristotle’s view, his belief that heavenly objects were different in character from Earth, was no longer tenable. As noted by a recent translator of Galileo’s work, Albert Van Helden: “Moreover, when an accurate depiction served his purpose as did his observations of Jupiter’s moons, Galileo depicted exactly what he saw, a startling observation that filled him with ‘intense longing,’ and led to sixty-five subsequent observations on succeeding nights. His was a diary of discovery that proved conclusively another similarity 182

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Figure 8.1. Positions of the moons of Jupiter (stars) orbiting around the planet (circle) on different nights. From Galileo Galilei, Sidereus Nuncius (1610).

between Earth and other heavenly bodies. Jupiter’s four moons orbited around their planet [figure 8.1].” This parallel of circumnavigation led Galileo to a firm and dangerous conclusion: We have moreover an excellent and splendid argument for taking away the scruples of those who, while tolerating with equanimity the revolution of the planets around the Sun in the Copernican system, are so disturbed by the attendance of one Moon around the Earth while the two together complete the annual orb around the Sun that they conclude that this constitution of the universe must be overthrown as impossible. For here we have only one planet revolving around another while both run through a great circle around the Sun: but our vision offers us four stars wandering around Jupiter like the Moon around the Earth while all together with Jupiter traverse a great circle around the Sun in the space of 12 years.2

Galileo also saw that the publication of his discovery could transform him from an underpaid professor at the University of Padua to philosopher and chief mathematician to the Grand Duke of Florence. Historian Richard S. Westfall gives us a view of Galileo’s mind at work, the astronomer as entrepreneur: 183

THE MANY VOICES OF MODERN PHYSICS By the end of the month he had prepared the Sidereus nuncius, a message from the stars to be sure, but a message composed with the grand duke always in mind. He wrote to Belisario Vinta, the Florentine secretary of state, from Venice, where he had gone to have it printed, about his observations: “as they are amazing without limit, so I render thanks without limit to God who has been pleased to make me alone the first observer of things worthy of admiration but kept secret through all the centuries.” He ran through his discoveries—the surface of the moon, the new stars, the nature of the Milky Way. “But that which exceeds all the marvelous things, I have discovered four new planets [the Galilean moons of Jupiter].” Vinta [first secretary of state of the Grand Duchy] answered in the least possible time. Immediately upon the arrival of Galileo’s letter, he had taken it to the grand duke, who was rendered “stupefied beyond measure by this new proof of your almost supernatural genius.” Assured that the prey was taking the bait, Galileo sprang the trap. He was willing, he told Vinta, to publish his observations only under the auspices of the grand duke, in order that “his glorious name live on the same plane with the stars.” As the discoverer of the new planets, it was his privilege to name them. “However, I find a point of ambiguity, whether I should consecrate all four to the Grand Duke alone, calling them with his name the Cosmici, or whether, since they are exactly four in number, I should dedicate them to the group of brothers with the name of Medicean Stars.”3

Although a scientific treatise, The Starry Messenger begins as a formal letter with Galileo’s salutation to its dedicatee, Cosimo II de’ Medici, Grand Duke of Tuscany, reserving the four moons for his illustrious name: But why do I mention these things as though human ingenuity, content with these [earthly] realms, has not dared to proceed beyond them? Indeed, looking far ahead, and knowing full well that all human monuments perish in the end through violence, weather, or old age, this human ingenuity contrived more incorruptible symbols against which voracious time and envious old age can lay no claim. And thus, moving to the heavens, it assigned to the familiar and eternal orbs of the most brilliant stars the names of those who, because of their illustrious and almost divine exploits, were judged worthy to enjoy with the stars an eternal life. As a result, the fame of Jupiter, Mars, Mercury, Hercules, and other heroes by whose names the stars are addressed will not be obscured before the splendor of the stars themselves is extinguished.4

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Here Galileo displays his powers of persuasion with the language of the royal court. As Benjamin Disraeli was purported to have said: “Everyone likes flattery; and when you come to Royalty you should lay it on with a trowel.”5 While the language itself becomes much less sycophantic in the following centuries, writing persuasive communications aimed at potential benefactors will remain a vital talent for the successful scientist.

The Herschels and King George III Galileo’s refracting telescope was a toy in the hands of a genius, an instrument whose limitations the genius of Isaac Newton would overcome with his invention of a practical reflecting telescope, one that contains a reflecting mirror instead of a refracting lens. Newton’s telescope was the instrument that would form the basis of modern astronomy, in whose birth two German immigrants to England played major roles: William Herschel and his sister Caroline. Theirs is a story that makes sense only if we think of England as a country of opportunity, one in which it was possible for a thirty-five-year-old performing musician and composer to reinvent himself into the leading English astronomer, a maker of state-of-the-art telescopes, telescopes superior to those then in use anywhere in the world. With one of these instruments, Caroline discovered five comets entirely new to astronomy; with another, William discovered the planet Uranus; and with another, the two identified hundreds of “island universes.” Caroline was not just William’s helper. William and Caroline formed a research team. Theirs is a tale of two “amateurs” who achieved well-deserved scientific fame, hobnobbing with the royal family and attaining royal recognition and funding for their work. Although William was no gentleman to begin with, he became a fellow of the Royal Society, was knighted, and founded the Royal Astronomical Society. His son John became a highly respected astronomer and rose to the baronetcy. Caroline’s career in astronomy was impressive independent of her brother. While one of a few women in all of science at the time, she gained the respect of leading astronomers in England and on the Continent. At the age of ninety-six, having returned to Hanover after her brother’s death, she received the following letter from Alexander von Humboldt, the leading German naturalist of the time whose works Charles Darwin devoured: Berlin, Sept. 25, 1846 most honoured lady and friend!— His majesty the King [Frederick William IV of Prussia], in recognition of the valuable services rendered to astronomy by you as the fellow-worker of

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THE MANY VOICES OF MODERN PHYSICS your immortal brother, Sir William Herschel, by discoveries, observations, and laborious calculations, commanded me, before his departure for Silesia, to convey to you, in his name, the large Gold Medal for Science.6

Although Caroline was ambitious—she once rode horseback through the night to Nevil Maskelyne, the Astronomer Royal, so that her priority in comet detection might be preserved7—she was careful in her first paper, one of the first by a woman to be published in Philosophical Transactions (1786),8 to project an extreme modesty she most likely did not feel. To Charles Blagden, the secretary of the Royal Society, she writes that she is reluctant to trouble him, but hopes that his friendship with her brother will be an adequate excuse for this intrusion. Ordinarily, Caroline would not pursue her stargazing except under her brother’s supervision, she writes, but at the time he happened to be visiting Germany. Of her comet discovery, she claims to give “an imperfect account” and to have had it checked for inaccuracies by her brother at his return. Five years earlier, in 1781, William had “discovered” Uranus with a sevenfoot-long telescope he built. He was the first to track its progress in the night sky and report so in a journal article. Was it a planet? Was it a comet? Just as he was not the first person to observe Uranus, he was not even the first to identify it correctly as a planet. Others did it for him, and it was not until the following year that William decided he agreed with them—it was a planet, not a comet. What’s more, while Uranus from Greek mythology is our name, it was not his. William’s was Georgium Sidus (George’s Star), in honor of his king and patron, King George III, as he proposed in a letter published in Philosophical Transactions of the Royal Society with Galilean royal flourishes: In the fabulous ages of ancient times the appellations of Mercury, Venus, Mars, and Saturn, were given to the Planets, as being the names of their principal heroes and divinities. In the present more philosophical era, it would hardly be allowable to have recourse to the same method, and call on Juno, Pallas, Apollo, or Minerva, for a name to our new heavenly body. The first consideration in any particular event, or remarkable incident, seems to be its chronology: if in any future age it should be asked, when this last-found planet was discovered? It would be a very satisfactory answer to say, “In the reign of King George the Third.” As a philosopher then, the name of georgium sidus presents itself to me, as an appellation which will conveniently convey the information of the time and country where and when it was brought to view. But as a subject of the best of Kings, who is the liberal protector of arts and science;—as a native of the country from

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ASTRONOMICAL VALUE whence this Illustrious Family was called to the British throne;—as a member of that Society, which flourishes by the distinguished liberality of its Royal Patron;—and, last of all, as a person now more immediately under the protection of the excellent Monarch, and owing every thing to His unlimited bounty;—I cannot but wish to take this opportunity of expressing my sense of gratitude, by giving the name Georgium Sidus, to a star, which (with respect to us) first began to shine under His Auspicious reign.9

While the name pleased George III—he appointed William as King’s Astronomer—the above naming argument did not persuade the international astronomy community. Science in general is an international enterprise that greatly favors a common naming system. Naming of the sort Herschel favored generally implies ownership; if you own it, you can name it. For example, when the British kicked the Dutch out of New Amsterdam, it became New “York.” William’s astronomical observation brought him international fame. This discovery, however, did not merely add another planet to our inventory. More important, it added a new method for astronomical discovery, a shift from positional astronomy. Positional astronomy points a telescope to the place where you think an object of interest might be. Instead, William systematically scanned the sky sector by sector, a procedure that made his discovery almost inevitable. While unlike his son, William wrote no treatises on method, he shared this methodological insight with a fellow astronomer, the Frenchman Charles Messier, with whom he corresponded in the latter’s French. Messier had noted that “no way can I figure out how you have returned many times to this star or comet because you have to observe it for many days following in order to perceive its movement since it does not at all behave like a comet.” Still unaware his comet was a planet, William attributes his successful sighting to the superiority of his seven-foot-long telescope: I was busy making observations concerning the parallax of the fixed stars and on March 13th [1781] I observed the stars of the fifth and sixth magnitude in the vicinity of Eta-Geminorum [a triple star system in the Gemini constellation]; seeing the comet, I recognized it immediately as my telescope is so good that it allowed me to see at first glance a small object very different in appearance from a fixed star. Having made a note of its location I revisited it for the first time four days later and finding that its position had changed, I no longer doubted that it was a comet. With this telescope and a new micrometer in order to determine the angle of the position . . . in two or three hours I was able to determine the comet’s movement without a scintilla of doubt.10

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With a twenty-foot-long telescope built by William, the crowning achievement of this unique brother-sister team was mapping out the shape of the Milky Way and observing over nine hundred new nebulae, gaseous bodies that in 1785 William reported could be “island universes.”11 Some of these we now know to be galaxies outside the Milky Way. In the same year, William drew up plans to build the largest, most powerful telescope in the world at forty feet in length. Having cajoled George III to invest a king’s ransom in the project, in 1789 William finally oversaw completion of the gigantic telescope. Historian Richard Holmes describes this astronomical instrument and its operation in wonderful detail as a spaceship traveling through the heavens: The forty-foot would be higher than a house, extremely susceptible to wind, and very exposed to adverse weather conditions, especially frost, condensation and air-temperature changes, which could “untune” the mirrors like musical instruments. The astronomer (Herschel was now approaching fifty) would be required to climb a series of ladders to a special viewing platform perched at the mouth of the telescope, from which a fall would almost certainly prove fatal. The assistant (Caroline) would have to be shut in a special booth below to avoid light pollution, where she would have her desk and lamp, celestial clocks, observation journals, and coffee flasks. But she would see virtually nothing of the stars themselves. Astronomer and assistant would be invisible to each other for hours on end, shouting commands and replies, although eventually connected by a metal speaking-tube. It would be rather as if they were the tiny crew of some enormous ship, one up on the bridge, the other below in the chart room, intimately dependent on each other but physically isolated. Perhaps this was the premonition of a new kind of vessel: a spaceship flying through the starry night.12

Temperamental in anything but perfect weather conditions and difficult to operate under the best of conditions, the forty-footer proved a disappointment in advancing British astronomy. Perhaps a better analogy for it would have been white elephant. Nevertheless, it became a tourist attraction and did succeed in its stated aim, as expressed in William’s construction proposal to the king: to serve as a symbol of “the honour of a liberal Monarch, and the glory of a nation which stands foremost in the cultivation of the arts and sciences.”13

Edwin Hubble and John Hooker The telescope at the Mount Wilson Observatory, with its one-hundred-inch mirror, became operational in 1917. Private philanthropy was the source of its funds, a 188

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campaign initiated by the Los Angeles hardware millionaire and amateur astronomer John D. Hooker, who died in 1911, six years before the telescope’s completion. In 1919 professional astronomer Edwin Hubble joined the observatory staff. Having become the world’s most famous astronomer, in 1936 he published a semitechnical book about his discoveries in The Realm of the Nebulae. In the book’s preface, Hubble pays homage to the “Hooker telescope” and the observatory’s founding organization: “The instrument which definitely established the identification [of the first galaxies outside the Milky Way]—and enlarged the domain of positive knowledge a thousand-million-fold—is the Hooker telescope—the 100-inch reflector of the Mount Wilson Observatory of the Carnegie Institution of Washington. It is the largest telescope in operation, it has the greatest light-gathering power, and it penetrates to the greatest distance. For these reasons, it defines the present extent of the observable region of space, and it has contributed the most significant data to the study of the region as a sample of the universe.”14 The restrained language here is more typical of modern acknowledgments of support. Hubble’s qualitative comparisons speak for themselves: largest telescope, greatest resolution, farthest distance, and most significant astronomical data collected. Most important, in 1929 Hubble had published “significant data” that put him and the Hooker telescope in the history books.15 In his scientific paper, Hubble concluded that the “apparent velocity” of the galaxies he tracked increased linearly with distance. In The Realm of the Nebulae, he devotes a chapter to his methodical determination of this velocity-distance relationship. In the book’s introduction discussing this surprising finding “of the first importance,” we find the usual restrained tone consistent with the just-the-facts ethos of science, but with a dash of metaphorical language thrown in to alert the reader to the importance of his discovery: The velocity-distance relation is not merely a powerful aid to research, it is also a general characteristic of our sample of the universe—one of the very few that are known. Until lately, the explorations of space had been confined to relatively short distances and small volumes—in a cosmic sense, to comparatively microscopic phenomena. Now, in the realm of nebulae [galaxies], large-scale, macroscopic phenomena of matter and radiation could be examined. Expectations ran high. There was a feeling that almost anything might happen and, in fact, the velocity-distance relation did emerge as the mists receded. This was of the first importance for, if it could be fully interpreted, the relation would probably contribute an essential clue to the problem of the structure of the universe. Observations show that details in nebular [galactic] spectra are displaced toward the red from their normal positions, and that the redshifts [a

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Figure 8.2. Visual display of Hubble’s measurements indicating increasing galaxy velocity with distance. From Edwin Hubble, The Realm of the Nebulae (1958), plate 8. Reprinted with permission of Yale University Press. measure of velocity] increase with apparent faintness of the nebulae. Apparent faintness is confidently interpreted in terms of distance. Therefore, the observational result can be restated—red-shifts increase with distance.16

Figure 8.2 shows Hubble’s visual representation of the increasing velocity (measured by redshift) with galaxy distance, an arresting combination of data in rows and columns besides telescopic images. The receding velocity given for 190

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the most distant galaxy (nebula in Gemini cluster) is an astonishing 7.5 percent the speed of light. That grabbed the astronomy world’s attention. About the significance of the redshift and distance relationship, however, Hubble cautiously suggests that “the nebulae are supposed to be rushing away from our region of space, with velocities that increase with distance.”17 He was never comfortable with the view that his data established an expanding big bang universe. Nonetheless, it is with good reason that astrophysicist J. Richard Gott opens The Cosmic Web with the wry but true statement that “it is fair to say that Edwin Hubble discovered the universe.”18 It also seems fair to say that Hubble’s acclaim would not have been possible without the giant telescope bankrolled by Hooker.

Penzias and Wilson and Bell Labs In its heyday, the once mighty Bell Telephone Laboratories was a unique industrial research juggernaut that hired the best and brightest to do science in the hope that any accompanying technological advances might lead to profitable new inventions (see chapter 7) or, failing that, reputation-enhancing scientific discoveries, even if without any monetary return on investment. Exhibit A of the latter was the fortuitous astronomical observation by Bell Labs physicists Arno Penzias and Robert Wilson confirming that, not only was the universe expanding, but that it began at t = 0 with a rapid expansion now known as the big bang. This observation occurred at the Bell Labs telescope called the Holmdel Horn Antenna, built in Holmdel, New Jersey, in 1959 to gather and amplify radio waves in early efforts to develop satellite communications. Shaped like an enormous horn, which looks more like a large Picasso sculpture than an astronomical instrument, this form of telescope measures the intensity of radio wave emissions from objects in outer space. As part of a test on August 12, 1960, it detected the radio waves from a message transmitted from California after bouncing off a large Mylar balloon placed in orbit as part of a NASA space research program. The message was from the president of the United States: “This is President Eisenhower speaking. This is one more significant step in the United States’ program of space research and exploration being carried forward for peaceful purposes. The satellite balloon, which has reflected these words, may be used freely by any nation for similar experiments in its own interest.”19 Within a few years, the Bell Labs telescope had become obsolete for use in satellite communications research. With more instrument time free, Penzias and Wilson jumped at the opportunity to use it to measure and analyze microwaves (which have much longer wavelengths than that of visible light) emanating from celestial sources in our galaxy. Before beginning their planned measurements, however, the young researchers had to calculate any background noise that might 191

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interfere with their measurements. A brief press release from Bell Labs went public over a month before the authors’ article in Astrophysical Journal Letters: After carefully measuring and accounting for all the known sources of noise radiation from the earth atmosphere and the galaxy, as well as from the antenna and associated equipment, Bell Laboratories scientists Arno Penzias and Robert W. Wilson found a residual amount of noise radiation which they could not explain. On consultation with colleagues in the radio astronomy field, they learned of the new theory proposed by Princeton physicists R. H. Dicke, P. J. Peebles, P. G. Roll and D. T. Wilkinson. One consequence of this theory is that there should be an observed radiation from the universe of the same order of magnitude as that observed at Bell Laboratories. The Princeton work is based upon a theory that the universe is expanding from a high-temperature collapsed state. The energetic thermal radiation resulting from the high temperature has been cooled by the expansion of the universe to a tiny fraction of its original temperature [from over a billion degrees down to about four degrees above absolute zero] and is believed to be the source of the effect observed at Bell Laboratories.20

This passage succinctly covers the two essential components of press releases: what the scientists discovered and its larger significance of interest to an audience without much scientific background. One of the aims of press releases is to convince news organizations to pick up and publish the story. We assume this one succeeded splendidly, as a front-page news article appeared in the New York Times. Its headline captures the essence of the press release: “Signals Imply a ‘Big Bang’ Universe.”21 (It is of course also possible that the Times might have gotten wind on this discovery from another source.) Press releases only touch the high points. One must look elsewhere for interesting further details. In The Inflationary Universe, for example, cosmologist Alan Guth relates an oft-repeated anecdote concerning Penzias and Wilson’s efforts to understand why they could not eliminate interfering noise or hiss in their antenna: The strength of this signal did not change when they pointed the antenna in different directions, it did not change with the time of day, and as the seasons progressed it became clear that it did not vary with season. The unremitting constancy of the signal suggested very strongly that it was noise within the system, but . . . could there be some other source of noise

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ASTRONOMICAL VALUE in the antenna that had been overlooked? Was it possible, for example, that the signals were related to the pigeons who enjoyed sauntering though the heated part of the horn? After ejecting the pigeons, the scientists put some effort into cleaning off the “white dielectric material,” as Penzias described it, with which the pigeons had coated the throat of the antenna. All this, however, had no significant effect on the mysterious hiss. Penzias and Wilson remained thoroughly puzzled, but they were determined to track down the source of the enigmatic signal.22

Their persistence and thoroughness, along with Bell Labs backing, landed Penzias and Wilson the 1978 Nobel Prize in Physics for measurement of a “mysterious hiss,” which turned out to be the cosmic microwave background permeating the entire universe due to the big bang. Even though Bell Telephone was a commercial monolith at the time, it recognized that reputation-enhancing science can emerge from funding the most basic of basic research.

NASA and the Hubble Space Telescope The NASA Hubble Space Telescope is roughly the same length as Herschel’s forty-footer. When on land, it is far inferior to current land-based observatories. However, when orbiting 340 miles above Earth’s surface—outside the dimming effects of Earth’s atmosphere—it has the power to “see” locations in the farthest reaches of the universe, some 13.4 billion light-years from Earth. With an estimated price tag of $700 million in 1972 (equivalent to $5 billion in 2022), financing the telescope took considerable powers of persuasion by a preeminent scientist. That scientist was John Bahcall, whose theory of solar neutrinos was later vindicated when Raymond Davis Jr. captured some in an elaborate underground apparatus. From the start, Bahcall was a persistent and effective lobbyist for the space telescope. He was joined by his friend Lyman Spitzer—originator of the first sound technical justification for a space telescope (in 1946), a professor of astronomy, and a neighbor at Princeton University. How does one convince a US Senate committee to fund a billion-dollar astronomy machine of no obvious practical benefits for the taxpayers they represent? In his 1977 testimony before the Committee on Commerce, Science, and Transportation, Bahcall opens with the gambit of “answering-big-scientific-questions,” followed by why the telescope can do so: The NASA Space Telescope is designed to answer questions like: How big is the universe? Did it have a beginning? Will it have an end? Will observations of black holes and quasars reveal new laws of physics? What kinds

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THE MANY VOICES OF MODERN PHYSICS of undiscovered things are there in outer space? How are stars formed? Are there other planetary systems like our own? The Space Telescope can provide new information on these fundamental questions because it will be located outside the earth’s atmosphere in a stabilized observatory. The earth’s atmosphere is a partially opaque curtain between us and the rest of the universe. Only a very narrow band of colors is transmitted unimpeded by the atmosphere. The images we do see here on earth are also blurred because of the irregular motions of cells of air in the earth’s atmosphere. Thus terrestrial observations through the atmospheric curtain are limited to visual colors and twinkling (blurry) stars. The Space Telescope, by being outside the earth’s atmosphere, will enable us to see images that are ten times smaller (or less fuzzy) than with ground-based optical telescopes. This tenfold increase in resolution will permit us to study nearby known objects in much greater detail or to detect stellar counterparts at about ten times greater distance than is possible from earth. If the universe had a beginning, we should be able to detect objects all the way back to between 75% to 95% of the beginning of time.23

Having wowed the committee with the telescope’s possible scientific payoffs, Bahcall turns at the end of his testimony to a series of economic reasons for funding. First, without it, NASA would have to disband an expert team of US and foreign astronomers assembled over the previous five years. Second, without it, the substantial investments already made earlier by industrial firms would go to waste. Third, the European Space Agency had pledged to spend almost $90 million ($440 million in 2022 dollars) on the project, and those funds would likely go elsewhere. Fourth, the Hubble Space Telescope would take advantage in a major way of the first space shuttle being built, an example of one multi-million-dollar project justifying another. In the final paragraph, Bahcall returns to a scientific argument for the telescope, grandly linking it with Galileo’s telescope: “I hope, and believe, that the Space Telescope might make the Big Bang cosmology appear incorrect to future generations, perhaps somewhat analogous to the way Galileo’s telescope showed that the earth-centered, Ptolemaic system was inadequate.” Bahcall’s arguments and analogy won the day. Congress approved $36 million for 1978 ($164 million in 2022 dollars), with a projected launch date of 1983—off by a mere seven years.24 In the weeks after the successful launch into orbit with space shuttle Discovery on April 24, 1990, it became increasingly clear that the telescope’s mirror was flawed, a defect caused by a hitherto undetected grinding error.25 The deviation, the thickness of only half a dime, subjected the telescope’s images to serious 194

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distortion that provided a prime opportunity for NASA jokes by late-night comedians and cartoonists. Apparently, US taxpayers had paid millions for 24,500 pounds of space junk. Who was to blame for the flawed mirror? What went wrong and why? To NASA, it was the fault of the manufacturer that the telescope’s mirror was defective; to the manufacturer, it was because of NASA’s failure of oversight. A Board of Investigation, a panel of experts headed by Lew Allen, director of the Jet Propulsion Laboratory, conducted a failure analysis. They determined that both parties were at fault, as reported in a 120-page NASA technical memorandum and announced at a news conference in Washington, DC. The report’s purpose was to identify the cause of the failure and assign responsibility, come what may, thereby reassuring any questioning congressional committees of due diligence. The language in the report’s executive summary is straightforward; while technical, it is meant to be understandable by any legislator or interested taxpayer, as evidenced by these few paragraphs: The primary mirror [in the space telescope] is a disc of glass 2.4 m [just under eight feet] in diameter, whose polished front surface is coated with a very thin layer of aluminum. When the glass is polished, small amounts of material are worn away, so that by selectively polishing different parts of the mirror, the shape is altered. During the manufacture of all telescope mirrors there are many repetitive cycles in which the surface is tested by reflecting light from it; the surface is then selectively polished to correct any errors in its shape. The error in the HST’s [Hubble Space Telescope’s] mirror occurred because the optical test used in this process was not set up correctly; thus the surface was polished into the wrong shape. The primary mirror was manufactured by the Perkin-Elmer Corporation, now Hughes Danbury Optical Systems, Inc., which was the contractor for the Optical Telescope Assembly. The critical optics used as a template in shaping the mirror, the reflective null corrector (RNC), consisted of two small mirrors and a lens. The RNC was designed and built by the Perkin-Elmer Corporation for the HST Project. This unit has been preserved by the manufacturer exactly as it was during the manufacture of the mirror. When the Board [of Investigation] measured the RNC, the lens was incorrectly spaced from the mirrors. Calculations to the effect of such displacement on the primary mirror show that the measurement, 1.3 mm [half the thickness of a dime], accounts in detail for the amount and character of the image blurring.

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THE MANY VOICES OF MODERN PHYSICS No verification of the reflective null corrector’s dimensions was carried out by Perkin-Elmer after the original assembly. There were, however, clear indications of the problem from auxiliary optical tests made at the time, the results of which have been studied by the Board. A special optical unit called an inverse null corrector, designed to mimic the reflection from the primary mirror, was built and used to align the apparatus; when so used, it clearly showed the error in the primary mirror. A second null corrector, made only with lenses, was used to measure the vertex radius [and important shape parameter in optics] of the finished primary mirror. Both indicators of error were discounted at the time as being themselves flawed. The Perkin-Elmer plan for fabricating the primary mirror placed complete reliance on the reflective null corrector as the only test to be used in both manufacturing and verifying the mirror’s surface with the required precision. NASA understood and accepted this plan. The methodology should have alerted NASA management to the fragility of the process and the possibility of gross error, that is, a mistake in the process, and the need for continued care and consideration of independent measurements.26

The authors do not beat around the bush in spelling out what went awry. They also identify the responsible parties. True, most of the sentences have passive voice verbs, a common rhetorical tactic for avoiding having to assign blame to the agent of an action, as in “The prisoner was executed.” However, several key passive voice sentences do specify the agent in the complement to the verb; namely, the Perkin-Elmer Corporation. And the responsible agent in one active voice sentence stands out clearly: “NASA understood and accepted this [Perkin-Elmer’s flawed] plan.” In the end, the US government sued the manufacturer, who settled for a mere $25 million ($57 million in 2022 dollars) without admitting fault, and Congress approved a very expensive repair mission to fix the identified problem.27 Back in his 1977 testimony, Bahcall mentioned the possibility of “in-orbit repair and replacement of equipment by shuttle crewmen,” should anything go wrong. Little did he realize how important that would become in 1990. NASA’s planning for the Hubble in-orbit repair mission took three years. A technical solution to its flawed optics had to be invented and approved, a training program had to be devised, and seven experienced astronauts had to be selected and subjected to over a year of rigorous training. On December 2, 1993, space shuttle Endeavour was launched toward the Hubble Space Telescope. The seven astronauts—six men and one woman—were all aware of the significance of the mission, to be televised for the world to see. At a press briefing in June, Hubble project scientist Edward J. Weiler made this 196

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Figure 8.3. Hubble photographs of the galaxy Messier 100 before and after Hubble repair. Image credit: NASA.

significance clear: “This project is going to be in the history books, whether we like it or not, whether as a national disgrace or a triumph.”28 The repair mission was a tribute to the expert failure analysis in the Lew Allen memorandum, the skills of the astronauts, the expertise of the NASA team behind them, and the design of the new technology for scientific discovery despite the earlier flaw. The before-and-after photographs of the galaxy Messier 100 in figure 8.3 make the point visually.29

International Patronage and the Cassini-Huygens Spacecraft It is no exaggeration to claim that the Cassini-Huygens mission to Saturn was one of the more successful exploratory missions ever launched into our solar system. Stowed away in the main vehicle—named the Cassini orbiter—was the Huygens probe, which parachuted down to Titan, Saturn’s largest moon, a moon slightly larger than the planet Mercury. Both vehicles were stuffed with scientific instruments and cameras designed to gather data and images under the most hostile of conditions. Total distance traveled by the pair reached almost five billion miles over twenty years, including 294 orbits of Saturn. As was the case for the Hubble Space Telescope, such ambitious space missions do not come cheap. This joint American-European endeavor cost $5.6 billion (in 2022 dollars) and generated 3,948 scientific papers, or about $1,418,000 each. The spacecraft’s journey to Saturn begins with the advocacy of astronaut Sally Ride. Her advocacy of space missions in general largely rests on an argument that they are in the national interest: 197

THE MANY VOICES OF MODERN PHYSICS The United States has clearly lost leadership in these two areas, and is in danger of being surpassed in many others during the next several years. . . . The National Space Policy of 1982, which “establishes the basic goals of United States policy,” includes the directive to “maintain United States space leadership.” It further specifies that “the United States is fully committed to maintaining world leadership in space transportation,” and that the civilian space program “shall be conducted . . . to preserve the United States leadership in critical aspects of space science, applications, and technology.” Leadership cannot simply be proclaimed—it must be earned. As NASA evaluates its goals and objectives within the framework of the National Space Policy, the agency must first understand what is required to “maintain U.S. space leadership,” since that understanding will direct the selection of national objectives. Leadership does not require that the U.S. be preeminent in all areas and disciplines of space enterprise. In fact, the broad spectrum of space activities and the increasing number of spacefaring nations make it virtually impossible for any nation to dominate in this way. Being an effective leader does mandate, however, that this country have capabilities which enable it to act independently and impressively when and where it chooses, and that its goals be capable of inspiring others—at home and abroad—to support them. It is essential for this country to move promptly to determine its priorities and to make conscious choices to pursue a set of objectives which will restore its leadership status.

The Cassini-Huygens scientific mission was central to Ride’s agenda for helping to keep NASA at the forefront of space exploration: The Cassini mission proposed in this initiative would be a considerably expanded version of the Cassini mission considered by the Solar System Exploration Committee. . . . This expanded mission would be launched in 1998 for the long interplanetary voyage to arrive at Saturn in 2005 with a full array of investigative instruments. An orbital spacecraft and three probes would conduct a comprehensive three-year study of the planet and its rings, satellites, and magnetosphere. One atmospheric probe would be launched toward Titan. The expanded Cassini mission would also carry one probe to investigate the Saturnian atmosphere, and one semi-soft lander which would reach the surface of Titan.30

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The Cassini-Huygens mission could get off the ground only with congressional approval. Such approval typically requires strong arguments of not only national interest and scientific payoff but also economic value. As but one small example, on August 9, 1988, at a Senate hearing, subcommittee member Wyche Fowler of Georgia defended funding the Cassini-Huygens mission as a necessary step in furthering “the American space program and a leadership role for American space science” in cooperation with the European Space Agency. Fowler provides this fiscal justification: “By combining CRAF [Comet Rendezvous Asteroid Flyby] and Cassini into a joint development program, significant economies are possible. I am told that each mission, if pursued separately would have a total cost of approximately $1 billion, while the joint program would have a total cost of $1.5 billion, thus representing a 25 per cent saving.”31 This is reasoning any devoted shopper can understand. Also important in terms of communicating economic value are success stories published after the funds have been won and spent. One such source of success stories in this case is NASA’s website. There we learn that the Huygens probe, the stowed-away passenger on the Cassini-Huygens spacecraft, reaped substantial dividends for its sponsoring institutions, the European Space Agency and NASA. Six years after launch, it uncoupled from Cassini over Titan and began a parachute descent, chronicled by NASA’s website in typical NASA-speak with a rare flicker of emotion: On Christmas Day 2004 at 02:00 UT [universal time], the Huygens lander, which had remained dormant for more than six years, separated from Cassini and began its 22-day coast to Titan. It entered Titan’s atmosphere at 09:05:56 UT Jan. 14, 2005, and within four minutes had deployed its 28-foot (8.5-meter) diameter main parachute. A minute later, Huygens began transmitting a wealth of information back to Cassini for more than two hours before impacting on the surface of Titan at 11:38:11 UT at a velocity of 15 feet per second (4.54 meters per second). Landing coordinates were 192.32 degrees west longitude and 10.25 degrees south latitude, about 4 miles (7 kilometers) from its target point. A problem in the communications program limited the number of images that Huygens transmitted to Cassini, from about 700 to 376. Yet, to the excitement of planetary scientists back on Earth, it continued its transmissions for another three hours and 10 minutes during which it transmitted a view of its surroundings (224 images of the same view).

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THE MANY VOICES OF MODERN PHYSICS Huygens appears to have landed on a surface resembling sand made of ice grains. Surface pictures showed a flat plain littered with pebbles as well as evidence of liquid acting on the terrain in the recent past. Subsequent data confirmed the existence of liquid hydrocarbon lakes in the polar regions of Titan.32

The Huygens probe’s images revealed a planet-size moon with a methane-filled atmosphere and surface bearing some resemblance to what might have been the case on Earth 2.4 billion years ago. The scientific payoff for the international patronage is thus not just knowledge about Saturn and one of its moons, but the evolution of Earth itself.

International Patronage and Gravitational Wave Detectors Gravitational waves are a form of radiation outside the electromagnetic spectrum of radio waves, microwaves, infrared, visible light, ultraviolet, X-ray, and gamma ray. By 2015, while all of these had been harnessed in the interest of astronomical discovery, gravitational waves had not. Predicted by Albert Einstein with his general relativity equations in 1916–1918, these waves are tiny ripples in the fabric of space-time created by cataclysmic astronomical events, such as black holes when they merge. Because gravitational waves are so weak when they reach us, it seemed unlikely they would ever be detected. And they never were, until September 14, 2015, and at a modest expense judged by the standards of America’s space program. While NASA thinks in billions, earthbound astronomers must rely on the far leaner budget of the National Science Foundation (NSF). Even so, the riskiness of this venture led its advocates into a long struggle for the needed start-up funding. The original idea was to detect gravitational waves in an experiment using laser beams, where two or more beams merge to create an interference pattern that can detect passing gravitational waves. It began as a possible answer to a problem posed in a thought experiment carried out in a relativity class at MIT given by Rainer Weiss in the late 1960s. Weiss described his classroom thought experiment in an interview with physicist Janna Levin: I gave as a problem, as a Gedanken [thought experiment] problem, the idea, “Well, let’s measure gravitational waves [wave-like stretching and squeezing of space itself] by sending light beams between things,” because that was something you could solve. The idea was that there was an object [a mirror reflecting light]. You’d put another object here and make a right triangle of objects, floating freely in a vacuum. And we’d send light beams between them and then be able to figure out, “What does the gravitational wave

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ASTRONOMICAL VALUE do to the time it takes light to go between those things?” [If gravitational waves had distorted space, the light beams will be measurably out of phase.] It was a very stylized problem, like a haiku, you know? You’d never think that it was of any value.33

Some fifteen years later, that haiku-like thought experiment, plus many other factors, led to a three-year feasibility study for a Big Science project to detect gravitational waves, the results of which were communicated in a 419-page report submitted to the NSF. According to Levin, “The estimate was [the project is doable at] just under $100 million [$300 million in 2022 dollars] for two instruments in the kilometer-scale range, bare-bones.”34 Soon after this report, the project got a name that does not exactly trip off the tongue: the Laser Interferometer Gravitational-Wave Observatory (LIGO). Preliminary studies with small prototype interferometers followed. It was not until almost a decade later that the NSF awarded $395 million ($800 million in 2022 dollars) to design, construct, and operate the first LIGO, a scientific instrument whose purpose was, not (alas) to detect gravitational waves, but to serve as the basis for designing an improved LIGO that actually would later do so. This was the largest grant NSF had ever made, a tribute to an unusual bureaucracy, one that believed in venture capital. It was also a tribute to Barry Barish, LIGO’s new prime investigator. In Barish LIGO had found its J. Robert Oppenheimer, the physicist whose management genius made the Manhattan Project possible. It was Barish who saw LIGO as essentially a management problem, an international effort as complex at least as the Manhattan Project.35 What exactly did the NSF and multiple other funding organizations fund? It was a pair of gravitational wave observatories with two four-kilometer-long arms able to detect changes in distance ten thousand times smaller than a proton. One observatory was located in Hanford, Washington; the other in Livingston, Louisiana. And on September 14, 2015, they detected the same passing gravitational wave—a ripple in space-time. LIGO’s scientific reach extended far beyond Washington and Louisiana. The discovery paper has 1,012 authors,36 all of whom contributed at least 50 percent of their professional time to the project. They hailed from Australia, Belgium, Brazil, Canada, China, France, Germany, Hungary, India, Italy, Japan, the Netherlands, Poland, the Republic of China-Taiwan, Russia, Spain, South Korea, the United Kingdom, and the United States. Stuck in a fairy-tale past where lonely theoreticians scribbled on blackboards and lonely experimenters fiddled with tabletop apparatus, the Nobel Prize committee awarded the 2017 Nobel Prize in Physics for the detection of gravitational waves to only three 201

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leading figures: Kip Thorne, Rainer Weiss, and Barry Barish. In their Nobel Prize lectures each made it clear that they were accepting the prize, not for themselves, but on behalf of the collaboration they led. The list of acknowledgments for international patronage in the LIGO discovery paper is as astonishing as the author list, presented in a dry language that is a far cry from Galileo-like flattery but impressive nonetheless simply by virtue of the sheer number of sponsors: The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck Society (MPS), and the State of Niedersachsen, Germany, for support of the construction of Advanced LIGO and construction and operation of the GEO 600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Instituto Nazionaledi Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS), and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector [a European collaboration of 106 institutions in 12 countries], and for the creation and support of the EGO [European Gravitational Observatory] consortium. The authors also gratefully acknowledge research support from these agencies as well as by the Council of Scientific and Industrial Research of India, Department of Science and Technology, India, Science & Engineering Research Board (SERB), Ministry of Human Resource Development, India, Spanish Ministerio de Economía y Competitividad, the Conselleria d’Economia i Competitivitat and Conselleria d’Educació, Cultura i Universitats of the Govern de les Illes Balears, the National Science Centre of Poland, the European Commission, the Royal Society, the Scottish Funding Council, the Scottish Universities Physics Alliance, the Hungarian Scientific Research Fund (OTKA), the Lyon Institute of Origins (LIO), the National Research Foundation of Korea, Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation, the Natural Sciences and Engineering Research Council of Canada, Canadian Institute for Advanced Research, the Brazilian Ministry of Science, Technology, and Innovation, Russian Foundation for Basic Research, the Leverhulme Trust, the Research Corporation, Ministry of Science and Technology (MOST), Taiwan, and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, MPS,

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ASTRONOMICAL VALUE INFN, CNRS and the State of Niedersachsen, Germany, for provision of computational resources.37

Despite the length of the discovery paper—far exceeding the limits set by Physical Review Letters—LIGO sent it to this prestigious journal hoping for rapid publication. In three weeks, it was in print and available online, a tribute to the good judgment of all concerned. An editor emailed the paper-writing team: “The stat that really struck me was that in the first 24 hrs. not only was the page for your PRL abstract hit 380K [thousand] times, but the PDF of the paper was downloaded from that page 230K times. This is far more hits than any PRL ever, and the fraction of times that it resulted in a download was unusually high. Hundreds of thousands of people actually wanted to read the whole paper!”38 The discovery also made it into newspapers and on social media around the world. As a consequence of this sudden fame, gravitational waves subsequently entered the pantheon of everyday science speak, joining black holes, the big bang, wormholes, and quarks, terms whose widespread use is decidedly not a sign of increasing scientific literacy. The discovery paper is written as a history of gravitational wave astronomy, starting with Einstein’s 1916 paper on general relativity and culminating in the LIGO revelation. The big reveal was that two black holes—two collapsed stars— spiraled toward each other, and a gravitational wave emerged from ringdown, the time for the wave intensity to reach a maximum as the black holes merge. Over a billion years later, this wave washed over Earth to be detected by LIGO: “The LIGO detectors have observed gravitational waves from the merger of two stellar-mass black holes. The detected waveform matches the predictions of general relativity for the in-spiral and merger of a pair of black holes and the ringdown of the resulting single black hole. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.”39 In figure 8.4, we reproduce the graphs from Barish’s Nobel Prize lecture, redesigned from the original scientific paper for easier comprehension by a general audience. While the visual impact is immediate due to the amazing agreement among the graphs, it needs to be said that LIGO results usually lack such visual drama. For added dramatic impact, the LIGO team converted their measurements into sound waves, so a cosmic chirp rings out upon the black hole merger. A recording of that chirp made this story hard to resist for any internet-based news organization.40 In his Nobel Prize lecture, Kip Thorne anticipates that LIGO will continue to produce astronomical value in understanding the cosmos: “At each higher order in the computation, there are new observables that can be extracted from 203

Figure 8.4. A dramatic measurement: “The first direct detection of gravitational waves and the first observation of a binary black hole merger.” Excellent agreement of predicted and measured curves from the LIGO detectors at both Hanford (top) and Livingston (middle). Same excellent agreement of measured curves from the two observatories (bottom). Original in color. This figure is a part of Barry Barish’s Nobel Prize lecture. Copyright © The Nobel Foundation, 2017.

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the observed waves. These include, most importantly, the individual masses M1 and M2 of the binary’s two bodies, and their vectorial spin angular momenta; and, if the binary’s orbit is not circular, then its evolving ellipticity and elliptical orientation, and relativistic deviations from elliptical motion. And at each order, there are new opportunities to test, observationally, Einstein’s general relativity theory—tests that are now being carried out with LIGO’s observational data.”41 Moreover, he anticipates a bright future for an astronomy that will employ in concert every means of detecting each form of cosmic radiation. This is a future that extends beyond his career—indeed, beyond his life. Just as in the discovery paper, Thorne places LIGO’s achievement in its historical context, but he reaches back to Galileo instead of Einstein: Four hundred years ago, Galileo built a small optical telescope and, pointing it at Jupiter, discovered Jupiter’s four largest moons; and pointing it at our moon, discovered the moon’s craters. This was the birth of electromagnetic astronomy. Two years ago, LIGO scientists turned on their Advanced LIGO detector and, with the data-analysis help of VIRGO [European detector in Pisa, Italy], discovered the gravitational waves from two colliding black holes 1.3 billion light years from Earth. When we contemplate the enormous revolution in our understanding of the universe that has come from electromagnetic astronomy over the four centuries since Galileo, we are led to wonder what revolution will come from gravitational astronomy, and from its multi-messenger partnerships [that is optical, infra-red, gamma, radio, and X-ray telescopes], over the coming four centuries.

The implied message behind the analogy with Galileo’s telescope is that future funding for LIGO and similar gravitational astronomy projects is well worth the sizable international investment required.

Just as the microscope has permitted scientists to visualize smaller and smaller objects, increasingly powerful and expensive telescopes have permitted the visualization of greater and greater distances from Earth. We start with Galileo Galilei, who explored our solar system—the center of the universe at the time—with a do-it-yourself portable telescope. Funded by King George III and with telescopes up to forty feet in length, the Herschel family explored and mapped the solar system and the stars in the Milky Way, with our sun just one of countless others. With a much more powerful telescope in California funded by wealthy businessmen, Edwin Hubble photographed tiny specks of light from 205

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galaxies beyond the Milky Way. Hubble’s measurements of galaxy distance and velocity provided tantalizing evidence that the universe might not be static but expanding after a big bang. With a radio telescope built by Bell Labs for research on satellite communications, two scientists stumbled on cosmic microwave background radiation—the relic radiation from the big bang. Funded by the largess of American taxpayers—part of a larger project to map the universe—the Hubble Space Telescope visualized in extraordinary detail the insides of galaxies and revealed that there are billions of galaxies beyond our own, while with international funding the Cassini-Huygens mission to Saturn photographed its rings, then parachuted down to one of its moons and photographed the surface up close and personal. In a daring quarter-century project funded in part by taxpayers from around the world, LIGO detected the gravitational waves predicted by general relativity, ripples in space-time created by the collision of two black holes over a billion years ago. This new astronomical observatory will likely be as important as the telescope for exploring the universe in the coming centuries and may one day even detect the remnant sounds from the big bang. The enormous expenditures needed to fund contemporary astronomical research like the above makes streams of persuasive communication in various genres vital, justifying the cost with arguments of national interest, the lure of potential scientific discoveries that rival Galileo’s, and stories of successful missions completed. Whether they are tax-collecting governments, taxpaying citizens, or wealthy individuals, patrons need to be reassured that the return on their investment will match or exceed their expectations while other funds are still available to meet pressing societal needs.

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Anticipated and Unanticipated Consequences

In an early paper from his illustrious career, sociologist Robert Merton defines unanticipated consequences of one’s actions in stodgy but perceptive prose: “However, deviations from the usual consequences of an act may be anticipated by the actor who recognizes in the given situation some differences from previous similar situations. But, insofar as these differences can themselves not be subsumed under general rules, the direction and extent of these deviations cannot be anticipated. It is clear, then, that the partial knowledge in the light of which action is commonly carried on permits a varying range of unexpected outcomes of conduct.”1 When Adolf Hitler decided to rid Europe of Jews, his actions inadvertently resulted in a clean sweep of elite physicists wishing to avoid the persecution awaiting many millions: Niels Bohr, Hans Bethe, Felix Bloch, Albert Einstein, James Franck, Otto Frisch, Lise Meitner, Rudolf Peierls, Joseph Rotblat, Emilio Segrè, Leo Szilard, Edward Teller, Stanislaw Ulam, Eugene Wigner, and Enrico Fermi, whose wife was Jewish.All were vital to the development of a bomb whose use helped end the war with Japan, an unanticipated consequence of statesponsored antisemitism.2 In Los Alamos, New Mexico, where the atomic bomb was assembled, the lives of those physicists who participated were disrupted by the unaccustomed need for intense interdisciplinary collaboration, a temporary way of working that led to an unanticipated permanent transformation in the organization of scientific research. 207

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The development of this new scientific thing also led to many different sorts of communications in addition to the usual suspects. We will be examining letters from physicists to politicians arguing for the urgency of the bomb’s development, classified scientific reports issued during its development about the technicalities and destructive capabilities, personal accounts about the story behind its top-secret development, and essays arguing about the morality of an anticipated consequence from its development: instant mass destruction in a flash of light brighter than the sun.

Splitting the Atom The atom has two main working parts: a nucleus and an electron or collection of electrons. The nucleus contains positively charged protons and neutral neutrons. The nucleus controls the decay or radioactivity of certain elements—the spontaneous loss of energy due to the emission of a subatomic particle. This process is the foundation of nuclear physics starting in the early twentieth century. The journey to the nuclear age begins in earnest in 1938 when radiochemist Otto Hahn meets in Copenhagen with his erstwhile collaborator Lise Meitner, exiled by antisemitism. He reports a perplexing experimental result: the bombardment of uranium nuclei with the newly discovered neutrons has yielded isotopes of radium. Meitner urges Hahn to return to Berlin and continue to investigate. Using a different experimental method, he finds not radium but barium, its atomic number about half that of uranium. What was the explanation for this unanticipated result? From Berlin an incredulous Hahn wrote to Meitner: “Perhaps you can come up with some sort of fantastic explanation. We knew ourselves that it [uranium] can’t actually burst apart into Ba [barium].”3 In conversation with her nephew Otto Frisch, also a Jewish physicist in exile, Meitner hits upon the “liquid drop model,” pioneered by George Gamow and refined by Niels Bohr. It is more than an analogy: it is a formulation with significant explanatory power: On the basis . . . of present ideas about the behavior of heavy nuclei [in particular here, uranium, comprising 92 protons and more than 140 neutrons], an entirely different and essentially classical picture of these new disintegration processes suggests itself. On account of their close packing and strong energy exchange, the particles in a heavy nucleus would be expected to move in a collective way which has some resemblance to the movement of a liquid drop. If the movement is made sufficiently violent by adding energy, such a drop may divide itself into two smaller drops. 

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THE ATOMIC BOMB In the discussion of the energies involved in the deformation of nuclei, the concept of surface tension has been used and its value has been estimated from simple considerations regarding nuclear forces. It must be remembered, however, that the surface tension of a charged droplet is diminished by its charge, and a rough estimate shows that the surface tension of nuclei, decreasing with increasing nuclear charge, may become zero for atomic numbers of the order of 100 [the atomic number of uranium is 92].  It seems therefore possible that the uranium nucleus has only small stability of form, and may, after neutron capture, divide itself into two nuclei of roughly equal size (the precise ratio of sizes depending on finer structural features and perhaps partly on chance). These two nuclei will repel each other and should gain a total kinetic energy of c. 200 Mev. [about two hundred million electron volts], as calculated from nuclear radius and charge. This amount of energy may actually be expected to be available from the difference in packing fraction between uranium and the elements in the middle of the periodic system. The whole “fission” process can thus be described in an essentially classical way, without having to consider quantum-mechanical “tunnel effects,” which would actually be extremely small, on account of the large masses involved.4 

Meitner and Frisch’s analogy is simply that the heavy elements, like uranium, are so large that they are as unstable as a large liquid drop. This led them to the conclusion that when struck by a speeding free neutron, a uranium “droplet” would split into two smaller drops, releasing energy in the process. What is not stated in their paper is almost as important as what is: after this splitting, the analogy would morph from liquid drop to chain reaction. In a uranium mass of uncertain size, the split uranium atom would emit neutrons, which could then strike and split another nearby uranium atom, and so on in a chain reaction with a tremendous release of energy in accord with Einstein’s famous equation E = mc2. This tacit implication was evident to savvy physicists at that time able to read between the lines. In the words of physicist Leo Szilard, yet another Jewish physicist in exile, “When I heard this [about the Meitner-Frisch paper in 1939] I immediately saw that . . . if enough neutrons are emitted . . . then it should be, of course, possible to sustain a chain reaction. All the things H. G. Wells predicted appeared suddenly real to me.”5 It was in 1914 that Wells, in the science fiction novel The World Set Free, had first imagined the existence of an atomic bomb—a black sphere with diameter of two feet containing uranium and thorium inside and handles outside to carry it around. 209

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After the Meitner-Frisch paper, research into the fission reaction proceeded with a stampede of discoveries.6 Bohr, for example, followed up with some brilliant detective work with natural uranium. It led physicists to the discovery that neutrons bombarding a rare isotope of uranium, uranium-235 (also written as U235), could initiate a chain reaction that made a bomb possible. A very tiny percentage of this isotope appears in natural uranium (greater than 99 percent U238). But physicists initially believed that no one would ever isolate enough of this isotope to realize a superweapon. That conclusion turned out to be wishful thinking. Rudolf Peierls—a Jewish physicist working in England—calculated that neutrons with very high energy, “fast neutrons,” would ignite a chain reaction in only a few pounds of uranium-235.

Secret Pleas for Action The rise of Nazi Germany, and the possibility that their physicists would develop a superbomb, made a race to a weapons program appear urgent. It was this that led Leo Szilard and Eugene Wigner to ask Albert Einstein to sign and send a letter to President Franklin Delano Roosevelt in the summer of 1939. Roosevelt already knew Einstein, not only by reputation but also personally, having invited the physicist and his wife to dinner at the White House.7 Having alerted Roosevelt to the fact that a mass of uranium could sustain a nuclear chain reaction “by which vast amounts of power and large quantities of new radium-like elements would be generated,” the letter recommends two courses of governmental action and warns that Germany may already be on the road to a superbomb: In view of this situation you may think it desirable to have some permanent contact maintained between the Administration and the group of physicists working on chain reactions in America. One possible way of achieving this might be for you to entrust with this task a person who has your confidence and who could perhaps serve in an official capacity. His task might comprise the following: a) to approach Government Departments, keep them informed of the further development, and put forward recommendations for Government action, giving particular attention to the problem of securing a supply of uranium ore for the United States. b) to speed up the experimental work, which is at present being carried on within the limits of the budgets of University laboratories, by providing funds, if such funds be required, through his contacts with private persons who are willing to make contributions for this cause, and perhaps also by obtaining the co-operation of industrial laboratories which have the necessary equipment.

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THE ATOMIC BOMB I understand that Germany has actually stopped the sale of uranium from the Czechoslovakian mines which she has taken over. That she should have taken such early action might perhaps be understood on the ground that the son of the German Under-Secretary of State, von Weizsäcker, is attached to the Kaiser-Wilhelm-Institut in Berlin where some of the American work on uranium is now being repeated. 8

Convinced, President Roosevelt authorized funds to get a small project under way, a project that would end up costing about $38 billion (in 2022 dollars), involving more than 125,000 scientists and support staff. Meanwhile, in England in early 1940, Frisch and Peierls wrote a short technical memorandum that was sent to the Committee on the Scientific Survey of Air Defense, the most important British committee concerned with wartime research. It begins with a chilling cover letter that gets right to the point: The attached detailed report concerns the possibility of constructing a “super-bomb” which utilizes the energy stored in atomic nuclei as a source of energy. The energy liberated in the explosion of such a super-bomb is about the same as that produced by the explosion of 1,000 tons of dynamite. This energy is liberated in a small volume, in which it will, for an instant, produce a temperature comparable to that in the interior of the sun. The blast from such an explosion would destroy life in a wide area. The size of this area is difficult to estimate, but it will probably cover the center of a big city. In addition, some part of the energy set free by the bomb goes to produce radioactive substances, and these will emit very powerful and dangerous radiations. The effect of these radiations is greatest immediately after the explosion, but it decays only gradually and even for days after the explosion any person entering the affected area will be killed. Some of this radioactivity will be carried along with the wind and will spread the contamination; several miles downwind this may kill people. In order to produce such a bomb it is necessary to treat a substantial amount of uranium by a process which will separate from the uranium its light isotope (U235) of which it contains about 0.7 percent. Methods for the separation of such isotopes have recently been developed. They are slow and they have not until now been applied to uranium, whose chemical properties give rise to technical difficulties. But these difficulties are by no means insuperable. We have not sufficient experience with large-scale chemical plant[s] to give a reliable estimate of the cost, but it is certainly not prohibitive.

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THE MANY VOICES OF MODERN PHYSICS It is a property of these super-bombs that there exists a “critical size” of about one pound. A quantity of the separated uranium isotope that exceeds the critical amount is explosive; yet a quantity less than the critical amount is absolutely safe. The bomb would therefore be manufactured in two (or more) parts, each being less than the critical size, and in transport all danger of a premature explosion would be avoided if these parts were kept at a distance of a few inches from each other. The bomb would be provided with a mechanism that brings the two parts together when the bomb is intended to go off. Once the parts are joined to form a block which exceeds the critical amount, the effect of the penetrating radiation always present in the atmosphere will initiate the explosion within a second or so.9

In chilling language any politician can follow, Peierls and Frisch’s cover letter lays out the destructive power of this superweapon and a plausible method for making one. Because this cover letter might have been read as Wells–like science fiction, the accompanying technical memorandum provided technical details to convince any scientific advisors that the basic nuclear physics was already in place. It was now a matter of engineering such a device, in particular, the technical challenges in manufacturing enough weapons-grade material of uranium-235, of which natural uranium only contains 0.7 percent. This cover letter and technical memorandum had the anticipated effect: the British government soon started a serious and secret atomic weapon program.10

First Controlled Chain Reaction The war with the Axis powers having begun, neither Nature, Science, Physical Review, nor Physical Review Letters was to hear much from many American or British atomic physicists until total victory was achieved. Silence and secrecy also prevailed, when, on a cold winter day in the squash courts below the disused University of Chicago football stadium in December 1942, Enrico Fermi and colleagues created a uranium-based chain reaction that might be used for not only power generation but also production of weapons-grade plutonium (plutonium-239), a feat commemorated today with a sculpture by Henry Moore constructed in the mid-1960s. Moore comments on what the sculpture, Nuclear Energy, meant to him: When I had made this working model I showed it to them [University of Chicago representatives] and they liked my idea because the top of it is like some large mushroom, or a kind of mushroom cloud [the destructive side of the atom]. Also it has a kind of head shape like the top of the skull but

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THE ATOMIC BOMB down below is more an architectural cathedral. One might think of the lower part of it being a protective form and constructed for human beings [the peaceful side of the atom] and the top being more like the idea of the destructive side of the atom. So between the two it might express to people in a symbolic way the whole event.11

In his postwar memoir, which focused on the peaceful side of the atom, Fermi described this first controlled fission reaction as being as easily manipulated as an automobile on a highway: On the morning of December 2, 1942, the indications were that the critical dimensions [in a large pile of graphite bricks containing uranium] had been slightly exceeded and that the system did not chain-react only because of the absorption of the cadmium strips [powerful absorbers of neutrons]. During the morning all the cadmium strips but one were carefully removed; then this last strip was gradually extracted, close watch being kept on the intensity. From the measurements it was expected that the system would become critical by removing a length of about eight feet of this last strip. Actually, when about seven feet were removed the intensity rose to a very high value but still stabilized after a few minutes at a finite level. It was with some trepidation that the order was given to remove one more foot and a half of the strip. This operation would bring us over the top. When the foot and a half was pulled out, the intensity started rising slowly, but at an increasing rate, and kept on increasing until it was evident that it would actually diverge. Then the cadmium strips were again inserted into the structure and the intensity rapidly dropped to an insignificant level. This prototype of a chain-reacting unit proved to be exceedingly easy to control. Intensity of its operation could be adjusted with extreme accuracy to any desired level. All the operator has to do is to watch an instrument that indicates the intensity of the reaction and move the cadmium strips in if the intensity shows a tendency to rise, and out if the intensity shows a tendency to drop. To operate a pile is just as easy as to keep a car running on a straight road by adjusting the steering wheel when the car tends to shift right or left. After a few hours of practice an operator can keep easily the intensity of the reaction constant to a very small fraction of 1 per cent. The first pile had no device built in to remove the heat produced by the reaction and it was not provided with any shield to absorb the radiations produced by the fission process. For these reasons it could be operated only at a nominal power which never exceeded two hundred watts [enough to

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THE MANY VOICES OF MODERN PHYSICS light two light bulbs]. It proved, however, two points: that the chain reaction with graphite and natural uranium was possible, and that it was very easily controllable. A huge scientific and engineering development was still needed to reduce to industrial practice the new art. Through the collaboration of all the men [and women] of the Metallurgical project [code name for Fermi’s group at the University of Chicago] and of the Du Pont Company, only about two years after the experimental operation of the first pile large plants based essentially on the same principle were put in operation by the Du Pont Company at Hanford, producing huge amounts of energy [for peaceful purposes] and relatively large amounts of the new element, plutonium [for an atomic weapon].12

Fermi tells us just what his team did and just what happened in a straightforward way. His is an impersonal prose stripped of the emotions he must have felt. Not “I gave the order,” but “the order was given”; not another step on the way to an atomic bomb, but a nuclear process whose control was no more difficult than driving along the highway, a process whose perpetuity is signaled by a switch from the past to the present tense. Paradoxically, Fermi’s restrained language still manages to convey a sense of the drama. Wigner, an observer of the first controlled chain reaction in Chicago, tells us what Fermi left out: “For some time, we had known we were about to unlock a giant; still, we could not escape an eerie feeling when we knew we had actually done it. We felt, as I presume everyone feels who had done something he knows will have very far-reaching consequences which he cannot foresee.”13

Gadget Development at Secret Site The Fermi group’s work came to fruition for wartime purposes in a small town that appeared suddenly on a mesa in a beautiful but remote part of New Mexico. Few knew of Los Alamos’s existence. Its workers had a single charge: engineer a superweapon by an uncontrolled chain reaction before the Germans. Shortly upon arrival, new recruits received a crash course on building the “gadget,” delivered by Robert Serber, a protégé of Los Alamos director J. Robert Oppenheimer. Those formerly classified lectures, The Los Alamos Primer, were distributed to incoming Los Alamos staff with a need to know. Because some had limited knowledge of the subject matter, Serber kept the technical and mathematical detail to a minimum. He opens with a blunt statement on “the object,” its destructive power, and the mechanism behind that power: 214

THE ATOMIC BOMB The object of the project is to produce a practical military weapon in the form of a bomb in which the energy is released by a fast neutron chain reaction in one or more of the materials known to show nuclear fission. The direct energy release in the fission process is of the order of 170 MEV [million electron volts] per atom. This is considerably more than 107 times the heat of reaction per atom in ordinary combustion processes. . . . Release of this energy [estimated to be equivalent to twenty thousand tons of TNT from a kilogram of uranium-235] in a large scale way is a possibility because of the fact that in each fission process, which requires a neutron to produce it, two neutrons are released. Consider a very great mass of active material, so great that no neutrons are lost through the surface and assume the material so pure that no neutrons are lost in other ways than by fission. One neutron released in the mass would become 2 after the first fission, each of these would produce 2 after they each had produced fission so in the nth generation of neutrons there would be 2n neutrons [exponential increase] available.14

Serber devotes a short section to the foreseen consequences of using the weapon—the damage that such a reaction could wreak. The language, the typical neutral language of science, omits any mention of the lives that it might cost. Serber divides the damage into two kinds: radiation and shock waves. Of radiation damage he says: A very large number of neutrons is released in the explosion. One can estimate a radius of about 1000 yards around the site of explosion as the size of the region in which the neutron concentration is great enough to produce severe pathological effects. Enough radioactive material is produced that the total activity will be of the order of 106 curies even after 10 days. Just what effect this will have in rendering the locality uninhabitable depends greatly on very uncertain factors about the way in which this is dispersed by the explosion. However, the total amount of radioactivity produced, as well as the total number of neutrons, is evidently proportional just to the number of fission processes, or to the total energy release.15

In his annotations in an edition published long after the war, Serber offers more mind-numbing numbers, an assessment based on postwar measurements. There would be lethal gamma-ray damage over a radius of 4,000–5,000 feet, blast or shock wave damage of 6,000 feet, shock wave velocity of 875 mph, wind 215

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velocity behind the shock wave of 165 mph, blast and fire damage to 10,000 feet, and temperature within 425 feet of blast as high as 12,500 degrees Fahrenheit, higher than the surface of the sun. The primer as a whole is a masterpiece in terms of making a convincing case to the Los Alamos audience of diverse scientific backgrounds that, given the state of knowledge at the time, delivering a “practical military weapon” in a short time is eminently doable.16 Serber lays out the pressing technical problems in building a workable gadget, discusses possible solutions, and leaves off with an immediate course of actions.

The Secret Road to Trinity The need for total secrecy in bomb development extended from Chicago, where Fermi demonstrated the first controlled fission reaction, to Los Alamos, where the fission-based bombs were built, to Oak Ridge, Tennessee, and Hanford, Washington, where weapons-grade uranium and plutonium were produced— and to the Trinity test site in the Jornada del Muerto Desert (which appropriately enough means “working day of the dead”), where the first plutonium “gadget” was put to the test. At these various sites, the man in charge of the Manhattan Project, General Leslie Groves, attempted to create a workplace designed to inhibit interdisciplinary interchange, a compartmentalization that was, in his view, the best way to guarantee secrecy. Colonel Kenneth Nichols, who implemented this compartmentalization, understood Groves’s motives: “He did not want too many individuals having complete knowledge of all the work. He believed compartmentalization was the only way to obtain secrecy to the maximum possible extent. Moreover, knowing the inquiring minds of scientists, he felt that they would spend too much time prying around into other parts of the project, and he wanted to keep everyone’s nose to the grindstone.”17 Fortunately, the attempt to impose a bureaucratic iron cage failed utterly, as failure would have been its unintended consequence. Los Alamos physicist Joseph O. Hirschfelder makes clear the necessity of free interchange: “At Los Alamos, very few chemists, physicists, or engineers were able to pursue their specialties very long. We were all seeking solutions to difficult problems and our research was not limited to areas where we had had previous experience or training . . . It would be difficult to carry out research in a university where we are all divided up into departments where most people are working on closely related problems. In industrial or government laboratories, interdisciplinary problems are solved by task forces composed of people having different skills and backgrounds.”18 A very young Richard Feynman, then at the beginning of his distinguished career, gives us a taste of what freedom of exchange felt like at Los Alamos when 216

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the head of the T (theoretical) Division, Hans Bethe, paid him the honor of treating him as an equal: Every day I would study and read, study and read. It was a very hectic time. But I had some luck. All the bigshots except for Hans Bethe happened to be away at the time, and what Bethe needed was someone to talk to, to push his ideas against. Well, he comes into this little squirt in an office and starts to argue, explaining his idea. I say, “No, no, you’re crazy. It’ll go like this.” And he says, “Just a moment,” and explains how he’s not crazy. I’m crazy. And we keep going on like this. You see, when I hear about physics, and I don’t know who I’m talking to, so I say dopey things like “no, no, you’re wrong” or “you’re crazy.” But it turns out that is exactly what he needed. I got a notch up on account of that, and I ended up as a group leader under Bethe with four guys under me.19

This camaraderie extended to Los Alamos social life, where most everything was shared, except atomic secrets. Elsie, wife of physicist Edwin McMillan, records the mood: “In age of the residents Los Alamos resembled a college campus. Ed and I were the oldsters. I had my 30th birthday up there. I don’t think I shall ever again live in a community where so many brains were, nor shall I ever live in a community so confined that visitors expected us to fight with each other. We didn’t have telephones, we didn’t have bright lights, but I don’t think I shall ever live in a community that had such deep roots of cooperation and friendship.”20 It is this intellectual and social camaraderie that made Trinity possible. What was the reaction the man in charge of Los Alamos, J. Robert Oppenheimer, to Trinity, this world-changing event? In John Adams’s opera Doctor Atomic, the high point is an aria sung by the Dr. Oppenheimer character and addressed to the holy trinity, the “three-person’d God.” Its lyrics are borrowed from a favorite poet of Oppenheimer, John Donne, who cries out for God’s intervention against the forces of original sin working within him: Batter my heart, three-person’d God, for you As yet but knocke, breathe, shine, and seeke to mend; That I may rise, and stand, o’erthrow mee, ‘and bend Your force, to breake, blowe, burn, and make me new. I, like an usurpt town to’ another due, Labour to’ admit you, but Oh, to no end; Reason, your viceroy in mee, mee should defend, But is captiv’d, and proves weake or untrue.

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THE MANY VOICES OF MODERN PHYSICS Yet dearly ‘I love you,’ and would be loved faine, But am betroth’d unto your enemie; Divorce mee, ‘untie or breake that knot againe, Take mee to you, imprison mee, for I Except you ‘enthrall mee, never shall be free, Nor ever chast, except you ravish mee.21

How real was this operatic anguish? While there is no evidence of Donne’s soul-searching by Oppenheimer, there is a great deal of persistent anxiety at the time. The uranium bomb was never tested; no one doubted it would work. The plutonium bomb was another matter. In theory, a series of simultaneous explosions would implode into a plutonium core, causing the detonation that led to a chain reaction. In theory but, possibly, not in fact. At one low point, George Kistiakowsky, a Harvard detonation expert, predicted in jest that “the test of the ‘gadget’ failed. Project staff resumes frantic work. Kistiakowsky is locked up and goes nuts.” His is an attempt at humor that betrays a deep anxiety about the possibility of failure.22 Just after Trinity’s success, Oppenheimer said only: “It worked,”23 relieved that his own deep anxiety had suddenly dissipated, albeit temporarily. The scientists who had observed the success of the Trinity test on July 16, 1945, reimagined it in clichés. They were, after all, physicists, not poets or novelists. Serber tells us that “the grandeur and magnitude of the phenomenon were completely breath-taking,”24 a resort to the commonplace also true of Hiroshima survivors. The survivor Kikue Shiota, for example, recalled August 6 as “an unimaginably beautiful day” punctuated by a “blinding light that flashed as if a thousand magnesium bulbs had been turned on all at once.”25 It would take a novelist to do the experience of the Trinity test some justice. In Joseph Kanon’s Los Alamos, for example, the sound of the explosion takes on a life of its own: How long did it take for the sound to follow? The hours of light were only a blink of seconds, and then the sound, bouncing between the mountains roared up the valley toward them, tearing the air. He staggered, almost crying out. What was it like near the blast? A violence without limit, inescapable. No one would survive. Then he dropped the piece of welding glass, squinting, and watched the cloud climb higher, rolling over on itself, on and on, its stem widening until the cloud finally seemed too heavy and everything collapsed into the indeterminate smoke. He stared without thinking. Behind it now he could see the faint glimmer of dawn, shy behind the mountain, its old wonder reduced to background lighting.26

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THE ATOMIC BOMB Figure 9.1. Photograph of Charles Blondin taking a passenger over Niagara Falls, 1859.

While the physicists and survivors spoke in clichés, General Groves did not. Reflecting on the long and perilous journey from Roosevelt’s White House to Hiroshima and Nagasaki, he turned to an odd analogous situation to describe his own: “I personally thought of [Charles] Blondin crossing Niagara Falls on his tight rope [figure 9.1], only to me the tight rope had lasted for almost three years and of my repeated confident-appearing assurances that such a thing was possible and that we could do it.”27 At one point, Blondin reportedly cooked and ate an omelet when halfway across. We regret that no photograph of this feat exists.

Secret and Open Bomb Debates After the Trinity test, the scientists involved faced an easily predictable consequence of their wholehearted devotion to winning the war. They had created a “practical military weapon” that left an ethical and political issue in its wake: whether it was right to use the atomic bomb against Japan, especially given that Germany had already surrendered. Before making the final decision on whether, when, and where to drop the bomb, the White House solicited their views as part of an interim committee created by Secretary of War Henry Stimson. In a classified memo, Oppenheimer, Fermi, Arthur Compton, and Ernest Lawrence gave a somewhat tepid endorsement of the decision President Harry S. Truman was about to make: The opinions of scientific colleagues on the initial use of these weapons are not unanimous; they range from the proposal of a purely technical demonstration to that of the military application best designed to induce surrender. Those who advocate a purely technical demonstration would wish to outlaw the use of atomic weapons, and have feared that if we use the

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THE MANY VOICES OF MODERN PHYSICS weapons now our position in future negotiations will be prejudiced. Others emphasize the opportunity of saving American lives by immediate military use and believe that such use will improve the international prospects, in that they are more concerned with the prevention of war than with the elimination of this specific weapon. We find ourselves closer to these latter views; we can propose no technical demonstration likely to bring an end to the war; we see no acceptable alternative to direct military use.28

Stimson’s opinion was “that to extract a genuine surrender from the Emperor and his military they must be administered a tremendous shock . . . proof of our power to destroy the empire.”29 President Truman agreed. New to the presidency, he was not about to change the course of American policy that had been set in stone by Roosevelt. Nor was he about to tell the Congress that $38 billion (in 2022 dollars) had been spent without their approval on a physicists’ hobby. And he was not going to tell the American people that thousands of their sons had lost their lives in the planned invasion of Japan because he had refused to employ this new weapon against the recalcitrant Japanese military. The line of argument at the time, from an accountant’s point of view, went as follows. What was the point of using this bomb as distinct from the countless bombs that had already turned most of Japan into a wasteland? The atomic bomb would cause no more damage than the firebombing of Tokyo, which left one hundred thousand dead and one million homeless. But it would accomplish a distinctly different task: sending a powerful, unequivocal message no ordinary bomb could. It would tell the Japanese and the world that the United States had created a diabolical weapon whose tremendous destructive force would create a light brighter than the sun, which, once seen, would never be forgotten. Understandably, an ethical unease concerning the bombing of Hiroshima and Nagasaki lingered long after the horrific events, and a second pressing issue emerged after the war, nuclear arms control, an open debate joined by literary critics and philosophers. In 1982, for example, it provoked a debate between Paul Fussell and Michael Walzer. This was followed up in 1995 by Walzer’s second thoughts, along with a contribution by John Rawls. Fussell was a noted literary critic; Walzer and Rawls were distinguished philosophers. Not coincidentally, the summer of 1995 was also the height of a nationwide debate concerning a Hiroshima exhibit at the National Air and Space Museum, which was allegedly sympathetic to the Japanese.30 That the concern over Hiroshima should be controversial even after four decades indicates a troubled American conscience, a persistent need for justification. Rawls makes a powerful case against the use of atomic weapons under any circumstances, founded on war theory. According to this theory, civilians not 220

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directly involved in the war effort are never legitimate targets: “We note the place of means-end reasoning in judging the appropriateness of an action or policy for achieving the aim of war or for not causing more harm than good. This mode of thought—whether carried on by (classical) utilitarian reasoning, or by cost-benefit analysis, or by weighing national interests, or in other ways—must always be framed within and be strictly limited by [just war] principles. The norms of the conduct of war set up certain lines that bound just action. War plans and strategies, and the conduct of battles, must lie within their limits.”31 Rawls wants to undermine an argument in favor of dropping the bomb, like Fussell’s, whose basis is cost-benefit analysis. The best estimate for the casualties the planned invasion of Kyushu and Honshu would cause is the earlier invasion of Okinawa. There, in addition to 20,000 America deaths, 110,000 Japanese died. The figure for Okinawan citizens is less certain: 40,000 is a plausible estimate. If we double these estimates, one for each Japanese island, we get 40,000 American and 300,000 Japanese deaths. Casualties at Hiroshima and Nagasaki are much disputed, but a plausible estimate is 214,000 Japanese deaths. These figures mean that the atomic bombs saved 86,000 Japanese and 40,000 American lives. You may or may not think a utilitarian argument is appropriate against Rawls’s unyielding ethics. You might also want to argue that Rawls was not, like Fussell, an infantryman in the Pacific who might have been killed in the invasion of Japan. You would be mistaken on that count at least.32 In his reflections on the use of the atomic bomb, the theologian Reinhold Niebuhr captures something missing in Rawls’s argument, the complex nature of political decision-making, whether its source is a statesman like Stimson or a physicist like Oppenheimer, in the role of a statesman. In these cases, Niebuhr avers, rationality can easily be subverted by national interests that overwhelm with “the force of a stampeding herd of cattle,” a striking metaphor, not only for the decision to bomb Hiroshima and Nagasaki but also Coventry and Dresden, as well as for the dilemma of two American presidents trapped by the role they had to play: There is . . . no “scientific method” which could guarantee that statesmen who must deal with the social and political consequences of atomic energy could arrive at the kind of “universal mind” which operated in the discovery of atomic energy. Statesmen who deal with this problem will betray “British,” “American,” or “Russian” bias, not because they are less intelligent than the scientists but because they are forced to approach the issue in terms of their responsibility to their respective nations. Their formulation of a solution is intimately and organically related to the hopes, fears, and

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THE MANY VOICES OF MODERN PHYSICS ambitions of nations. They must deal with history as a vital and not a rational process. As a vital process it is always something less and something more than reason. It is less than rational in so far as the power impulses of nations express themselves as inexorably as the force of a stampeding herd of cattle. It is something more than rational in so far as human beings have aspirations and loyalties transcending both impulse and prudence.33

Right from the beginning, arms control was also on the minds of many Los Alamos physicists. There are three key documents, three failures that culminate in the near disappearance of physicists from the main corridors of power: the Franck Report of June 11, 1945; the Szilard petition of July 3, 1945; and a 1953 article by Oppenheimer in the prestigious journal Foreign Affairs. The first two occurred before the war’s end. Signed by prominent nuclear physicists, the Franck Report offered the Truman administration an alternative course of action: a demonstration of the bomb in an uninhabited area. It also warned that dropping the bomb would lead to a nuclear arms race. It was kept secret until the year after the war ended. Signed by seventy Manhattan Project scientists, the Szilard petition recommended first publicly offering Japan a chance to surrender under terms all the world could read. It also warned of a postwar nuclear arms race, “opening the door to an era of devastation on an unimaginable scale.” This plea never reached Truman. There was a war on; arms control was not a priority. Oppenheimer’s article is another matter. The war was now over. Close to the centers of political power, charismatic, and well-respected, he was in a good position to give advice that President Dwight D. Eisenhower would heed and indeed might have heeded. His was a plea for more candor and openness with Americans concerning atomic weaponry, information that would fall far short of assisting in Soviet bomb development: “Once, clearly, the problem of proper candor at home is faced—the problem of a more reasonable behavior toward our own people and our representatives and officials with regard to the atom—then the problem of dealing with our allies will be less troublesome. For it is pretty much the same information, the same rough set of facts, that both our people and our allies need to have and understand.”34 While attention was paid, Oppenheimer had made an important enemy in Lewis Strauss, head of the International Atomic Energy Agency, an advocate of the strictest atomic secrecy. It was Strauss who engineered a hearing that led to the loss of Oppenheimer’s security clearance. Thus ended not only Oppenheimer’s role as an advisor, but any possibility that the government would solicit potentially unwanted advice from scientists like Oppenheimer that deviated from the strictly technical or the party line.35 222

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Big Science In the film Tora! Tora! Tora! Admiral Isoroku Yamamoto, the architect of the attack on Pearl Harbor, says prophetically: “I fear all we have done is to awaken a sleeping giant and filled him with a terrible resolve.” Although there is no evidence that Yamamoto spoke these words—they were apparently invented by the scriptwriters—never perhaps in the history of cinema has so deep an insight been incorporated into so shallow a film. For it was World War II in general and the Manhattan Project in particular that turned the United States into a scientific juggernaut, a fit antagonist for that other emerging world power: the Soviet Union. While sporadic large-scale science projects existed long before World War II, Big Science was an unanticipated consequence from the success of the Manhattan Project, and it has since produced a long list of groundbreaking discoveries not otherwise possible, some of which were discussed in the previous two chapters. In the words of historian Peter Galison, “The picture of a collaborative, factory-scale effort” has largely displaced “the ideal of individual and small-group work.”36 Why is Big Science a good practice for advancing science? Employing an analogy from electrical circuits, historian of science Gerald Holton gives us a sense of the kind of intellectual synergy on a large scale that Richard Feynman experienced in miniature in his Los Alamos interactions with Hans Bethe: What took place here was analogous to impedance matching, the method by which an electronics engineer mediates between the different components of a larger system. That is, special coupling elements are introduced between any two separately designed components, and these allow current impulses or other message units to pass smoothly from one to the other. Similarly, in these quickly assembled groups of physicists, chemists, mathematicians and engineers, it was found that the individual members could learn enough of some one field to provide impedance matching to one or a few other members of the group. They could thus communicate and cooperate with one another somewhat on the model of a string of different circuit elements connected in one plane, each element being well enough matched to its immediate neighbors to permit the system to act harmoniously. While an applied organic chemist, say, and a pure mathematician, by themselves, may not understand each other or find anything of common interest, the addition of several physicists and engineers to this group increases the effectiveness of both chemist and mathematician, if each scientist is sufficiently interested in learning something new.37

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This new way of doing physics has led to a new sort of physicist: “Who can be described at once as a physicist—that is, one who is in touch with the evolution of the discipline and its key theoretical and experimental issues, as a conceiver of apparatus and engineer, i.e., knowledgeable and innovative in the most advanced techniques . . . and entrepreneur, i.e., capable of raising large sums of money, of getting people with different expertise together, of mobilizing several kinds of human, financial, and technical resources.”38 This profile describes several distinguished Los Alamos alumni: Luis Alvarez, Robert Bacher, Ernest Lawrence, Edward Lofgren, Edwin McMillan, Wolfgang Panofsky, and Robert R. Wilson. Despite the benefits of Big Science, that more and more it is collaborations that make big discoveries casts a shadow on the reward system of science. Led by Barry Barish, Rainer Weiss, and Kip Thorne, for example, the team that detected gravitational waves was a collaboration of over 1,200 scientists from over one hundred institutions from eighteen different countries. Authors of the discovery article include not only Lisa Barsotti, a principal research scientist at MIT’s Kavli Institute for Astrophysics and Space Research, but also Gregory Ogin, an assistant professor of physics at Whitman College in Walla Walla, Washington. During his scientific career, one of the leading lights at Los Alamos, Hans Bethe, won the Henry Draper Medal, the National Medal of Science, the Max Planck Medal, the Franklin Medal, the Eddington Medal, the Oersted Medal, the Bruce Medal, the Benjamin Franklin Medal, the Enrico Fermi Award, the Rumford Prize, and the Nobel Prize. How many prestigious prizes will Barsotti or Ogin win for their efforts, if lost in a sea of collaborators? In his Nobel Prize lecture, Thorne celebrates the work of these virtually invisible collaborators. He sees himself merely as an icon, one visual representative of the LIGO collaboration: “The Nobel Prize for ‘decisive contributions’ to this triumph was awarded to only three members of the Collaboration: Rainer Weiss, Barry Barish, and me. But, in fact, it is the entire collaboration that deserves the primary credit. For this reason, in accepting the Nobel Prize, I regard myself as an icon for the Collaboration.”39 Awards like the Nobel Prize were initiated well before Big Science. It is an unanticipated consequence of its current predominance that their sole focus on single or a few investigators seldom makes sense.

With the publication of the Lise Meitner–Otto Frisch Nature paper in 1939 about the liquid-drop nuclear fission of uranium and other heavy elements, the atomic bomb became a new scientific thing known mainly to physicists, who rapidly grasped its unstated deadly possible application. The Manhattan Project, which followed in the midst of World War II, spawned a cache of 224

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secret communications related to that application. We have in several top-secret documents a road map for building an atomic bomb, arguments for doing so posthaste, and the destructive consequences of succeeding. As an unintended consequence of the secrecy surrounding the Manhattan Project, we also have in place of the usual stream of scientific papers a stream of reminiscences that give us what no scientific paper could: a sense of an international team of scientists and engineers working together on a single problem, a presage of the way of doing Big Science now firmly in place. The destructive power of atomic bombs also forced physicists to take a stand by speaking in the languages of ethics and politics and ushered in an age of nuclear anxiety for everyone.40

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A major intellectual upheaval erupted when Albert Einstein, usurper-in-chief, published a series of scientific articles and a slim popular science volume on relativity theory in the early twentieth century. These publications forever changed the meaning of time, space, velocity, acceleration, gravity, mass, and energy. Einstein, however, was not alone in the endeavor to upend our perceptions of the world; physicists since Einstein have created a cosmic vision full of the bizarre and beautiful, extending from the smallest scale imaginable to the entire universe and beyond. This book has sought to capture this collective vision through the words and images of world-leading physicists and science writers. Their vision is easily as strange, wondrous, and at times seemingly far-fetched as any in the literature of science fiction. One of the physicists’ main tools for evoking this vision is the thought experiment, with and without visual accompaniment. By this means—among others—physicists look to convince their scientific colleagues and the science-curious public that the seemingly impossible is not just possible, but true or at least probably true. As the examples in this book demonstrate, Einstein’s thought experiments unsettle commonsense notions about time and space for one observer in uniform straight motion relative to another. They also bring to life his three conceptual pillars for general relativity: equivalence of gravity and acceleration, distortions of space and time in a gravitational field, and the relativity of accelerated motion. 226

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What’s more, quantum thought experiments summon an invisible Mr. Tompkins-in-Wonderland microworld parallel to but completely different from the one we inhabit. These thought experiments, as well as analogies and pictures, inevitably fall short. As many physicists have noted, the uncertainty and strangeness of the quantum world consistently defy satisfactory depiction with words or pictures. Ironically, thought experiments also figure prominently in the mounting of arguments against quantum mechanics as the final word on the real world. These have sparked heated debates in the physics and philosophy of science community for the past ninety years. Our example visual representations, independent of any thought experiment, picture the world through the eyes of physicists. And they can serve an argumentative function as well. For example, the persuasiveness behind the Standard Model table of particles at least partially rests on its resemblance to the extraordinarily successful periodic table of elements. This single remarkable table represents the fundamental particles whose interactions produce all the chemical elements and unifies three of the four forces that control our universe—a table that physicists hope can eventually be expanded to include the fourth force, gravity, and unite general relativity and quantum mechanics to boot. Of two leading but highly speculative unification theories beyond the Standard Model, each has a visual that represents the dominant analogy behind the theory: infinitesimally small vibrating strings for the fundamental particles in string theory and infinitesimally small loops of space as the basis for the creation of not only the expanding universe but also time itself in loop quantum gravity theory. Analogy is of vital importance in communicating science, especially for a wide audience. The analogies of fundamental particles to strings and quanta of space to loops are among the more striking examples. A series of shifting analogies is also central to cosmological theory: the universe as static sphere, expanding balloon, never changing but ever flowing river, expanding church bell on its side, colliding branes, and even a block of Swiss cheese. Most of these cosmic analogies also come with arresting visuals. A couple of intriguing questions hoover over recent popular science books and articles on physics theory, especially with regard to multiple universes, more than three spatial dimensions and one of time, branes, and theories of everything. However persuasive the thought experiments, visuals, analogies, and arguments therein, has physics theory on these matters outpaced experiment to an unhealthy degree? And what constitutes sufficient hedging language and caveats for popular science physicists to adequately caution readers that their bold theories are not scientific fact or have not reached consensus? 227

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Definition is everywhere in scientific writing, and it is a vastly underappreciated communicative tool. By this means, scientists and science writers turn newly invented materials into what we refer to as “scientific things”; that is, things seen through the eyes of science. As a result of definitions along with their amplification, often with pictures, readers gain a new perspective on what a thing can be and do. Our examples include many quantum materials. There are metals that lose all resistance to the movement of electrons at ultracold temperatures, collections of millions of atoms that behave quantum mechanically like a single superatom, and fluids that flow through solid barriers unimpeded and up the sides of a bowl. Other examples include ultrathin nanomaterials that spread out in only two dimensions—length and width but no thickness to speak of, large artificial atoms with electrons but no nucleus, quantum particles that occupy two states at the same time, and a hypothetical particle that sprouts a north pole but no south. And there is that most miraculous of scientific things, invented in the twentieth century: the transistor. It can rectify alternating current to direct current, amplify that current, and almost instantaneously switch it from on to off. This scientific thing can now be found in many ordinary objects that have transformed daily life: radios, televisions, computers, cell phones, global positions systems, and more. Occasionally, scientists and science writers must draw upon the everyday language of persuasion alongside the conventional means of technical communication. One of our examples is funding requests for astronomical discovery machines that are astronomically expensive, such as the Hubble Space Telescope and the Laser Interferometer Gravitational-Wave Observatory. A common argument here is that some new technology costing a king’s ransom is essential not just to the advancement of science, but to the well-being and glory of the nation. Another example is the secret communications during World War II arguing for the urgent need to develop an atomic bomb. Also germane here are ethical and political arguments by physicists and others about whether this physics-based technology should be or should have been dropped on Japan, twice. In the course of this book, we have popped in on physicists cryptically speaking to each other in scientific papers and speaking to the rest of us in communications meant for nonphysicists willing to wrestle with sometimes opaque text. Outsiders have also chimed in: journalists, science writers, historians, philosophers, poets, even a patent attorney. The discoveries, reported in a chorus of divergent voices, have not only radically altered our picture of the world near us but also expanded our view of our place within a vast cosmic drama, transformed our daily lives, and heightened our anxiety concerning the future in a world capable of instant self-destruction. 228

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Recommended Reading For those wanting even more examples of inventive thought experiments, analogies, metaphors, visuals, definitions, and the like, or looking for further enlightenment on the topics we have covered, we present our recommendations for ten popular science books on modern physics by physicists. We follow that with ten books by science writers who are not practicing physicists. There is a small library of worthy such books, but these are among our favorites, chronologically ordered by year of first publication. Many though not all are discussed in the previous chapters. First, the physicists: 1. Albert Einstein, Relativity: The Special and General Theory, trans. Robert W. Lawson (Princeton, NJ: Princeton University Press, 2016). First published in German in 1917, this little book is a masterpiece in our view. Nothing quite like it had been written before or has been written since. Einstein’s mastery of the illustrative thought experiment is on full display throughout. Clearly, Einstein devoted serious thought and effort to communicating his radical new theory to readers outside the narrow physics community. Be warned, however: Einstein’s book is accessible, but it is not light reading or for those in a hurry. The book’s subtitle in the original German, gemeinverständlich, roughly translates to “generally understandable.” But Einstein apparently joked that the subtitle should have been gemeinunverständlich, meaning “generally un-understandable.” Given that the book is still popular after more than a century and has gone through numerous editions and translation into many languages, we respectfully beg to differ. Most popular science books grow dated with time and forgotten. This one will never be. It set the standard for others to build upon. 2. George Gamow, Mr. Tompkins in Paperback (Cambridge: Cambridge University Press, 1993). No eminent physicist did more to communicate an amusing side to physics than George Gamow, a Russian-born theoretical physicist and major contributor to the development of the big bang theory. This publication is actually an updated combination of two of his earlier books that tells the story of relativity and the atom in narrative form with pictures: Mr. Tompkins in Wonderland (1940) and Mr. Tompkins Explores the Atom (1945). The titular oddball Mr. Tompkins is an unusual bank clerk who seems to regularly dream about physics, not loans, mortgages, or savings accounts. The “wonderland” Mr. Tompkins first enters in a dream state has a 10 mile per hour speed limit for light, as opposed to the actual 670 million miles per hour. As a result,

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THE MANY VOICES OF MODERN PHYSICS the relativistic effects on time and space that normally do not kick in until some object is moving at close to the actual speed of light become part of everyday life, even a man riding a bicycle. In chapters exploring the atom, Mr. Tompkins dreams up another wonderland, where Planck’s constant for the quantum of action is “very big,” instead of the actual incredibly tiny 7 × 10−34 joule seconds. Hence, strange quantum effects become part of everyday life. In the book’s foreword, Roger Penrose captures Mr. Tompkins’s enduring appeal: “By his ingenuity and narrative skills, Gamow is able to transform some of the puzzling and obscure mysteries of this basic physics—a physics which, indeed, is still modern—into magical and enthralling stories for children.” And the child in every adult, we would add. 3. Steven Weinberg, The First Three Minutes: A Modern View of the Origin of the Universe, 2nd ed. (New York: Bantam Books, 1984). First published in 1977, this timely book appeared the year before the Norwegian Nobel Committee recognized the discoverers of astronomical observations confirming the big bang theory. The centerpiece of this bestselling book is Weinberg’s compelling chronological narrative for what happened from one-hundredth of a second after the big bang through the first three minutes. But there’s much more in this slim volume. That includes a recapitulation of the supporting astronomical observations for the big bang and Weinberg’s speculations on what happened both before the first one-hundredth of a second and long after the first three minutes. This book went viral because, at the time, the general public knew little if anything about this remarkable physics-based origin story. While much more has been learned about the universe in the decades since, the book remains well worth reading as a lucid account by a distinguished physicist with highly refined literary skills. For a more complete and up-to-date look at the universe, see Welcome to the Universe: An Astrophysical Tour by three astrophysicists—Neil deGrasse Tyson, Michael A. Strauss, and J. Richard Gott (Princeton, NJ: Princeton University Press, 2016) 4. Richard Feynman, QED: The Strange Behavior of Light and Matter (Princeton, NJ: Princeton University Press, 1985). In this book—a masterpiece of verbal-visual science communication—Feynman explains the theory behind the unification of quantum mechanics and electrodynamics, a theory called QED for short, a theory of which he was a principal architect. While Einstein was the master of the thought experiment, Feynman was the master of the visual in the service of a thought experiment. This book is chock full of diagrams— over ninety visuals in only 150 pages. But there are only three paradigmatic

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EPILOGUE diagrams from which most of the others sprout: a beam of light striking a glass surface, passing inside the glass to varying thicknesses, then reflecting back into a detector; a stream of light reflecting off a mirror into a detector; and a diagram of Feynman’s invention that represents the interaction of photons and electrons in empty space, the so-called Feynman diagram. By means of these visuals and the accompanying thought experiments, Feynman offers readers deep insight into the strange behavior of the microworld. 5. Stephen Hawking, A Brief History of Time, 2nd ed. (New York: Bantam Books, 1996). In terms of sales, this is the most successful popular science book ever written, hands down. In terms of number of books bought and never or little read, it undoubtedly holds that record as well by a long shot. Even physicists find some parts opaque. It must be admitted that at times Hawking jumps from one thought to the next, assuming a knowledge of physics that most general readers could not reasonably possess. And while A Brief History of Time is an undeniably catchy title, the book itself does not provide a brief narrative on time as the title advertises, but a smorgasbord on modern physics theories, featuring Hawking’s own on black holes and theory for the origin and evolution of the universe. That said, we include the book here because the prose often radiates Hawking’s charismatic public personality and wit, while the subject matter is hard to resist by any scientifically curious reader—black holes, primordial mini black holes, wormholes, the origin and fate of our universe, uncertainty principle, unification of relativity and quantum mechanics, time travel, and more. 6. Kip S. Thorne, Black Holes & Time Warps: Einstein’s Outrageous Legacy (New York: W. W. Norton, 1994). While Einstein’s Relativity does a magnificent job of explaining special relativity, it is a little less successful with general relativity. It is also short. For those interested in a more complete picture of both special and general relativity, Kip Thorne’s hefty book is worth a look. What’s more, it is a work of bold literary experimentation. It begins with a science fiction story of over forty pages. This story is a logical extension of the many previously published thought experiments with spaceships and other modes of transportation to explain relativity and incorporates the black holes, wormholes, and quasars investigated with general relativity by Thorne and many others. The thought experiment asks readers to “imagine yourself the owner and captain of a great spacecraft [that can travel near to the speed of light], with computers, robots, and a crew of hundreds to do your bidding.” Now go explore the “outrageously bizarre [astronomical] objects” predicted by

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THE MANY VOICES OF MODERN PHYSICS relativity. Thorne’s introductory science fiction chapter incorporates footnotes keyed to the fourteen subsequent chapters that explain the science within the story. This hybrid structure is vaguely reminiscent of Vladimir Nabokov’s Pale Fire. With it, Thorne cleverly manages to annotate his science fiction tale by means of popular science that explains the science in the fiction. Thorne is also coauthor of a famous textbook for physics graduate students, Gravitation (Princeton, NJ: Princeton University Press, 2017), written in a similarly inventive literary style with Charles W. Misner and John A. Wheeler. 7. Alan H. Guth, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (New York: Basic Books, 1997). Since the publication of Steven Weinberg’s The First Three Minutes, innumerable popular science books have revised the basic narratives for the origin and evolution of the big bang universe. Guth’s The Inflationary Universe is one of the better ones, though never attaining anywhere near the public attention it surely deserves. Its title might have been The First 10 –32 Seconds. Guth is one of the originators of the seemingly bizarre theory that at around 10 –35 seconds the universe expanded at a speed far faster than the speed of light powered by a mysterious propulsive force. And as soon as this mysterious super expansion began, it vanished. Guth’s book covers why cosmology needs such a theory, what it explains about the universe, what evidence there is for it, and how the universe might have emerged out of apparent nothingness before the inflation period. With personal anecdotes strewn within the text, readers are granted periodic brief glimpses into the life of a young theorist working at the bleeding edge of physics. Physicists have refined the inflationary theory since Guth’s book and are putting it to the test now with measurements on the cosmic microwave background. The story continues. A Nobel Prize could hang in the balance. 8. Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Universe (New York: W. W. Norton, 1999). Among his popular science writing peers, Greene has no peer. He came to the fore as a popular science writer not so much because of his reputation as a physicist beyond his special field, but his superior communication skills. In particular, he has thoroughly mastered the telling thought experiment, bringing to this form of expression his own style with a certain flair. He is similarly adept with illuminating analogies and visuals. Whatever the complexity of the topic, it is apparent Greene has thought deeply about the best way to communicate it to the most readers without oversimplifying. The Elegant Universe is thus highly readable, even though its subject, string theory, is perhaps the mathematically

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EPILOGUE most complex theory ever devised by physicists. The overall logical structure of The Elegant Universe allows Greene to cover the major highlights in modern theoretical physics: relativity theory and quantum mechanics, their unification along with the four forces in string theory, and the implications of that unification to our understanding of the universe. Even though string theory still lacks experimental evidence or even a plausible means of testing it, this classic book remains a must read for anyone interested in theoretical physics in the twentieth and twenty-first centuries. 9. Lisa Randall, Knocking on Heaven’s Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World (New York: HarperCollins, 2011). Like Greene, Randall has a knack for making the latest theoretical physics understandable and plausible for the science curious public. That includes her brilliant, but unproven, cowritten theory for uniting gravity with the three other forces by the positing of an additional dimension of space. (She even wrote the lyrics for a full-blown modern opera in which her theory figures prominently, surely a first in scientific communication for the public.) What distinguishes Knocking on Heaven’s Door is its extensive treatment of the grandest physics machine ever built, the Large Hadron Collider near Geneva, Switzerland. Randall communicates how the various components of this giant machine—a particle accelerator meant to simulate conditions of the very early universe—“fit together in marvelous ways.” As we learn in Randall’s book, this machine is not a symbol of technological achievement by a single country, but a worldwide community of thousands of engineers, computer programmers, and scientists, plus the necessary support staff. While most of us will never actually visit the Large Hadron Collider or be treated to a VIP tour, we can experience it vicariously through Randall’s evocative account. Indeed, her virtual tour, including her stories of the many ups and downs during the fifteen years on the way to final construction and operation, is far more comprehensive than any physical tour could be. 10. Katie Mack, The End of Everything (Astrophysically Speaking) (New York: Scribner, 2020). In popular science writing on the cosmos, the emphasis is on the time span between the very early universe—within the first minute—and our universe. Theoretical cosmologist Katie Mack tells the whole story, from the first billionth of a billionth of a billionth of a second to hundreds of billions of years hence, giving most attention to the bitter end. The End of Everything expertly presents the latest research on the three main cosmic doomsday scenarios: the big crunch, heat death or big freeze, and big rip. In the first, the universe’s expansion grinds to a halt and reverses direction, ending in a final

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THE MANY VOICES OF MODERN PHYSICS big crunch into a state like that at the origin. In the second, the universe’s expansion continues to the point where all galaxies, stars, and planets fly away from each other until they vanish from sight, all black holes evaporate, and total darkness reigns. In the third, the rate of expansion increases much more than current predictions, violently tearing apart atoms and molecules everywhere and ending the universe more rapidly than in the second scenario. What makes The End of Everything especially engaging is Mack’s clear and sometimes funny verbal-visual explanations for the science behind the three scenarios.

Authorship of top-of-class popular science books is by no means limited to physicists. Next up are our ten favorites from among the many superb physics-based books by gifted science writers who are not practicing physicists or, in some cases, even trained in theoretical physics: 1. Bertrand Russell, ABC of Relativity, 4th ed. (London: Routledge, 2009). One of the preeminent philosophers of the twentieth century, Russell wrote this slim and lucid volume for popular consumption, first published in 1925. (In later editions, it was revised and updated by physicist and relativity expert Felix Pirani.) According to Russell, explaining relativity demanded a popular science book capable of changing “our imaginative picture of the world.” Russell achieved just that with a cornucopia of ingenious thought experiments and analogies presented from a distinguished philosopher’s perspective, combined with dashes of understated British wit and literary flair. Russell being Russell, he also spelled out the philosophical consequences of relativity—the need to rethink common technical terms like mass, energy, velocity, length, and time. As Russell wryly notes, one of those consequences is definitely not that “everything is relative.” The ABC of Relativity is a unique, satisfying mixture of popular science and philosophy of science and an excellent companion to Einstein’s Relativity. 2. Eve Curie, Madame Curie: A Biography (Boston: Da Capo Press, 2001). Totally lacking in our recommended books by physicists is any firm sense of the life of the physicists themselves beyond the superficial. Of course, there are many excellent scholarly and popular book-length biographies of the leading figures from the twentieth and twenty-first centuries. First published in 1937, Madame Curie: A Biography is one such book. It is all the more special because the chosen subject is not only that rare creature, a woman physicist, but the only recipient of Nobel Prizes in both physics (studies of radioactivity) and chemistry (discoveries of radium and polonium). Her life story has been amply documented in biographical movies, television shows, plays, and books. Our

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EPILOGUE recommended biography is by her daughter Eve, a bestseller published three years after her mother’s death. In the “Autobiographical Notes” to her biography of husband Pierre, Marie Curie wrote: “I have been frequently questioned, especially by women, how I could reconcile family life with a scientific career. Well it has not been easy; it required a great deal of decision and of self-sacrifice.” Eve’s book illustrates in detail how her mother managed it from an adult daughter’s and professional writer’s perspective. Madame Curie is a traditional biography in that it is an inspiring story of triumph and overcoming the odds and many hardships—though glossing over some of the subject’s all-toohuman shortcomings. One of its messages, however, is unusual for its time but especially pertinent now: women can equal the most gifted and determined men in contributing to science, even physics. 3. Richard Rhodes, The Making of the Atomic Bomb (New York: Simon & Schuster, 1986). The Manhattan Project might be the most dramatic of all physics stories out there, with the possible exception of the trial of Galileo Galilei. There is the extraordinary flowering of research on the structure and interactions of the atom in the early twentieth century, including the radioactivity research of Marie and Pierre Curie. There is a gathering of nearly all the hotshot young physicists and many other disciplines in a top-secret makeshift town during World War II. There are battling egos and larger-than-life personalities involved, including one who plays bongos and cracks safes for fun, and another who reads the Bhagavad Gita in Sanskrit during his free time and sports a widebrimmed porkpie hat everywhere. There are reminiscences from prominent women like Laura Fermi and Leona Marshall Libby. There are spies like Klaus Fuchs. There is the famous evening stroll of Niels Bohr and Werner Heisenberg in Copenhagen to discuss the possibility of atomic bombs. There is the gadget itself. Rhodes’s The Making of the Atomic Bomb is the definitive historical account of that story, capturing all of the above and much more. Rhodes is not an academic or scientist, but a professional writer. He imbues his book with the qualities of a good suspense novel where readers already know the deadly denouement. His copious quoting of his vast cast of characters brings their personalities and voices to life. And utterly chilling is Rhodes’s recreation of what happened in 1945 at ground zero in Japan, twice, with extensive quotations from eyewitnesses. While more than three decades old, this biography of a physics-based technology seems unlikely to be surpassed any time soon. 4. Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (Princeton, NJ: Princeton University Press, 1996).

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THE MANY VOICES OF MODERN PHYSICS Popular science physics books tend to dwell on the wildly successful or highly speculative. Historians of science provide a much needed corrective to the rosy picture by investigating when scientists follow the wrong path for whatever reason—from nice try but wrong to outright fraud or pigheadedness. Kragh’s Cosmology and Controversy follows the progress of two competing cosmological theories, each spearheaded by prominent physicists. Both theories proposed plausible explanations for Edwin Hubble’s astronomical data supporting an expanding universe. On one side was the “winning” big bang theory backed by George Gamow and even embraced by the Catholic Church. On the other side was the “nice try” steady state theory backed by Fred Hoyle. The steady state theory initially seemed a little more sensible, as Hoyle argued, since it only required the spontaneous and steady appearance of hydrogen atoms as seeds for new stars rather than a whole universe springing out of apparently nothing. It ultimately did not pass the test of time upon the arrival of astronomical measurements of the cosmic microwave background, the remnant of the big bang. Today the steady state theory is known by few outside of historians and cosmological physicists. Yet, it was a central player in the emergence of modern cosmological theory, as Kragh’s scholarly book documents in full. 5. Michael Riordan and Lillian Hoddeson, Crystal Fire: The Invention of the Transistor and the Birth of the Information Age (New York: W. W. Norton, 1997). Crystal Fire, by historians of science Riordan and Hoddeson, is to the transistor as Richard Rhodes’s The Making of the Atomic Bomb is to the gadget. In it, there is a gathering of extraordinary physics talents in the world’s leading industrial research lab, Bell Laboratories. There are three Nobel Prize–winning central characters: an abrasive theorist with towering ego and ambition, a quiet and reserved theorist who would go on to win a second Nobel Prize, and an outgoing American experimentalist born in China. There are also many other lesser known yet important characters who contributed to the technology that launched the information age. Riordan and Hoddeson tell not just the gripping story of the birth of and development of the transistor, the solid-state physics behind it, and the beginnings of Silicon Valley, but also the process of invention within a large industrial research organization in the second half of the twentieth century. Deservingly, Crystal Fire won the 1999 Sally Hacker Award from the Society for the History of Technology for books aimed at nonacademic audiences. 6. Peter Galison, Einstein’s Clocks, Poincaré’s Maps: Empires of Time (New York: W. W. Norton, 2003). Every science-literate person knows that Albert Einstein

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EPILOGUE invented special relativity theory. What’s not at all well-known is that he did not pull the theory out of thin air, nor deduce it based on past physics theory alone. Most are also unaware that one of the leading scientists in the world at the beginning of the twentieth century, Henri Poincaré, came up with a very similar and equally plausible theory to Einstein’s special relativity at about the same time. In Einstein’s Clocks, Poincaré’s Maps, historian of physics Peter Galison argues that Einstein and Poincaré gained insight into the need to redefine time by having been exposed to practical time synchronization problems of the day related to establishing train timetables between distant cities, setting up telegraph networks with undersea and overland cables, and mapping time coordinates across the globe. At least in part, these came to light to Einstein through his work in the Swiss patent office in Bern and to Poincaré through his work for the French Bureau of Longitudes in Paris. The solution for both men was to synchronize clocks by sending light signals between them and taking into account the time difference for light to travel between points. Poincaré’s relativity theory fell a little short because it did not fully dispense with a universal ether or absolute space. What makes Einstein’s Clocks, Poincaré’s Maps especially engaging is its brilliant connections between the lofty world of ideas and modern technology of that time. 7. Louisa Gilder, The Age of Entanglement: When Quantum Physics Was Reborn (New York: Vintage, 2008). Gilder’s main claim to fame is having written a single book, published eight years after she graduated from Dartmouth College. But what a first and so far only book: part historical fiction, part popular science book, and part history of quantum science. Gilder communicates quantum science by imagining conversations pasted together and refashioned for narrative purposes from letters, memoirs, lab notes, and scientific papers of real-life physicists. Within these dialogues she also imagines circumstantial details, like “Bohr’s brow furrows.” It thus reads like a novel, not a popular science book. While many fiction writers have composed absorbing novels with central characters as scientists (Andrea Barrett, Allegra Goodman, Alan Lightman, Marisha Pessl, Richard Powers, to name a few), no one reads those books to learn much if anything about the science. Given that Gilder is neither a physicist nor historian of science, we greatly admire her skill at communicating both the science of quantum mechanics and the long history behind the effort to experimentally test Einstein’s argument that quantum mechanics is not “complete,” that some alternative approach will one day emerge to replace or modify it with a strictly deterministic theory in Einstein’s sense. Others have told the story behind this science equally as well by different

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THE MANY VOICES OF MODERN PHYSICS literary tactics. We chose The Age of Entanglement for the freshness of Gilder’s narrative approach. 8. Jim Holt, Why Does the World Exist? An Existential Detective Story (New York: Liveright, 2012). Cosmologist and big bang doubter Fred Hoyle thought it absurd to argue that a whole universe could appear out of nothingness, like “a party girl jumping out of a cake.” For Why Does the World Exist? science writer par excellence Jim Holt visited prominent male philosophers and physicists as well as a novelist with philosophical turn of mind (John Updike), and interviewed them all on why there is something and not nothing, among other things. Unsurprisingly, while the philosophers tend to wrestle with the question of whether or not some divine or superintelligent being is the responsible culprit, the physicists stick more or less with physics and variations on the standard big bang theory. Physicist Andrei Linde, for example, argues that an inflationary universe could have sprung out of almost nothing, “a hundred-thousandth of a gram of matter,” which in turn could have jumped into existence as a quantum fluctuation out of nothing. But what is nothing exactly? Alex Vilenkin wittingly defines it as “a closed spacetime of zero radius.” A related question is, of course, why would a universe pop out of a closed space-time of zero radius only one time? The thought-provoking answers of both philosophers and physicists to Holt’s questions make for a fascinating read, though predictably Holt does not arrive at a firm answer to his central question. 9. Harry Collins, Gravity’s Kiss: The Detection of Gravitational Waves (Cambridge: MIT Press, 2017). Sociologist of science Harry Collins has devoted almost his entire career, nearly fifty years, to studying the community of physicists who work on detecting the gravitational waves predicted by general relativity. In the course of that time, he “went native” in the sense that he became a member of this community as much as any physicist. Until recently, he had no idea whether their bold project would strike paydirt in his lifetime. Many failures preceded final success, all of which he reported on in journal articles and books before the current recommended one here. For decades, success seemed a long shot. But the first gravitational waves were indeed detected in 2016 at the Laser Interferometer Gravitational-Wave Observatory. Collins wrote Gravity’s Kiss as primarily a diary of the five months starting from the initial successful measurements to the triumphant announcement in a press release and subsequent journal publications. This is a tale largely told through email exchanges among key participants. Collins’s unique approach offers

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EPILOGUE an inside look into Big Science in action as communicated through select emails—a form of written scientific communication now almost as important as journal articles, but less easily accessed by scholars. 10. Philip Ball, Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different (Chicago: University of Chicago Press, 2018). We consider Beyond Weird the clearest, most up-to-date book on quantum theory by anyone. Former editor of Nature and author of numerous popular science books, Ball is keenly attuned to the latest developments in both quantum theory and experiment. The book’s subtitle alerts readers to the author’s assumption about his ideal reader—namely, someone already familiar with the key concepts behind quantum theory—the uncertainty principle, superposition, wave-particle duality, entanglement, non-locality, decoherence, and many worlds. That said, his expositions are so good, we believe any reader can gain insight into these “beyond weird” concepts from reading Ball. He systematically corrects the many misconceptions that have spread about quantum weirdness through previous thought experiments and analogies between our “real” world and the quantum world. Ball’s elucidating the original science writings on quantum theory and their shortcomings makes the quantum mysteries graspable without resort to complex equations—no small achievement.

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AFTERWORD RANDY ALLEN HARRIS

It is a great pleasure, but simultaneously a great sorrow, to write an afterword for this unique and lovely book. For such occasions, one always learns the hard way, we have the word bittersweet. The pleasure you will know already if you got here after reading the foregoing book. If you skipped ahead in the hopes of some advance guidance, you won’t yet fully share in that pleasure. I’ve sometimes skipped ahead to afterwords myself, but then, I’ve never known what afterwords are for. Still don’t. But I do know that if you haven’t read the book yet, you’re in the wrong place. Go read it. I’ll still be here. The inversely affecting sorrow you will also know, now that we can be sure you’ve read and enjoyed the book, since this is the last one Alan G. Gross and Joseph E. Harmon will ever write together. (If you somehow got here without this knowledge, I am sorry to be the one to tell you: Alan has passed away.) The sorrow is correspondingly greater for those of us who have known Alan personally and professionally, not only as a voice in a text but as a voice in our ear—a friend, a colleague, a warm but sharp critic of our efforts to play our own role in the making and sharing of knowledge. But it cannot be avoided by anyone who has read even a few pages of him, on his own or alongside Joe. So, this afterword is a lament and a celebration in almost equally balanced proportions. It is a lament for the loss of a singular voice and a requiem for a rich partnership, in one pan of the scale; in the other, a celebration of this especially 240

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rewarding book, The Many Voices of Modern Physics, and of the legacy they have left behind, the knowledge that Harmon and Gross, Joe and Alan, have made and shared with us as a joint force in assaying one of our most consequential human enterprises, science. Joe and Alan’s joint project to reveal the nuts and bolts and special grace of scientific communication has been a boon to contemporary science studies, and a great delight in my own reading and scholarship. If this is your first book by Alan and Joe, though, you’re in luck. There will be no more new ones, but there is a brilliant back catalog in which you can indulge yourself. I will talk first about Alan, then Joe and the book, then their wider project, by telling the story of how we met.1 I was beguiled academically into science studies thirty-plus years ago by Alan’s impressive articles. He was the most prominent of an emerging school of critics and theorists bringing the ancient field of rhetoric to bear on science, including Carolyn R. Miller, Lawrence J. Prelli, Charles Bazerman, John Angus Campbell, Greg Myers, and Jeanne D. Fahnestock (these names will be important shortly). Not just the most prominent in this group but also the most productive, Alan had spooled out a sheaf of compelling articles, collected them into a book, The Rhetoric of Science, and framed it with a manifesto for the field. Somehow, I ended up in the crosshairs of Art Walzer, the reviews editor for Rhetoric Society Quarterly. He offered me the plum job of reviewing The Rhetoric of Science, with Alan getting the chance to reply.2 I had just defended my dissertation and was a couple of years into a corporate career with little intention of returning to the academy—so, a nobody. Meanwhile, there were Alan’s heavyweight colleagues, just named, who I would have expected to relish the opportunity to review the book, especially because it had neglected the lot of them almost entirely. The title declared the book to be a definitive account of the exciting new field it named. But Alan, apparently, stood alone in that field. He either fully ignored or just casually waved at the work of Miller, Prelli, Bazerman, and the rest of the school. If I had been one of them, I would have been chomping at the bit to get at him, waiting by the phone for a call from Art. Maybe they were too busy, or too polite, or maybe Art never called.3 Maybe Art was looking for a rhetoric-of-science punk rather than a rhetoric-of-science bigwig. He did make it clear when he contacted me that some pugnacity was expected, suggesting that Alan would return the favor. The exchange was to be the inaugural entry for a new section entitled “Forum” and Art wanted to start it with a bang. Alan’s book looked like a trademarking exercise, something that might have been more accurately titled The Rhetoric of Science ( to Alan G. Gross, Inc.).

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Not only did it ignore or indifferently breeze over the work of his colleagues, it paid minimal attention to the pillars of a two-millennium rhetorical tradition. The book was staking out the subfield in Alan’s own terms, and even the Rhetoric part of the title was shorthand for Rhetoric-according-to-Gross. Alan had a soft spot for Aristotle and Chaïm Perelman but had minimal time for any of the other usual suspects from that long tradition.4 We get stasis theory without Hermagoras, metaphor without Burke, style without Campbell, epistemic rhetoric without Robert L. Scott, a “radical” stance without the sophists or Nietzsche. (If you don’t recognize some or any of these names, don’t worry. Just know that for most rhetoricians not named Alan, they are canonical.) Alan’s book was like an definitively styled book on technocapitalism by Elon Musk that doesn’t mention Steve Jobs, Bill Gates, or Jeff Bezos—perhaps not an unlikely prospect, come to think of it, but a telling comparison all the same. Alan also didn’t bother much with any notable patterns in the field—influential theories, emerging themes, methods of study, central claims. It just gave us an exhibition of brilliant (Gross™) critical analyses of scientific episodes that crucially implicated strategies of symbolic deployment in science and their effects. While I was now out of the academy a couple of essays written during my grad school days had recently come out and—like Alan’s book, I confess—they had a whiff of flag-planting imperialism about them, presuming to lay out the defining themes and blossoming subgenres and the contours of an emerging canon for rhetoric of science. Looking back, I can see that they did pretty much everything Alan had declined to do with his book, and one of them even left the shallow end of the pool where I belonged to splash aggressively in the “radical” waters Alan was charting.5 Accordingly, I had both admiration and outrage to express about his book. So, when Art called, I said yes. But approaching the ring where Alan G. Gross awaited, doubts began to orbit around my head like a parade of fretting cartoon counselors. Maybe, one of them said, this is a setup. Another: Yeah, maybe you’re the patsy they serve up to the champ for an easy payday and an entertaining thrashing. OMG! I thought, or whatever one thought before texting took over the language. Another counselor reminded me that Walzer is featured in the acknowledgments of The Rhetoric of Science. Then: Walzer is at University of Minnesota with The Great and Terrible Gross! In the same department! Down the hall, I’ ll bet, where they meet for lunch and hatch their plans! 242

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OMFG! I realized. Of course it’s a setup! Still, Good Reader, I entered the ring. I led with my chin. “Just who does Alan Gross think he is to give us the rhetoric of science?” I yowled.6 It gets worse. I disputed the in the title for its trademarking implications and for the book’s corresponding neglect of other worthy rhetoricians of science. Then I disputed rhetoric in the title for the book’s neglect of so much of the rhetorical tradition. Relenting, I added, “I have no beef with of or science.”7 Just who does this puppy think he is? Alan may have thought. But did not write. My chin was out, but he put a conspiratorial arm around my shoulder in his reply. You only find a couple of the words in my title problematic? he implies; “I am uneasy with all of it: the definite article, the two nouns, and the preposition.”8 Then he answers me point by point. On my complaint about the imperialist pretensions of the, he tells me “right church” but “wrong pew.” His use of the does not signal proprietary “vanity,” he says, but disciplinary “ambition.” On my complaint about his neglect of rhetoric, he confesses that what he does in the book no more equals an application of the tradition “than a Kentucky Colonel equals a colonel.” But that’s because, not to put too fine a point on it, the tradition is crap. “After Aristotle, rhetoric only attracted second-rate minds,” he says, “and even the Rhetoric, as brilliant as it is, isn’t the old boy at his best.” The scholarship that most of us saw as the foundation of our field could, for Alan, boast only of a single, soft Aristotelian text, from which it was all downhill until—what? Alan G. Gross could lead it to salvation? This every-word-of-the-title-bothers-me response was not just for show. Superficially it might look like Alan is merely riffing on my theme, nodding and winking all the while, not really suggesting there was anything wrong with his book. But he put the book through two more editions, the third actually changing that problematic title dramatically, dropping both rhetoric and science into a subtitle, and shifting away from the trademarking implications. It now exists as Starring the Text: The Place of Rhetoric in Science Studies.9 The arm around my shoulder wasn’t fake, either. In part, I suppose, his kindness was because I was a small fry that he was too considerate to squash, but in much larger part it was because he knew I was right (something I absolutely did not anticipate). He befriended me for real. We had a long correspondence and met many times over the years, and he was unflaggingly supportive of my scholarship (though not without some very sharp criticism, now and again, which was mutual). I treasure the shelf of books he sent me as they came out, all affectionately inscribed. While he was highly congenial in that “Forum” reply, and even gestured at a team effort, naming a few of his rhetoric-of-science colleagues,10 his response is emblematic of Alan’s early Bad Boy stance in rhetoric: the whole field of 243

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rhetoric needed renovation, he proclaimed, and everyone else was too timid to bring it about. But there are also distinct whiffs of the more restrained approach he developed, very unexpectedly to most of us, within a few short years. What happened to cause that change is too complex to explore here, and I’m not convinced I understand it fully myself, but one way to characterize the scholarly stance he adopted in the decade after The Rhetoric of Science is that he decided to live mostly within the confines of a tradition that he still viewed as not up to the job of accounting for the full power of science. Rather than beefing up that tradition to support his big claims, he deradicalized and started making smaller, but more elegant and more factually angled, claims, turning toward the communicative mechanics and structure of texts and turning his back on the epistemic and ontological implications of rhetoric that drove his early radicalism. Rhetoric, for most of us in the field, is the study of how all symbolic activity affects the world, how it creates and shapes the beliefs of humans and leads them to storm the Bastille, or defend it, to get a vaccination or avoid one at all costs, and to everything else they adopt or reject in their cooperative, antagonistic, social and political and personal lives. The creative and shaping force that circulates in these symbolic actions we call persuasion, and many of us see persuasion as the creative force in making knowledge as well. Communication is a subset of rhetorical activity, since there is no communication without some quotient of persuasion. Even a flat, just-the-facts kind of sentence like “A plateau appears as a mass ratio of sRNA to DNA of 0.025 per cent” brings along regimes of persuasion that may not immediately provoke us to storm the Bastille but serve to substantiate sRNA (soluble ribonucleic acid; now known as transfer RNA, or tRNA) and DNA (deoxyribonucleic acid) as organic molecules necessary for the growth and propagation of life, moving us to anticipate that a mass ratio between them has potentially significant implications for the existence of all organisms on our planet. Plateau is a slightly jaunty way to hail a graph—a metaphor, not a technical geographic term—that signals here a flat portion of a line in a plot of that mass ratio (the “amount of E. coli P32 sRNA found in the E. coli DNA band . . . as a function of increasing amounts of P32 sRNA”), which in turn signals that only a very small portion of the DNA is able to “digest” an sRNA molecule under the conditions the authors and their colleagues set up in their Cold Spring Harbor lab.11 One “premise” in the suasive regimes motivating this sentence, for instance, is that the molecules one can extract from a bacterium (specifically, the bacterium known by the nickname that stands for Escherichia coli, which in turn commemorates the person who “discovered” it, Theodor Escherich) hold constant throughout all of creation. What is true of E. coli DNA is true of fish and goat and human DNA. 244

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But a focus on communicative mechanics lowers the emphasis on persuasion and belief and largely assumes a default “transparency” setting such that the relevant symbols (sRNA, DNA, mass ratio, plateau, . . . ) function only to convey already existing knowledge and facts, packed alongside one another into the relevant syntactic relationships, and playing little to no role in the creation of any knowledge or facts. And science wants the emphasis on conveyance over creation, of course, to represent knowledge as found or discovered, not made by bringing symbols together in persuasive ways. That’s why we get “a plateau appears,” as if there were no agents or causation of any kind behind its mysterious manifestation, rather than something like, as in Newton’s idiom, “we drew a straight line to get you to conceive of the relation . . .” The Alan G. Gross of The Rhetoric of Science was at the forefront of the creating-knowledge school in science studies, but he soon shifted so substantially toward the conveying-knowledge school that he became uncomfortable with this “earlier version of myself.”12 Early Alan, for instance, says that “the sense that a molecule . . . exists at all, the sense of its reality, is an effect only of words, numbers, and pictures judiciously used with persuasive intent.”13 He is talking specifically of DNA here, but clearly meant the claim to extend to all molecules and all scientific constructs—sRNA, tRNA, quarks, mesons, beakers of acid, all of them. This radical claim, effectively that all of science is an effect “only of ” symbols, came to haunt Later Alan. With Starring the Text, he excised it completely. In fact, he excised the entire offending chapter that contained it, “The Tale of DNA.” Joe Harmon was catalytic in Alan’s change. Joe had come at the rhetoric and communication of science from the opposite end, not from theorizing and criticizing like Alan, but from paying his bills by producing scientific and technical writing for a national laboratory. He was, that is, (and remains) a practicing scientific communicator. So he has a mechanic’s-eye view of the nuts and bolts that hold the knowledge together and fasten the facts around it. He threads those nuts. He tightens those bolts. But he also managed to be an independent scholar from very early on, in his spare time, producing very interesting scholarship along two general paths. One path reveals a fascination with brief glimpses of what he termed the “literary” flashes that can be, very rarely, encountered in the endemically drab texts of science and technology he spent so much time with—the isolated simile, pun, or alliterative phrase he happened upon in the otherwise stylistically “barren” landscape of technical texts, the occasional metaphor peeking out from under the “long noun phrases, quantifications, abbreviations, and specialized technical terminology” that dominate scientific prose.14 Joe published a few articles cataloging these 245

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findings, curatorial pieces attending to what he called “Perturbations in the Scientific Literature.”15 The other path was more historical, with particular attention to grammatical and structural development in scientific texts; this path, in particular, was winding toward a book on the evolution of scientific and technical prose that he saw as a very distant prospect, perhaps unreachable.16 But in the late 1980s and early 1990s as he was taking these intertwining paths, he saw a new literature growing up around him. It featured authors like Bazerman, Prelli, Myers, and the radical Dr. Gross. It fascinated him and quickly delivered him to the conclusion that “beyond a shadow of a doubt . . . rhetoric matters in science.”17 Rhetoric was not just the source of scattered aesthetic curiosities and communicative perturbations, he saw. It was essential to the functioning of scientific texts. The nuts and bolts of those texts served persuasive ends. Joseph E. Harmon invited Alan G. Gross to give a talk at the Argonne National Laboratory, where he plied his craft. Naturally, the talk outraged some of the scientists who attended it—Alan had not yet renounced his radicalism—but the two of them almost immediately (at lunch, after the talk) fell into sync about the book that had been beckoning and frustrating Joe. Alan sketched out an architecture and a research program, and they soon began a painstaking linguistic, rhetorical, and generic assay of 1,800 scientific articles (more or less), over four centuries, in three languages, from elite journals publishing in the five major scientific fields. The result, nine years later, was (1) the monumental Communicating Science: The Scientific Article from the 17th Century to the Present, and, along the way, (2) the partnership that gave us five more remarkable books, including The Many Voices of Modern Physics. The Many Voices of Modern Physics exemplifies what Joe and Alan did best together, and better than anyone. The great contribution of their work together is that they reveal the fundamentals of scientific communication not in terms of direct conveyance, nor in terms of epistemic persuasion, but in the sweet spot that recognizes largely communicative textual dimensions like precision, clarity, and consistency, working hand-in-glove with the largely rhetorical dimensions of formal arrangement, recurring appeals, and argumentative structure. The Goodman and Rich appearing-plateau sentence I noted earlier, for instance, did not drop randomly onto my page. I plucked it from Communicating Science, where Alan and Joe (along with Michael Reidy) tell us, with some understatement, that the “plateau on [the] line graph . . . has only the scientific significance that Goodman and Rich bestow upon it by the power of their argument.”18 That’s an only Alan could live with, tied to significance rather than to reality. But much of that argumentative power comes by activating the regimes of persuasion through their coding into particular linguistic nuts and 246

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bolts (“these results show,” “if we assume,” “it is likely that,” “It has long been known,” “it has been demonstrated,” . . . ). Communicating Science also gives us some insight into the discomfort Alan expressed over the definite article, two nouns, and preposition of his title, The Rhetoric of Science, in his response to my complaints about his title. We have already heard about the definite article, the, and one of the nouns, rhetoric. But in a passage framing the methodology for Communicating Science, we get to hear about the problems with the other noun, science.19 What’s important, though, is that it’s not just Alan speaking. It’s Alan-Joe, or Joe-Alan, with Michael singing harmony. They inventory the coverage of The Rhetoric of Science: here an article or pamphlet, there a treatise or notebook; heavily skewed toward a few singular Great Men; equally skewed toward physics and biology; almost entirely focused on the Anglo-American historical corridor. Their verdict is damning: “It would not be much of an exaggeration to say that . . . science—its actual intellectual topography—is virtually ignored.”20 This was ten years later, and the survey included Bazerman’s and Prelli’s books as well, not just Alan’s own. But it lays bare a crucial strain of Alan’s discontent with the project that The Rhetoric of Science was trying to build. The (in)adequacy of rhetoric was almost beside the point. The real failure of that project was the slaphappy and unconstrained way Alan (and others) had previously put it to work. In other words, while Communicating Science was the fulfillment of Joe’s dream, which Alan came to share, it was also a pivotal act of redemption for Alan, Later Alan atoning for the sins of Early Alan, which he might not have realized without Joe. It is also an incredibly valuable contribution to science studies. I called this book “monumental” a few paragraphs back. That was not an exaggeration. Alan was often modest about it (his inscription in the copy he gave me is “I apologize for this perhaps slightly dull contribution to knowledge”), but Communicating Science was a game changer. It shows in very specific terms how, why, and when we get from discourse like Exhibit A to discourse like Exhibit B. Exhibit A This made me take Reflections into consideration, and finding them regular, so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation Optick instruments might be brought to any degree of perfection imaginable, provided a Reflecting substance could be found, which would polish as finely as glass, and reflect as much light, as glass transmits, and the art of communicating to it a Parabolick figure be also obtained. . . . Amidst these thoughts I was

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THE MANY VOICES OF MODERN PHYSICS forced from Cambridge by the Intervening Plague, and it was more then two years, before I proceeded further.21 Exhibit B The unlabeled bacterial DNAs used in this investigation were prepared by the method of Marmur. Calf thymus and salmon sperm DNA were obtained from Sigma Chemical Company and California Corporation. The DNAs from the bacteriophages were prepared . . . the DNA was denatured by heating . . . then quickly chilled. . . . Denaturization was followed by measuring.22

Exhibit A is from Isaac Newton’s 1672 letter on his theory of light. The immediate source of Exhibit B is our friends Goodman and Rich again, but the purging of the personal it reveals is evolutionary, with epistemic selectional pressures disfavoring information about whether Howard Goodman or Alexander Rich, or Melissa Quinn (whom they thank in a metatextual speech act for “capable technical assistance”23), or someone even more completely erased from the research, was obtaining and preparing and heating and chilling the DNA. The argument becomes more persuasive in science if it is abstracted away from the obtainers and preparers and especially the arguers and gives a starring role to the obtained and prepared materials. Goodman and Rich don’t matter, and they know they don’t matter, for the experimental execution to be epistemically revealing. If they had left Cold Spring Harbor for two years because of a plague, who would care? so long as their bacteriophage DNAs were appropriately denatured. Communicating Science, which charts the evolution of these depersonalizing, agent-removing, method-and-material-promoting stylistic moves, was followed by two more such contributions, both of them pursuing the same kind of field-renovating mission, both relying on the same kind of data-driven approach, and both bringing the same kind of systematicity to an underexplored area, a shockingly neglected area in one case and a riotously emergent area in the other. The neglected area was the verbal-visual interface in scientific texts. There was a cottage industry by this time in rhetorically inflected textual analyses of science, and while there was some scattered attention to scientific visuals, there were approximately zero accounts of the remarkably seamless way that texts and visuals function together in scientific discourse. Shockingly neglected is not too strong a characterization, which you can test with a moment’s scan of any scientific journal; Goodman and Rich’s article, as an example close to hand, for instance, has six graphics, nearly one per page, and their appearing-plateau 248

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sentence is meaningless without the presence of their figure 3.24 The interpenetration of language and imagery is not only pervasive to a degree that makes it, or should make it, definitional of scientific communication, it is also utterly fundamental to scientific epistemology. Alan and Joe remediate this astonishing gap in Science from Sight to Insight: How Scientists Illustrate Meaning, the first, and still the only, monograph theorizing the total rhetorical integration of texts and images in science. The riotously emergent area of scientific communication, of course (we’re up to 2016 now), was the explosion of digital technologies, which was (and is) reshaping communicative practices on an almost daily basis, prominently including those of science. Alan and Joe do an impressive amount of groundwork in The Internet Revolution in the Sciences and Humanities.25 But Twitter and Reddit were barely scratching at the window of scientific communication at the time and TikTok was nowhere to be seen, all of which are actively reshaping the styles and genres of scientific communication.26 At an absolute minimum, you’ll be reading this months, but also possibly years, after I sat here putting my fingers to a keyboard, so there may well be—indeed, proportional to the time between my here (it’s a deck in August 2022, by the way, overlooking the cove off Otter Point in Nova Scotia; remarkably pleasant) and your here (which I hope is also remarkably pleasant), there absolutely will be—digital communicative shifts of various sorts that make Twitter and Reddit and TikTok rather quaint, if not fully obsolete. Even their title is dating steeply, as the word internet becomes increasingly archaic and revolution should at least be pluralized, if not replaced by something like upheaval. It is an important book reflecting the best Alan and Joe could do in an utterly mercurial situation. It remains valuable especially for the way it frames the communicative issues (including volatility) and charts the early years of science on the internet; for both reasons, it is foundational in significant ways.27 But giving it the kind of disciplinary authority that Communicating Science and Science from Sight to Insight have achieved was always an impossible dream.28 Many authorial partnerships are a flip of the coin, or a systematic alternation, for whose name comes first, but it is significant that Alan is lead author on all of these books. There is a parallel track their partnership took, though, one that leads more directly to The Many Voices of Modern Physics. On that track, Joe takes lead author spot. It includes The Scientific Literature: A Guided Tour; as well, on a kind of side line, The Craft of Scientific Communication.29 These three books, also nuts and bolts and rhetorical levers books, focus more intently, and lovingly, on specific communicative practices. Craft might seem like an odd book to describe in these terms. It’s a style guide for scientists and other technical communicators 249

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to shape their precise, detailed, exacting prose under the requisite considerations of clarity, consistency, and accuracy, but also, to use a word not common in connection with scientific communication, under considerations of aesthetics; to also write engagingly. Having practiced this craft, I can attest to the book’s utility. Having taught this craft, and hence pored over tons of such guides, I can attest to its uniqueness. It is not primarily prescriptive (“Define the scope of the study / Define the problem / State the objective / Identify gaps . . .”30). Its slant is descriptive, working from both specific exemplars and inductive generalizations (“While the science in the best modern scientific articles is never conventional, over time science has adopted a conventional form for the introduction that relies . . .”31). All of the specific exemplars are as clear, graceful, and streamlined as you would expect, curated from the massive storehouse of scientific prose these two assembled, chiefly out of their Communicating Science project, but Joe and Alan also can’t resist throwing in a few treats just for the fun of it (“Actually, this paper doesn’t need an introduction,” they quote from the notorious parody article, “Super G-String,” “since anyone who’s the least bit competent in the topic of the paper he’s reading doesn’t need to be introduced to it, and otherwise why’s he reading it in the first place? Therefore, this section is for the referee.”32). This sense of fun and aesthetic appreciation are the defining traits of this parallel track. All categorizations of cultural activity are ultimately artificial, but we’ll call this Joe’s track, not just for its convenient alignment with his lead authorship but because it traces back rather naturally to his early fascination with stylistic perturbations in scientific prose. (The more theoretical and analytical books we will label as falling along Alan’s track, for the same convenient and lineage reasons.33) The Scientific Literature is as close to a museum exhibit as any book could be. Officially Joe and Alan are editors, but the term tour guides suggested by the subtitle is much more accurate. The book collects and displays 124 passages of scientific writing from three languages (English, alongside French and German passages in translation), along both historical and conceptual lines, crosscut by style, discipline, genre, and nationality. We even get three categories of perturbations (playfulness, belligerence, and aesthetic grace34). The passages are really well chosen. While many of them come from highly technical journals (Physical Review, PNAS, Bulletin de la société chimique de France, Sitzungsberichte der Physikalisch- medizinischen Gesellschaft zu Würzburg), they are largely comprehensible, and appreciable, by an educated lay reader. Joe and Alan lead us through their exhibition halls with wit, geniality, and consistent illumination. The book is an utter delight—nearly requisite as a companion to Communicating Science, and also nicely complementary to Science from Sight to Insight, but fully satisfying on its own. 250

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Which, after all of our considerations of their partnership and productions, brings us finally to a word about the current and final exhibition by these two masters of scientific communication, the reason we are here, Joe and Alan’s The Many Voices of Physics. It is a remarkable capstone to their splendid partnership, something I hope all the foregoing anecdotes and characterizations have helped you appreciate. It also brings us to the conundrum of afterwords. What can I say about a book you have just read? (If you still haven’t read it, please return to the first paragraph of this afterword and take it seriously this time.) The kind of descriptive and qualitative accounts I have been giving their other books surely won’t do. Description is pointlessly redundant. The content and structure and aims of the book are fresh in your mind. You already know, for instance, that the curated examples are much more deeply embedded in the unfolding text of Many Voices than in Scientific Literature, so that the passages are more like episodes in a narrative than framed artifacts hanging beside each other on the wall. Qualitative commentary is equally pointless and perhaps presumptuous. You have your own opinion. So, I have decided to opt for an imaginary scenario in which we have both recently finished the book and met for coffee (or tea or beer or wine . . . ) to do a little curating of our own, sharing our favorite moments from the book—let’s say our top three. Alas, I will miss yours “now,” though I am always available by email if you want to drop me a line at some future now. I’ll cheat a bit, though. I won’t quote my favored passages here, except for a few scraps, which I would do over coffee, and even more eagerly over beer, since they are right here in the book and since you can’t hear my dulcet inflections. But here are my three, in countdown order. 3. The passage coming in at number three is not by a scientist but by one of the great intellects and prose stylists of the twentieth century, Bertrand Russell, whose little Relativity volume Joe and Alan quote for its fantastic midwayplatform analogy (p. 29–31). My affection for the passage may date me as much as it dates Bertie. I haven’t been to a carnival in many decades, and I haven’t had the experience he describes since adolescence. It’s a midway ride with concentric rotating platforms, where each platform moves slightly faster as you progress inward until a few brief steps have you clutching onto a handle and spinning too fast to return; I remember four spinning sections.35 If you have no personal experience with such a ride, think of one like the Rotor or the Gravitron, which rotates so quickly it pastes you against the outside by centrifugal force; now divide the floor up into concentric platforms moving at uniform but increasing speeds, and put the whole mechanism in reverse, so the inside disc is moving the fastest. If my description isn’t helping, you may never have been a carnival-ride 251

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partaker. Never mind. Having undergone the experience would add a bit of remembered proprioception to Russell’s description, but he renders the device clearly in this passage: “a series of moving platforms, going round and round in a circle. The outside one goes at four miles an hour; the next goes four miles an hour faster than the first; and so on. You can step across from each to the next, until you find yourself going at a tremendous pace” (p. 29). Russell’s point, of course, is not that you’ll be heaving cotton candy and caramel apples when you make your way to the inner platforms, but that there are infinitesimal differences in the relative speeds of those platforms to the ground on which the contraption is situated. If the farthest one out is rotating at 4 mph (≈6.5 km/h), and the second one is 4 mph faster than that, it is ever-so-slightly less than the commonsense expectation of 8 mph (≈13 km/h) faster relative to the ground. Then comes the fantasy. Russell shows us that as we move farther and farther in, through millions of such spinning platforms, we can never reach the speed of light because those tiny discrepancies build insurmountably. It’s a classic analogical thought experiment, curated in the halls of Many Voices, which our guides sum up beautifully by saying that what Russell establishes here is that “the speed of light is the speed limit of the universe,” like a traffic sign posted that, instead of 50 or 60 mph (80 km/h or 100 km/h), features the symbol c. Russell’s platforms, they tell us, are actually stepping us through the Lorentz transformation equations. 2. Any passage by Richard Feynman is going to find itself easily among the top rankings of audaciously witty scientific prose. Accordingly, Joe and Alan season the whole book with Feynmanisms, but I want to single out his brilliantly layered analogy of a water droplet, expanded for reasons of “visibility” two thousand, then four million, then a billion times, until we stand beside it and look not at a smooth, transparent, liquid but at “something like a crowd at a football game” with blurry-edged “atomic” blobs jostling and bouncing against each other in an alien-but-now-familiar jumble of motion (p. 138–39). The passage is exhilaratingly impressive on its own, but it is what our guides make of it for us that puts it on this list. They use it to ease us into a discussion of “quantum magic.” Having “watched” a water droplet balloon up until paramecia are putzing around like aimless, sightless fish; then again, past the organic world, until it is a bustling crowd of molecules; then again, until it is an endless field of quivering and twisting atomic clouds; the magic of reconceptualized metals, gases, liquids, even complex objects like computers comes more naturally. Feynman comes back later in the parade of reimaginings to point out that things “on a small scale behave like nothing on a large scale, . . . as we go down and fiddle around with the atoms down there, we are working with different laws, and we can expect to do different things” (p.147). 252

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1. As you will have noted, I have an obvious weakness for analogies, but my top selection is a wonderful example of more literal prose. It features the inevitable analogic entrenchments of all language (featuring terms like wavelength, absorb, and jump for the phenomena of light) but forgoes any novel figuration to explain color. “Chalk is white,” Steven Weinberg says laconically, and adds the monosyllable that in English condenses the fundamental drive of all science: “Why?” (p. 105) Then he serves up the standard middle school explanation of color in a few deft strokes (different substances reflect different constellations of light waves; for chalk, that constellation is perceived as white). Done! Well, no. We get another “Why?” which Weinberg satisfies with consummate elegance in terms of energies and atoms (p. 106) getting us from middle school Newtonianism to Bohrian quantum theory. Once again our guides, Joe and Alan, continue a conceptual journey initiated by a perfectly selected passage, also into the fantastic subatomic world, perhaps the most rewarding journey of this very rewarding book. They show us how Weinberg, working in the opposite direction to Feynman, moves his explanations “up” to chemistry (chalk, after all, is made of calcium, carbon, and oxygen), then “up” again to biology (the calcium, carbon, and oxygen coming from bodies of tiny ancient shellfish), implicating a theory of everything. Joe and Alan bring in the voices of Eugene Wigner, Philip Anderson, and David Deutsch to probe the possibilities for a unification of physics. This short stretch of the book (p. 106–10) is a superb example of what they do throughout Many Voices: they reproduce and represent scientific texts, but they also explicate them critically, not just for what they do well but also for their wayward claims and untethered assumptions. That is a hallmark of several of Joe and Alan’s collaborations, but this book suitably does it best, guiding us through the potent discourses of science. In doing so, they have realized their shared aspirations to reveal the linguistic, rhetorical and semiotic machinery of the texts that have governed our most fundamental understanding of the material world. Their collaboration started with that dream. “After two decades,” Joe wrote of his partnership with Alan in 2014, “we have not stopped dreaming.”36 The intellectual tragedy of Alan’s passing is grievous. There will be no more work by him, nor by the two of them. But Joe’s personal tragedy is that he has been left abruptly to dream on his own.

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NOTES

Introduction 1. Peter Galison, Image and Logic: A Material Culture of Microphysics (Chicago: University of Chicago Press, 1997). 2. Andrew Pickering, Constructing Quarks: A Sociological History of Particle Physics, 2nd ed. (Chicago: University of Chicago Press, 1999). 3. Thomas S. Kuhn, The Structure of Scientific Revolutions (Chicago: University of Chicago Press, 1970). 4. Rom Harré, Great Scientific Experiments: Twenty Experiments That Changed Our View of the World (Mineola, NY: Dover, 2002). 5. Alan Lightman, The Discoveries: Great Breakthroughs in 20th-Century Science (New York: Vantage Books, 2006). 6. Laura Garwin and Tim Lincoln, eds., A Century of Nature: Twenty-One Discoveries That Changed Science and the World (Chicago: University of Chicago Press, 2003). 7. Aristotle, On Rhetoric, trans. George A. Kennedy (New York: Oxford University Press, 1991), 296. 8. Chaïm Perelman and Lucie Olbrechts-Tyteca, The New Rhetoric: A Treatise on Argumentation, trans. John Wilkinson and Purcell Weaver (Notre Dame, IN: Notre Dame Press, 1969) 372. 9. Perelman and Olbrechts-Tyteca, New Rhetoric, 371. 10. Perelman and Olbrechts-Tyteca, 385. 11. Alan G. Gross and Ray D. Dearin, Chaim Perelman (Albany: State University of New York Press, 2003), 76. 12. W. H. Leatherdale, The Role of Analogy, Model, and Metaphor in Science (Amsterdam: North-Holland, 1974); Mary B. Hesse, Models and Analogies in Science (Notre Dame, IN: University of Notre Dame Press, 1966); Alan G. Gross, Starring the Text: The Place of Rhetoric in Scientific Studies (Carbondale: Southern Illinois University Press, 2006), 32–45. 13. Marcello Pera, The Discourses of Science, trans. Clarissa Botsford (Chicago: University of Chicago Press, 1994), 73–76. 14. Lise Meitner and O. R. Frisch, “Disintegration of Uranium by Neutrons: A New Type of Nuclear Reaction,” Nature 143, no. 3615 (February 11, 1939): 239–42. 15. James Robert Brown and Yiftach Fehige, “Thought Experiments,” Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, August 12, 2014, http://plato.stanford.edu/archives/spr2016/ entries/thought-experiment/. 16. Nathan Crick, “Conquering Our Imagination: Thought Experiments and Enthymemes in Scientific Argument,” Philosophy & Rhetoric 37, no. 1 (2004): 21–41; John Norton, “Thought Experiments in Einstein’s Work,” in Thought Experiments in Science and Philosophy, ed. T. Horwitz and G. J. Massey (Savage, MD: Rowman and Littlefield, 1991), 129. 17. Longinus, On the Sublime, trans. W. H. Fyfe (Cambridge, MA: Loeb Classic Library, 1995), 215.

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NOTES TO PAGES 8–19 18. Alan G. Gross and Joseph E. Harmon, Science from Sight to Insight: How Scientists Illustrate Meaning (Chicago: University of Chicago Press, 2014). 19. Gross and Harmon, Science from Sight to Insight, 86–87. Retrograde motion can also be explained geometrically if one assumes the Earth is stationary, but that requires introduction of circles within circles, or epicycles. 20. Galileo Galilei, Dialogue Concerning the Two Chief World Systems, trans. Stillman Drake (Berkeley: University of California Press, 1967), 342. 21. John Norton, “The Worst Thought Experiment,” in The Routledge Companion of Thought Experiments, ed. M. T. Stuart, J. R. Brown, and Y. Fehige (London: Routledge, 2017), 454–68. 22. Gross and Dearin, Chaim Perelman, 77. 23. Perelman and Olbrechts-Tyteca, New Rhetoric, 393. 24. Joseph E. Harmon and Alan G. Gross, The Craft of Scientific Communication (Chicago: University of Chicago Press, 2010), 50–52. 25. Jeanne Fahnestock, “Accommodating Science: The Rhetorical Life of Scientific Facts,” Written Communication 3 (1986): 257–96; Greg Myers, “Discourse Studies in Scientific Popularizations,” Discourse Studies 5 (2003): 265–79. 26. Lisa Randall, Knocking on Heaven’s Door: How Physics and Scientific Thinking Illuminate the Universe and the Modern World (New York: HarperCollins, 2011), 241–42. 27. Perelman and Olbrechts-Tyteca, New Rhetoric, 210–14. 28. Albert Einstein, “On the Electrodynamics of Moving Bodies,” in Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics, ed. John Stachel (Princeton, NJ: Princeton University Press, 1998), 125–27. 29. Stephen Hawking, A Brief History of Time (New York: Bantam Books, 1998), 95–101. 30. Alan G. Gross, Joseph E. Harmon, and Michael Reidy, Communicating Science: The Scientific Article from the 17th Century to the Present (New York: Oxford University Press, 2002), 161–86. 31. Florian Cajori, A History of Mathematical Notations, vol. 2, Notations Mainly in Higher Mathematics (Mineola, NY: Dover, 1993), 185. 32. Joseph E. Harmon, “Current Contents of Theoretical Scientific Papers,” Journal of Technical Writing and Communication 22 (1992): 357–75. 1. Special Relativity 1. Walter Isaacson, Einstein: His Life and Times (New York: Simon & Schuster, 2007), 127. 2. Albert Einstein, “On the Electrodynamics of Moving Bodies,” in The Principle of Relativity, trans. W. Perrett and G. B. Jeffery (New York: Dover, 1952), 37. 3. John D. Norton, “Einstein’s Special Theory of Relativity and the Problems in the Electrodynamics of Moving Bodies That Led Him to It,” in The Cambridge Companion to Einstein, ed. M. Janssen and C. Lehner (Cambridge: Cambridge University Press, 2014), 73; Isaacson, Einstein, 115; Gerald Holton, Thematic Origins of Scientific Thought: Kepler to Einstein (Cambridge, MA: Harvard University Press, 1988), 220–25. 4. Einstein, “On the Electrodynamics of Moving Bodies,” 37–38. 5. John Stachel, Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics (Princeton, NJ: Princeton University Press, 1998), 103–4. 6. Galileo Galilei, Dialogue Concerning the Two Chief World Systems, trans. Stillman Drake (Berkeley: University of California Press, 1953), 187. 7. Galilei, Dialogue Concerning the Two Chief World Systems. 8. Stephen G. Brush, “Why Was Relativity Accepted?” Physics in Perspective 1 (1999): 189–214.

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NOTES TO PAGES 20–41 9. “Einstein Expounds on His New Theory,” New York Times, December 3, 1919. 10. Albert Einstein, Relativity: The Special and General Theory, trans. Robert W. Lawson, 100th anniversary ed. (Princeton, NJ: Princeton University Press, 2016), 11. 11. Hanoch Gutfreund and Jürgen Renn, The Formative Years of Relativity (Princeton, NJ: Princeton University Press, 2017), 142. 12. Einstein, Relativity, 36–37. 13. Einstein, 37–38. 14. Max Born, Einstein’s Theory of Relativity, trans. H. L. Brose (New York: E. P. Dutton, 1922), 196–97. 15. Hermann Minkowski, “Space and Time,” in Space and Time: Minkowski’s Papers on Relativity, trans. Fritz Lewertoff and Vesselin Petkov (Montreal: Minkowski Institute Press, 2012), 41, 46. 16. Born, Einstein’s Theory of Relativity, 196–97. 17. Arthur Eddington, Space, Time and Gravitation: An Outline of the General Relativity Theory (Cambridge: Cambridge University Press, 1920), 17–18. 18. Bertrand Russell, ABC of Relativity, 4th ed. (London: Routledge, 2009), 23. 19. Russell, ABC of Relativity, 25–26. 20. Enrique Zeleny, “Russell’s Thought Experiment in Special Relativity,” WOLFR A M Demonstrations Project, March 2011, https://demonstrations.wolfram.com/ RussellsThoughtExperimentInSpecialRelativity. 21. Russell, ABC of Relativity, 9; emphasis added. 22. Einstein, Relativity, 10. 23. Eddington, Space, Time and Gravitation, vii. 24. Born, Einstein’s Theory of Relativity, v–vi. 25. George Gamow, Mr. Tompkins in Paperback (Cambridge: Cambridge University Press, 1965), xi. This edition combines Mr. Tompkins in Wonderland (1940) and Mr. Tompkins Explores the Atom (1944). 26. Gamow, Mr. Tompkins in Paperback, 2–4. 27. Gamow, 20. 28. Sander Bais, Very Special Relativity: An Illustrated Guide (Cambridge, MA: Harvard University Press, 2007), 60–61. 29. Bais, Very Special Relativity, 62. For clarity in this context, we have changed Bais’s symbols for time from w to t. 30. A. John Mallinckrodt, “The So-Called Twin Paradox,” last modified 2001, https://www. cpp.edu/~ajm/materials/twinparadox.html; Michel Janssen, “Special Relativity,” in The Cambridge Companion to Einstein, ed. M. Janssen and C. Lehner (Cambridge: Cambridge University Press, 2014), 499–504. 31. Minori Harada, “The Twins Paradox Repudiation,” Physics Essays 24, no. 3 (2011): 454–55; Kaberi Hazra, “On the Resolution of the Twins Paradox,” Current Science 95, no. 6 (2008): 706–8. 2. General Relativity 1. Arthur I. Miller, Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc (New York: Basic Books, 2002), 18. 2. Albert Einstein, “The Foundation of the General Theory of Relativity,” in The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity,” ed. Hanoch Gutfreund and Jürgen Renn, trans. Alfred Engel (Princeton, NJ: Princeton University Press, 2015), 183–232. 3. Einstein, “Foundation of the General Theory of Relativity,” 184.

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NOTES TO PAGES 42–56 4. Tony Rothman, “The Forgotten Mystery of Inertia,” American Scientist 105, no. 6 (2017): 344–47, doi:10.1511/2017.105.6.344. 5. Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality (New York: Vintage Books, 2005), 37. 6. See, for example, Greene, Fabric of the Cosmos, 23–24. 7. Albert Einstein, Relativity: The Special and General Theory, 100th Anniversary Edition (Princeton, NJ: Princeton University Press, 2016), 80–82, trans. Robert W. Lawson from Über die spezielle und die allgemeine Relativitätstheorie: Gemeinverständlich (Braunschweig: Vieweg, 1917). 8. See, for example, Kip S. Thorne, Black Holes and Time Warps: Einstein’s Outrageous Legacy (New York: W. W. Norton, 1994), 97–100. 9. Albert Einstein, Relativity, 88–90. 10. Abraham Pais, “Subtle Is the Lord . . .”: The Science and the Life of Albert Einstein (Oxford: Oxford University Press, 1982), 178–79. 11. Albert Einstein, “The Meaning of Relativity: Four Lectures Delivered at Princeton University, May 1921,” in The Formative Years of Relativity: The History and Meaning of Einstein’s Princeton Lectures, ed. and with commentary by Hanoch Gutfreund and Jürgen Renn (Princeton, NJ: Princeton University Press, 2017). 12. Einstein, Relativity, 93–94. 13. Einstein, 94–96. 14. George Gamow, Mr. Tompkins in Paperback (Cambridge: Cambridge University Press, 1965), 32–36. 15. Einstein, “Foundation of the General Theory of Relativity,” 214. 16. Roger Penrose, “The Rediscovery of Gravity: The Einstein Equation of General Relativity,” in It Must Be Beautiful: Great Equations of Modern Science, ed. Graham Farmelo (London: Granta, 2002), 49. 17. S. James Gates Jr., Frank Blitzer, and Stephen Jacob Sekula, Reality in the Shadows (or) What the Heck’s the Higgs (New York: YBK Publishers, 2017), 50–51. 18. Einstein, “Meaning of Relativity,” 244. 19. Penrose, “Rediscovery of Gravity,” 49. 20. Gates, Blitzer, and Sekula, Reality in the Shadows, 51. 21. Einstein, “Foundation of the General Theory of Relativity,” 226. 22. Einstein, 226. 23. Einstein, Relativity, 89–90. 24. Wilfred Owen, Poems (London: Chatto and Windus, 1921), 12. 25. F. W. Dyson, A. S. Eddington, and C. Davidson, “A Determination of the Deflection of Light by the Sun’s Gravitational Field from Observations Made at the Total Eclipse of May 29, 1919,” Philosophical Transactions A 220 (1920): 314. 26. Dyson, Eddington, and Davidson, “Determination of the Deflection of Light,” 332. 27. Einstein, Relativity, 148. 28. Jürgen Neffe, Einstein: A Biography, trans. Shelley Frisch (New York: Farrar, Straus and Giroux, 2007), 9–15. 29. Alistair Sponsel, “Constructing a ‘Revolution in Science’: The Campaign to Promote a Favorable Reception for the 1919 Solar Eclipse Experiments,” British Journal for the History of Science 35, no. 4 (2003): 463. 30. Arthur Eddington, Space, Time and Gravitation: An Outline of the General Relativity Theory (Cambridge: Cambridge University Press, 1920), 116.

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NOTES TO PAGES 56–68 31. Clifford M. Will, “The 1919 Measurement of the Deflection of Light,” Classical and Quantum Gravity 32 (2015): 124001. 32. Walter Isaacson, Einstein: His Life and Times (New York: Simon & Schuster, 2007), 542. 33. Stephen Hawking, The Illustrated A Brief History of Time (New York: Bantam Books, 1996), 110–11. 34. Jeanne Fahnestock, Rhetorical Style: The Uses of Language in Persuasion (New York: Oxford University Press, 2011), 235–37. 35. Hawking, Brief History of Time, 92. 36. Christopher Evans, Pablo Laguna, and Michael Eracleous, “Ultra-Close Encounters of Stars with Massive Black Holes: Tidal Disruption Events with Prompt Hyperaccretion,” Astrophysical Journal Letters 805, no. 2 (2015): L19. 37. Gary Taubes, “Publication by Electronic Mail Takes Physics by Storm,” Science 259 (1993): 1246–48; “MacArthur Grants Recognize Nine Researchers,” Science News, September 25, 2002, https://www.science.org/content/article/macarthur-grants-recognize-nine-researchers. 38. Jacob Aron, “Black Holes Devour Stars in Gulps and Nibbles,” New Scientist, March 28, 2015, https:// www.newscientist.com/article/mg22530144-400-black-holes-devour-stars-in-gulps-and-nibbles. 39. “Jacob Aron on Science Writing: ‘Analogies Are like Forklift Trucks,’” Guardian, April 25, 2013, https://www.theguardian.com/science/2013/apr/15/jacob-aron-science-writing-analogies. 40. Carlo Rovelli, Reality Is Not What It Seems: The Journey to Quantum Gravity (New York: Riverhead Books, 2017), 82. 3. Quantum Mechanics 1. Waldemar Kaempffert, “Details Concepts of Quantum Theory: Heisenberg of Germany Gives Exposition before British Scientists,” New York Times, September 2, 1927. 2. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Oxford: Oxford University Press, 1958), vii. 3. Werner Heisenberg, The Physical Principles of the Quantum Theory, trans. Carl Eckhart and Frank C. Hoyt (New York: Dover, 1930), 10. 4. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, “Quantum Behavior,” in The Feynman Lectures on Physics, vol. 3 (Reading, MA: Addison-Wesley, 1965), 1. 5. Jennifer Burwell, Quantum Language and the Migration of Scientific Concepts (Cambridge: MIT Press, 2018), 28. 6. M. Planck, “On the Theory of the Energy Distribution Law of the Normal Spectrum” [Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum], Verhandlungen der Deutschen Physikalischen Gesellschaft 2 (1900): 237–45. Revision of the translation by D. ter Haar in The Old Quantum Theory (Oxford: Pergamon, 1967), 82–90. 7. Alan Lightman, “The Quantum,” in The Discoveries: Great Breakthroughs in 20th-Century Science (New York: Vintage, 2006), 8–10. 8. Max Planck, The Origin and Development of the Quantum Theory, trans. H. T. Clarke and L. Silberstein (Oxford: Oxford University Press, 1922), 3. 9. Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity, 1894–1912 (Chicago: University of Chicago Press, 1978). 10. Thomas S. Kuhn, The Essential Tension: Selected Studies in Scientific Tradition and Change (Chicago: University of Chicago Press, 1977), 242. 11. W. Heisenberg, “Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik,” Zeitschrift für Physik 43, no. 3–4 (1927): 172–98, trans. J. A. Wheeler and W. H.

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NOTES TO PAGES 70–82 Zurek, “The Physical Content of Quantum Kinematics and Dynamics,” in Quantum Theory and Measurement (Princeton, NJ: Princeton University Press, 1983), 64–65. 12. Arthur I. Miller, Imagery in Scientific Thought: Creating 20th-Century Physics (Cambridge: MIT Press, 1986), 127. 13. Louisa Gilder, The Age of Entanglement: When Quantum Physics Was Born (New York: Vintage, 2009), 91. 14. Werner Heisenberg, “The Development of Quantum Mechanics,” Nobel Prize lecture, December 11, 1933. 15. George Gamow, Thirty Years That Shook Physics: The Story of Quantum Theory (New York: Dover, 1966), 107–9; see also George Gamow, Mr. Tompkins in Paperback (Cambridge: Cambridge University Press, 1965), 75–78. 16. Gamow, Thirty Years That Shook Physics, 107–9. 17. Gamow, 113–14. 18. David Cassidy, “Quantum Mechanics, 1925–1927: The Gamma-Ray Microscope,” American Institute of Physics, https://history.aip.org/exhibits/heisenberg/gamma-ray-microscope.html. 19. Leonard Susskind and Art Friedman, Quantum Mechanics: The Theoretical Minimum (New York: Basic Books, 2014), 4–13. 20. Susskind and Friedman, Quantum Mechanics, 89. 21. Susskind and Friedman, 7–9. 22. Susskind and Friedman, 10. 23. Susskind and Friedman, 3. 24. Gamow, Mr. Tompkins in Paperback, 65–66. 25. Gamow, 67. 26. Jim Al-Khalili, Quantum: A Guide for the Perplexed (London: Weidenfeld & Nicolson, 2004), 66–67. 27. Max Born, “The Statistical Interpretation of Quantum Mechanics,” in The Dreams That Stuff Is Made of: The Most Astounding Papers on Quantum Physics and How They Shook the Scientific World, ed. Stephen Hawking (Philadelphia: Running Press, 2011), 448–61. 28. Burwell, Quantum Language and the Migration of Scientific Concepts, 8. 29. Steven Weinberg, “The Trouble with Quantum Mechanics,” New York Review of Books, January 19, 2017. 30. Feynman, Leighton, and Sands, “Quantum Behavior,” 4–5. 31. Susskind and Friedman, Quantum Mechanics, 236. 32. Feynman, Leighton, and Sands, “Quantum Behavior,” 7. 33. Philip Ball, Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different (Chicago: University of Chicago Press), 39. 34. Arthur Fine, “The Einstein-Podolsky-Rosen Argument in Quantum Theory,” Stanford Encyclopedia of Philosophy, October 31, 2017, https://plato.stanford.edu/entries/qt-epr; Fine, The Shaky Game: Einstein, Realism, and the Quantum Theory, 2nd ed. (Chicago: University of Chicago Press, 1996), 78. 35. Erwin Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik” [The present situation in quantum mechanics], Die Naturwissenschaften 23, no. 48 (1935): 807–12, trans. John D. Trimmer, in Quantum Theory and Measurement, ed. John Archibald Wheeler and Wojciech Hubert Zurek (Princeton, NJ: Princeton University Press, 1983), 157; emphasis in translation and original German. 36. John D. Trimmer, “The Present Situation in Quantum Mechanics: A Translation of

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NOTES TO PAGES 96–109 19. Milton C. Nahm, ed., Selections from Early Greek Philosophy (New York: Appleton-CenturyCrofts, 1964), 38–43. 20. Brian Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Universe (New York: W. W. Norton, 1999), 67–71. 21. Greene, Elegant Universe, 71–74. 22. Greene, 67. 23. Greene, 143–45. 24. Greene, 141. 25. Greene, 208. 26. Greene, 147. 27. Jim Holt, “Unstrung,” New Yorker, September 24, 2006, https://www.newyorker.com/ magazine/2006/10/02/unstrung-2; Sebastian de Haro, Dennis Dieks, Gerard ‘t Hooft, and Erik Verlinde, “Forty Years of String Theory: Reflections on the Foundations,” Foundations of Physics 43, no. 5 (2013): 1–7. 28. Carlo Rovelli, Seven Brief Lessons on Physics (New York: Riverhead Books, 2014), 43. 29. Carlo Rovelli, Reality Is Not What It Seems: The Journey to Quantum Gravity, trans. Simon Carnell and Erica Segre (New York: Riverhead Books, 2014), 159. 30. Rovelli, Reality Is Not What It Seems, 153. 31. Rovelli, 174. 32. Carlo Rovelli, Quantum Gravity (Cambridge: Cambridge University Press, 2004), 31. 33. Carlo Rovelli, “Loop Quantum Gravity: The First Twenty Five Years.” arXiv.org, January 28, 2012, https://arxiv.org/abs/1012.4707. 34. Subrahmanyan Chandrasekhar, “Beauty and the Quest for Beauty in Science,” Physics Today 32, no. 7 (1979): 25–30. 35. Frank Wilczek, A Beautiful Question: Finding Nature’s Deep Design (New York: Penguin, 2015), plates VV, WW. 36. Wilczek, Beautiful Question, 298. 37. de Haro et al., “Forty Years of String Theory,” 5. 38. John Ellis, “The Superstring: Theory of Everything or Nothing?” Nature 323 (1986): 595–98. 39. R. B. Laughlin and David Pines, “The Theory of Everything,” Proceedings of the National Academy of Sciences 97 (2000): 28–31. 40. Steven Weinberg, Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature (New York: Vintage, 1994), 21–23. 41. Weinberg, Dreams of a Final Theory, 211. 42. Jordi Cat, “The Physicists’ Debates on Unification in Physics at the End of the 20th Century,” Historical Studies in the Physical and Biological Sciences 28, no. 2 (1998): 253–99. 43. David Deutsch, The Fabric of Reality (London: Penguin Books, 1997), 18–19. 44. Sean Carroll, Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime (New York: Dutton, 2019). 45. Deutsch, Fabric of Reality, 132. 46. Deutsch, 181–82. 47. Thomas S. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought (Cambridge, MA: Harvard University Press, 1957). 48. Thomas S. Kuhn, Black-Body Theory and the Quantum Discontinuity, 1894–1912 (Chicago: University of Chicago Press, 1978). 49. Deutsch, Fabric of Reality, 335.

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NOTES TO PAGES 110–125 50. Rovelli, “Loop Quantum Gravity,” 6–7. 5. Cosmic Conjectures 1. Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1999), 940. 2. Edward Harrison, “Newton and the Infinite Universe,” Physics Today 39, no. 2 (1986): 24–32. 3. Albert Einstein, Relativity: The Special and General Theory, 100th Anniversary Edition (Princeton, NJ: Princeton University Press, 2016), 123. 4. Albert Einstein, “Cosmological Considerations in the General Theory of Relativity,” in The Principle of Relativity, trans. W. Perrett and G. B. Jeffery (New York: Dover, 1952), 183–84. 5. Einstein, Relativity, 126. 6. Einstein, 153. 7. Cormac O’Raifeartaigh, “Albert Einstein and the Origins of Modern Cosmology,” Physics Today, February 3, 2017, doi:10.1063/PT.5.9085. 8. Einstein, “Cosmological Considerations,” 188. 9. Paul J. Steinhardt and Neil Turok, Endless Universe: Beyond the Big Bang (London: Orion Books, 2007), 24. 10. Einstein, Relativity, 123. 11. Fred Hoyle, “Steady State Cosmology Revisited,” in Cosmology and Astrophysics: Essays in Honor of Thomas Gold, ed. Y. Terzian and E. M. Bilson (Ithaca, NY: Cornell University Press, 1982), 51. 12. Fred Hoyle, The Nature of the Universe (Harmondsworth, UK: Penguin, 1963), 109–12. 13. Fred Hoyle, “A New Model for the Expanding Universe,” Monthly Notices of the Royal Astronomical Society 108 (1948): 376. 14. E. Margaret Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle, “Synthesis of the Elements in Stars,” Review of Modern Physics 29, no. 4 (1957): 547–650. 15. Hoyle, Nature of the Universe, 59–62, 74–78. 16. Jean-Pierre Luminet, “Editorial Note to ‘The Beginning of the World from the Point of View of Quantum Theory’ by Georges Lemaître,” General Relativity and Gravitation 43 (2011): 2911–28. 17. George Gamow, Creation of the Universe (New York: Viking, 1953), 23–24. 18. Stephen Hawking, A Brief History of Time, 2nd ed. (New York: Bantam Books, 1996), 45. 19. Steven Weinberg, The First Three Minutes: A Modern View of the Origin of the Universe, 2nd ed. (Toronto: Bantam Books, 1984), 2. 20. Weinberg, First Three Minutes, 94–95. 21. George Gamow, “The Evolution of the Universe,” Nature 162 (1948): 680–82. 22. Alan H. Guth, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (New York: Basic Books, 1997), 14. 23. Guth, Inflationary Universe, 173. 24. Guth, 272–73. 25. Guth, 89. 26. Guth, 235. 27. Steve Bradt, “3 Questions: Alan Guth on New Insights into the ‘Big Bang,’” MIT News, March 20, 2014, https://news.mit.edu/3-q-alan-guth-on-new-insights-into-the-big-bang. 28. NASA, “Timeline of the Universe,” December 22, 2012, https://map.gsfc.nasa.gov/media/060915/index.html. 29. Katie Mack, The End of Everything (Astrophysically Speaking) (New York: Scribner, 2020), 36–50. 30. Mack, End of Everything, 46–47.

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NOTES TO PAGES 127–145 31. Particle Data Group at Lawrence Berkeley National Laboratory, “History of the Universe,” 2013, https://particleadventure.org/history-universe.html. 32. Edward R. Tufte, The Visual Display of Quantitative Information (Cheshire, CT: Graphics Press, 1983), 40–41. 33. Patchen Barss, “What If the Universe Has No End?” BBC Future, January 19, 2020, https:// www.bbc.com/future/article/20200117-what-if-the-universe-has-no-end. 34. John Horgan, “Physicist Slams Cosmic Theory He Helped Conceive,” Scientific American, December 1, 2014, https://blogs.scientificamerican.com/cross-check/ physicist-slams-cosmic-theory-he-helped-conceive. 35. Steinhardt and Turok, Endless Universe, 61–63. 36. Steinhardt and Turok, 61–62. 37. For Roger Penrose’s version of a cyclic universe, see Fashion, Faith, and Fantasy in the New Physics of the Universe (Princeton, NJ: Princeton University Press, 2016), 371–95. 38. Hawking, Brief History of Time, 140–41. 39. Natalie Wolchover, “Physicists Debate Hawking’s Idea That the Universe Had No Beginning,” Quanta Magazine, June 6, 2019, https://w w w.quantamagazine.org/ physicists-debate-hawkings-idea-that-the-universe-had-no-beginning-20190606. 40. Brian Greene, The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos (New York: Vintage, 2011), 65–67. 41. Greene, Hidden Reality, 11. 42. Jorge Luis Borges, Labyrinths: Selected Stories and Other Writings (New York: New Directions, 1964), 51. 43. David Kaiser, Quantum Legacies: Dispatches from an Uncertain World (Chicago: University of Chicago Press, 2020), 255. 6. Quantum Magic 1. Martin Heidegger, What Is a Thing? trans. W. B. Barton Jr. and Vera Deutsch (Chicago: Henry Regency, 1968). 2. Richard P. Feynman, Robert B. Leighton, and Matthew Sands, “Atoms in Motion,” in The Feynman Lectures on Physics, vol. 1 (Reading, MA: Addison-Wesley, 1965), 2; emphasis added. 3. Feynman, Leighton, and Sands, “Atoms in Motion,” 2–3. 4. Stephen Blundell, Superconductivity: A Very Short Introduction (Oxford: Oxford University Press, 2009), 2. 5. Blundell, Superconductivity, 56–58; see also “Superconductors and the BCS Theory,” YouTube, May 23, 2012, https://www.youtube.com/watch?v=1AnePH6LlxI. 6. Other materials than metals—in particular, complex ceramics—were discovered in the 1980s to be superconducting at much higher temperatures than near absolute zero. 7. Malcolm W. Browne, “2 Groups of Physicists Produce Matter That Einstein Postulated,” New York Times, July 14, 1995, https://www.nytimes.com/1995/07/14/us/2-groups-of-physicists-producematter-that-einstein-postulated.html. 8. Eric A. Cornell and Carl E. Wieman, “The Bose–Einstein Condensate,” Scientific American 278, no. 3 (1998): 40–45. 9. For an animated version of this process, see the Wikipedia entry for “Bose-Einstein Condensation,” https://en.wikipedia.org/wiki/File:Bose-Einstein_Condensation.ogv. 10. Eric A. Cornell and Carl E. Wieman, “Bose-Einstein Condensation in a Dilute Gas: The First 70 Years and Some Recent Experiments,” Reviews of Modern Physics 74, no. 3 (2002): 875–93.

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NOTES TO PAGES 145–160 11. Browne, “2 Groups of Physicists Produce Matter That Einstein Postulated.” 12. William P. Halperin, “Eighty Years of Superfluidity,” Nature 553 (2018): 413–14. 13. J. R. Minkel, “Strange but True: Superfluid Helium Can Climb Walls,” Scientific American, February 20, 2009, https://www.scientificamerican.com/article/superfluid-can-climb-walls; Allan Griffin, “Superfluidity: A New State of Matter,” in A Century of Nature: Twenty-One Discoveries That Changed Science and the World, ed. Laura Garwin and Tim Lincoln (Chicago: University of Chicago Press, 2003), 51–57. 14. Richard P. Feynman, “There’s Plenty of Room at the Bottom,” Caltech Engineering and Science 23 (1960): 22–36. 15. Richard Smalley, “Discovering the Fullerenes,” Nobel Prize lecture, December 7, 1996, https://www.nobelprize.org/uploads/2018/06/smalley-lecture.pdf. 16. Smalley, “Discovering the Fullerenes.” 17. Les Johnson and Joseph E. Meany, Graphene: The Superstrong, Superthin, and Superversatile Material That Will Revolutionize the World (Amherst, NY: Prometheus Books, 2018). 18. Alastair I. M. Rae, “Waves, Particles and Fullerenes,” Nature 401 (1999): 651. 19. Marc Kastner, “Artificial Atoms,” Physics Today 46, no. 1 (1993): 24. 20. R. C. Ashoori, “Electrons in Artificial Atoms,” Nature 379 (1996): 413–19. 21. Richard Turton, The Quantum Dot: A Journey into the Future of Microelectronics (Oxford: Oxford University Press, 1996), 3. 22. Alexander L. Efros, “Quantum Dots Realize Their Potential,” Nature 575 (2019): 604–5. 23. David Deutsch, The Beginning of Infinity: Explanations That Transform the World (London: Penguin Books, 2011), 295. 24. Rivka Galchen, “Dream Machine: The Mind-Expanding World of Quantum Computing,” New Yorker, May 2, 2011, https://www.newyorker.com/magazine/2011/05/02/dream-machine. Note that, for the sake of simplicity, science writers tend to only mention two possible simultaneous states for quantum superposition. But many more are possible. 25. Alan H. Guth, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (New York: Basic Books, 1997), 173–75. 26. Steven Leibson, “IBM Unveils 127-Qubit Quantum Computer,” Electronic Engineering Journal, January 31, 2022, https://www.eejournal.com/article/ibm-unveils-127-qubit-quantum-computer. 27. Guth, Inflationary Universe, 29–30. 28. Ethan Siegel, “The Enduring Mystery of Detecting the Universe’s Only Magnetic Monopole,” Forbes, February 7, 2019, https://www.forbes.com/sites/startswithabang/2019/02/07/ the-enduring-mystery-of-detecting-the-universes-only-magnetic-monopole/#6564c63cf0e8. 29. Dan Hooper, Dark Cosmos: In Search of Our Universe’s Missing Mass and Energy (New York: HarperCollins, 2006), 193–94. 30. Hooper, Dark Cosmos, 196. 31. Heidegger, What Is a Thing?, 13. 32. Deutsch, Beginning of Infinity, 295. 7. Transistor Actions 1. E. G. Rudberg, “Award Ceremony Speech: Nobel Prize in Physics,” Nobel Prize speech, 1956, https://www.nobelprize.org/prizes/physics/1956/ceremony-speech. 2. For selection of videos with animations for better understanding semiconductors and the transistor effect, see Khan Academy, “Band Theory of Solids,” https://www.khanacademy.org/ science/in-in-class-12th-physics-india/in-in-semiconductors; Khan Academy, “The PN Junction”

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NOTES TO PAGES 162–176 and “PN Junction Biasing,” https://www.khanacademy.org/science/in-in-class-12th-physics-india/ in-in-semiconductors; Khan Academy, “Transistor Working,” https://www.khanacademy.org/ science/science-india/in-in-class-12th-physics-india/in-in-semiconductors/in-in-transistors/v/tran sistor-working-class-12-india-physics-khan-academy; Bill Hammack, “How the First Transistor Worked,” YouTube, December 7, 2010, https://www.youtube.com/watch?v=RdYHljZi7ys; Bell Telephone Laboratories, “AT&T Archives: Genesis of the Transistor,” YouTube, August 22, 2011, https://www.youtube.com/watch?v=WiQvGRjrLnU; Electrical 4U, “MOSFET Transistor Basics & Working Principle,” YouTube, September 2, 2016, https://www.youtube.com/watch?v=p34w6ISouZY. 3. Les Johnson and Joseph E. Meany, Graphene: The Superstrong, Superthin, and Superversatile Material That Will Revolutionize the World (Amherst, NY: Prometheus Books, 2018), 151–52. 4. Walter Brattain, “Discovery of the Transistor Effect: One Researcher’s Personal Account,” Adventures in Experimental Physics 5 (1976): 2. 5. William B. Shockley, “Transistor Technology Evokes New Physics,” Nobel Prize lecture, December 11, 1956, 360, https://www.nobelprize.org/prizes/physics/1956/shockley/lecture. 6. Ernest Braun, “Select Topics from the History of Semiconductor Physics and Its Applications,” in Out of the Crystal Maze: Chapters from the History of Solid State Physics, ed. Lillian Hoddeson (New York: Oxford University Press, 1992), 474. 7. Michael Riordan and Lillian Hoddeson, Crystal Fire: The Invention of the Transistor and the Birth of the Information Age (New York: W. W. Norton, 1997), 88. 8. Walter Brattain, “Discovery of the Transistor Effect,” 3–4. 9. Riordan and Hoddeson, Crystal Fire, 95–96. 10. J. Bardeen and W. H. Brattain, “The Transistor: A Semi-Conductor Triode,” Physical Review 74 (1948): 230. 11. See, for example, Frederick Seitz and Normal G. Einspruch, Electronic Genie: The Tangled History of Silicon (Urbana: University of Illinois Press, 1998), 85–86. 12. Bardeen and Brattain, “Transistor,” 230–31. 13. Lillian Hoddeson and Vicki Daitch, True Genius: The Life and Science of John Bardeen (Washington, DC: Joseph Henry Press, 2002), 140. 14. Jon Gertner, The Idea Factory: Bell Labs and the Great Age of American Invention (New York: Penguin Books, 2012), 99. 15. Hoddeson and Daitch, True Genius, 131. 16. William Shockley, “Transistor Physics,” American Scientist 42, no. 1 (1954): 69–70. 17. Bardeen and Brattain, “Transistor,” 231. 18. Michael Riordan interview of Morris Tanenbaum, “Oral History: Goldey, Hittinger and Tanenbaum,” IEEE History Center, Institute of Electrical and Electronics Engineers, 2008, https:// ethw.org/Oral-History:Goldey,_Hittinger_and_Tanenbaum#Silicon_vs._Germanium. 19. Seitz and Einspruch, Electronic Genie, 175. 20. Michael Riordan, “The Lost History of the Transistor,” IEEE Spectrum 41 (2004): 44–49. 21. Alfred Bernhard Nobel, “Full Text of Alfred Nobel’s Will, November 27, 1895,” trans. Jeffrey Ganellen, https://www.nobelprize.org/alfred-nobel/full-text-of-alfred-nobels-will-2. 22. Christoph Bartneck and Mathias Rauterberg, “The Asymmetry between Discoveries and Inventions in the Nobel Prizes in Physics,” Technoetic Arts: A Journal of Speculative Research, 6, no. 1 (2008): 73–77. 23. D. Kahng and M. M. Atalla, “Silicon-Silicon Dioxide Field Induced Surface Devices,” in IREAIEEE Solid-State Device Research Conference (Pittsburgh: Carnegie Institute of Technology, 1960). 24. Greg Myers, “From Discovery to Invention: The Writing and Rewriting of Two Patents,” Social Studies of Science 25, no. 1 (1995): 57–105.

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NOTES TO PAGES 176–192 25. M. M. Atalla, “Semiconductor Devices Having Dielectric Coatings,” US Patent Office, US3206670A, 1 (1965). 26. Atalla, “Semiconductor Devices Having Dielectric Coatings,” 3–4. 27. Atalla, 7. 28. Hassan Mujtaba, “AMD 2ndGen EpyC Processors Feature a Gargantuan 39.54 Billion Transistors,” Wccftech.com, October 22, 2019, https://wccftech.com/amd-2nd-gen-epyc-rome -iod-ccd-chipshots-39-billion-transistors. 29. William B. Shockley, “Transistor Technology Evokes New Physics,” Nobel Prize lecture, December 11, 1956, https://www.nobelprize.org/prizes/physics/1956/shockley/lecture. 30. Seitz and Einspruch, Electronic Genie, 186–89. 8. Astronomical Value 1. Mary G. Winkler and Albert Van Helden, “Representing the Heavens: Galileo and Visual Astronomy,” Isis 8, no. 2 (1992): 213. 2. Galileo Galilei, Sidereus Nuncius, trans. Albert Van Helden (Chicago: University of Chicago Press, 1989), 28r. 3. Richard S. Westfall, “Science and Patronage: Galileo and the Telescope,” Isis 76, no. 1 (1985): 19. 4. Galileo, Sidereus Nuncius, 2v. 5. “Flattery,” in Oxford Essential Quotations, 5th ed. (Oxford: Oxford University Press, 2017), https:// www.oxfordreference.com/view/10.1093/acref/9780191843730.001.0001/q-oro-ed5-00004456. 6. Mrs. John Herschel, Memoirs and Correspondence of Caroline Herschel (New York: D. Appleton, 1876), 336. 7. Emily Winterburn, “Learned Modesty and the First Lady’s Comet: A Commentary on Caroline Herschel’s ‘An Account of a New Comet,’” Philosophical Transactions A 373 (2010): 20140210. 8. Caroline Herschel, “An Account of a New Comet,” Philosophical Transactions of the Royal Society of London 76 (1786): 1–3. 9. “A Letter from William Herschel, Esq. F. R. S., to Sir Joseph Banks, Bart. P. R. S.,” Philosophical Transactions of the Royal Society of London 73 (1783): 2. 10. Simon Schaffer, “Uranus and the Establishment of Herschel’s Astronomy,” Journal of the History of Astronomy 12 (1981): 11–26. 11. Richard Holmes, The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science (New York: Pantheon Books, 2008), 122–23. 12. Holmes, Age of Wonder, 163–64. 13. William Herschel quoted in Age of Wonder, 178. 14. Edwin Hubble, The Realm of the Nebulae (New York: Dover, 1958), x. 15. Edwin Hubble, “A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae,” PNAS 15, no. 3 (1929): 168–73. 16. Hubble, Realm of the Nebulae, 16–18. 17. Hubble, 33; emphasis added. 18. J. Richard Gott, The Cosmic Web: Mysterious Architecture of the Universe (Princeton, NJ: Princeton University Press, 2016), 1. 19. John Graham-Cumming, Geek Atlas: 128 Places Where Science and Technology Come Alive (Sebastopol, CA: O’Reilly Media, 2009), 412. 20. Bell Telephone Laboratories, “Newly Discovered Radio Radiation May Provide a Clue to the Origin of the Universe,” May 23, 1965, https://media-bell-labs-com.s3.amazonaws.com/ pages/20140518_1641/1965_BL_Press_Release_on_Radiation.pdf.

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NOTES TO PAGES 192–208 21. Walter Sullivan, “Signals Imply a ‘Big Bang’ Universe,” New York Times, May 21, 1965. 22. Alan H. Guth, The Inflationary Universe: The Quest for a New Theory of Cosmic Origins (New York: Basic Books, 1997), 61. 23. John N. Bahcall, The Space Telescope: Out Where the Stars Do Not Twinkle (Washington, DC: Government Printing Office, 1977). 24. Not treated here is a source of continuing debate and controversy: the question whether this or other Big Science projects deserve funding over pressing societal needs. See, for example, physicist Alvin M. Weinberg, “Impact of Large-Scale Science on the United States,” Science 134 (1961): 161–64. 25. Eric J. Chaisson, The Hubble Wars: Astrophysics Meets Astropolitics in the Two-Billion-Dollar Struggle over the Hubble Space Telescope (Cambridge, MA: Harvard University Press, 1998). 26. Lew Allen, Roger Angel, John D. Mangus, George A. Rodney, Robert R. Shannon, and Charles P. Spoelhof, The Hubble Space Telescope Optical Systems Report (Washington, DC, NASA, 1990), TM-103443, iii–iv. 27. Robert S. Caper, “Hubble Makers to Pay Millions,” Hartford Courant, October 5, 1993. 28. Ron Cowan, “The Big Fix: NASA Attempts to Repair the Hubble Space Telescope,” Science News 144, no. 19 (1993): 296. 29. NASA, “Pictures of Galaxy M100 with Hubble’s Old and New Optics,” January 13, 1994, https://hubblesite.org/contents/media/images/1994/01/123-Image.html. 30. Sally K. Ride, NASA Leadership and America’s Future in Space: A Report to the Administrator, NASA, August 1987, https://history.nasa.gov/riderep/cover.htm. 31. Wyche Fowler, Congressional Record—Senate, vol. 134, part 15, 2133, August 9, 1988. 32. NASA, “In Depth: Huygens,” NASA Science Solar System Exploration, May 6, 2021, https:// solarsystem.nasa.gov/missions/huygens/in-depth. 33. Janna Levin, Black Holes Blues and Other Songs from Outer Space (New York: Anchor Books, 2017), 17. 34. Levin, Black Holes Blues, 89. 35. Levin, 180–85. 36. B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger,” Physical Review Letters 116 (2016): 061102-1 37. Abbott et al., “Gravitational Waves,” 061102-8–061102-9. 38. Harry Collins, Gravity’s Kiss: The Detection of Gravitational Waves (Cambridge: MIT Press, 2017), 230. 39. Abbott et al., “Gravitational Waves,” 061102-8. 40. LIGO, “The Sound of Two Black Holes Colliding,” February 11, 2016, https://www.ligo. caltech.edu/video/ligo20160211v2. 41. Kip S.Thorne, “LIGO and the Discovery of Gravitational Waves, III,” Nobel Prize lecture, December 8, 2017, https://www.nobelprize.org/uploads/2017/12/thorne-lecture.pdf. 9. The Atomic Bomb 1. Robert K. Merton, “The Unanticipated Consequences of Purposive Social Action,” American Sociological Review 1, no. 6 (1936): 894–904. 2. Not all the leading atomic physicist emigrates agreed to participate. Lise Meitner reportedly declined an invitation to join the project in 1943, saying, “I will have nothing to do with a bomb.” See Ruth Sime, Lise Meitner: A Life in Physics (Berkeley: University of California Press, 1996), 305. 3. Ruth Lewin Sime, “Science and Politics: The Discovery of Nuclear Fission 75 Years Ago,” Annalen der Physik 526, no. 3–4 (2014): A27–A30.

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NOTES TO PAGES 209–220 4. Lise Meitner and O. R. Frisch, “Disintegration of Uranium by Neutrons: A New Type of Nuclear Reaction,” Nature 143 (1939): 239–40. 5. Quoted in Richard Rhodes, The Making of the Atomic Bomb (New York: Simon & Schuster, 1986), 266. 6. Rudolf Peierls, “Reflections on the Discovery of Fission,” Nature 342 (1989): 852–54. 7. Jean Edward Smith, FDR (New York: Random House, 2008), 578–79. 8. Einstein-Szilard, letter to Franklin D. Roosevelt, August 2, 1939, Franklin D. Roosevelt Presidential Library and Museum, Hyde Park, New York. 9. “The Frisch-Peierls Memorandum,” in Rudolf E. Peierls, Atomic Histories (New York: Springer Verlag, 1993), 187–88. 10. Rhodes, Making of the Atomic Bomb, 324–25. 11. David H. Katzive, “Henry Moore’s Nuclear Energy: The Genesis of a Monument,” Art Journal 32, no. 3 (1973): 284–88. 12. Enrico Fermi, “The Development of the First Chain Reacting Pile,” Proceedings of the American Philosophical Society 90 (1946): 20–24. 13. Leona Marshall Libby, Uranium People (New York: Charles Scribner’s and Sons, 1979), 127. 14. Robert Serber, The Los Alamos Primer: The First Lectures on How to Build an Atomic Bomb (Berkeley: University of California Press, 1992), 3–4. 15. Serber, Los Alamos Primer, 42–44. 16. Rhodes, Making of the Atomic Bomb, 460–65. 17. James Kunetka, The General and the Genius (Washington, DC: Regnery History, 2015), 111. 18. Joseph O. Hirschfelder, “The Scientific and Technological Miracle at Los Alamos,” in Reminiscences of Los Alamos, 1943–45, ed. Lawrence Badash, Joseph O. Hirschfelder, and Herbert P. Broida (Dordrecht: D. Reidel, 1980), 73–75. 19. Richard P. Feynman, Surely You’re Joking, Mr. Feynman (New York: W. W. Norton, 2018), 131–32. 20. Elsie McMillan, “Outside the Inner Fence,” in Reminiscences of Los Alamos, 1943–45, ed. Lawrence Badash, Joseph O. Hirschfelder, and Herbert P. Broida (Dordrecht: D. Reidel, 1980), 43. 21. John Hayward, ed., Donne: Complete Verse and Selected Prose (London: Nonesuch Library, 1955), 285. 22. Robert W. Seidel, Los Alamos and the Development of the Atomic Bomb (Los Alamos: Owl Crossing, 1995), 85. 23. Kai Bird and Martin J. Sherwin, American Prometheus: The Triumph and Tragedy of Robert Oppenheimer (New York: Vintage Books, 2006), 308. 24. Rhodes, Making of the Atomic Bomb, 673. 25. Meilan Solly, “Nine Eyewitness Accounts of the Bombings of Hiroshima and Nagasaki,” Smithsonian Magazine, August 5, 2020, https://www.smithsonianmag.com/history/ nine-harrowing-eyewitness-accounts-bombings-hiroshima-and-nagasaki-180975480. 26. Joseph Kanon, Los Alamos: A Novel (New York: Dell, 1997), 507–8. 27. Cynthia C. Kelly, ed., The Manhattan Project: The Birth of the Atomic Bomb in the Words of Its Creators, Eyewitnesses, and Historians (New York: Black Dog and Leventhal, 2007), 297, 310, 312. 28. J. Robert Oppenheimer, “Science Panel’s Report to the Interim Committee, June 16, 1945, Recommendations on the Immediate Use of Nuclear Weapons,” Atomic Heritage Foundation, https://www.atomicheritage.org/key-documents/interim-committee-report-0. 29. Barton J. Bernstein, “Roosevelt, Truman, and the Atomic Bomb, 1941–1945: A Reinterpretation,” Political Science Quarterly 90, no. 1 (1975): 37–38.

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NOTES TO PAGES 220–242 30. Alan G. Gross, “When Nations Remember: Hiroshima in the American Consciousness and Conscience,” Prospects: An Annual of American Cultural Studies 27 (2002): 467–88. 31. John Rawls, “50 Years after Hiroshima,” Dissent 42, no. 3 (1995): 323–27. 32. “Thinkers at War—John Rawls,” Military History Matters, June 3, 2014, https://www.military-history.org/articles/thinkers-at-war-john-rawls.htm. 33. Reinhold Niebuhr, “A Faith to Live By: The Dilemma of Modern Man,” Nation, February 22, 1947, 208. 34. J. Robert Oppenheimer, “Atomic Weapons and Atomic Policy,” Foreign Affairs 31, no. 4 (1953): 533. 35. Bird and Sherwin, American Prometheus, 468–97. 36. Peter Galison, Image and Logic: A Material Culture of Microphysics (Cambridge, MA: Harvard University Press, 1997), 35. 37. Gerald Holton, “Scientific Research and Scholarship: Notes toward the Design of Proper Scales,” Daedalus 9, no. 2 (1962): 362–99. 38. Armin Hermann, John Krige, Ulrike Mersits, Dominique Pestre, and Laura Weiss, History of CERN: Building and Running the Laboratory, vol. 2 (Amsterdam: North Holland, 1990), 799. 39. Kip. S. Thorne, “LIGO and the Discovery of Gravitational Waves, III,” Nobel Prize lecture, December 8, 2017, https://www.nobelprize.org/uploads/2017/12/thorne-lecture.pdf. 40. Spencer R. Weart, Nuclear Fear: A History of Images (Cambridge, MA: Harvard University Press, 1988). Afterword 1. I’ve told this story before—see “X Marks the Spot: An Appreciative Response to Morales’s Review of Landmark Essays on Rhetoric of Science: Case Studies and Issues and Methods,” Social Epistemology Review and Reply Collective 10, no . 9 (2021): 61–67—but nowhere has it been more appropriate than here. 2. Alan G. Gross, The Rhetoric of Science (Cambridge, MA: Harvard University Press, 1990). 3. Miller did review the book a few years later, and was certainly more circumspect than I was, but she also doesn’t regard it as the achievement Gross seemed to be aiming for, similarly noting its neglect of others in the field and slyly observing that “one learns more from this book about science than about rhetoric.” Carolyn Miller, review of The Rhetoric of Science, by Alan G. Gross, and Persuading Science: The Art of Scientific Rhetoric, ed. Marcello Pera and William R. Shea, Configurations 1, no. 2 (1993): 281. 4. My omission in this short list of Lucie Olbrechts-Tyteca, Perelman’s important coauthor of The New Rhetoric: A Treatise of Argumentation, trans. John Wilkinson and Purcell Weaver (Notre Dame, IN: University of Notre Dame Press, 1969), is not accidental here—because the soft spot I note did not seem to extend to her. Alan calls The New Rhetoric “his [Perelman’s] masterpiece . . . written in collaboration with L. Olbrechts-Tyteca” (Rhetoric of Science, 18); writing with Ray Dearin, he later characterized that book as resulting from “a decade of feverish intellectual activity on his part—and a decade of tedious, painstaking effort on hers.” Gross and Dearin, Chaïm Perelman (Albany: State University of New York Press, 2003), 6. However, they also explicitly note that this characterization derives from Perelman himself (xi), an observation that is hard to discredit. See especially Robert L. Scott’s observations on Perelman’s ego, in “Chaïm Perelman: Persona and Accommodation in the New Rhetoric,” Pre/Text 5, no. 2 (1984): 90. For corrective versions of Olbrechts-Tyteca’s role, see David A. Frank and Michelle Bolduc’s “Lucie Olbrechts-Tyteca’s New Rhetoric,” Quarterly Journal of Speech 96, no. 2 (2010): 141–63, and especially Barbara Warnick,

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NOTES TO PAGES 242–246 “Lucie Olbrechts-Tyteca’s Contribution to the New Rhetoric,” in Listening to Their Voices: The Rhetorical Activities of Historical Women, ed. Molly Meijer Wertheimer (Columbia: University of South Carolina Press, 1997), 69–85. 5. The “radical” one is R. Allen Harris, “Assent, Dissent, and Rhetoric in Science,” Rhetoric Society Quarterly 20, no. 1 (1990): 13–37; the other relevant piece is “Rhetoric of Science,” College English 53, no. 3 (1991): 282–307. 6. Randy Allen Harris, review of The Rhetoric of Science, by Alan G. Gross, Rhetoric Society Quarterly 21, no. 4 (1991): 31. I have “restored” the italics on the word the in this quotation, which were lost in the publication process along with all the other mention or emphasis italics I used in the manuscript. 7. Harris, review of The Rhetoric of Science, 33. 8. Alan G. Gross, “Response to Harris,” Rhetoric Society Quarterly 21, no. 4 (1991): 35. All other quotations in this passage have the same citation; his response is a one-pager. 9. Starring the Text: The Place of Rhetoric in Science Studies (Carbondale: Southern Illinois University Press, 2006). 10. This will be my last complaint about Alan, I promise. I loved him dearly and remember him fondly, but I do need to note that the only colleagues he identified as in “the same [rhetoric-of-science] boat” with him were men: Bazerman, Campbell, and Myers, whom he identifies as Chuck, John, and Greg. The same is true of another band-of-brothers rhetoricians-of-science enumeration he offered the year previously (this time of Campbell, Walzer, and John Lyne). Miller and Fahnestock, leading lights at the time, did not manage to register with him in this response. In the event, they have had a greater impact on the field than the scholars he mentioned and rhetoric of science is notable for the influence of female-identifying scholars; other prominent folk in the matrilineage of the field include Jean Dietz Moss, Judy Segal, Leah Ceccarelli, Colleen Derkatch, Lisa Keränen, Jordynn Jack, Aimee Kendall Roundtree, and Ashley Rose Mehlenbacher. To Alan’s credit, I am quite sure he would commend me for noting the patriarchal blinders he wore in the 1990s, along with many, many scholars of the period. 11. The quotations are from Howard M. Goodman and Alexander Rich, “Formation of a DNA-Soluble RNA Hybrid and Its Relation to the Origin, Evolution, and Degeneracy of Soluble RNA,” Proceedings of the National Academy of Sciences 48, no. 12 (1962): 2106, the second one from the caption to their figure 3. But I was sent to the Goodman and Rich paper because Alan G. Gross, Joseph E. Harmon, and Michael Reidy quote from it in their Communicating Science: The Scientific Article from the 17th Century to the Present (New York: Oxford University Press, 2002), 26. We will, of course, return to this book in due course. 12. Starring the Text, 5. This “early version” of Gross makes the creating-knowledge claim most insistently and compactly in “Rhetoric of Science Is Epistemic Rhetoric,” Quarterly Journal of Speech 76, no. 3 (1990): 304–6. This is the essay, to put a bow on my remarks in note 10, in which he lists Campbell, Walzer, and Lyne as his notable rhetoric-of-science confreres. 13. Rhetoric of Science, 54. 14. “Understanding Scientific Communication: A Collaboration with Alan G. Gross,” Poroi 10, no. 2 (2014): 2. 15. “Literary” and “barren” are from his “Metaphor in Science Writing,” Technical Communication 32, no. 1 (1985): 48. “Perturbations in the Scientific Literature” is the title of his article in the Journal of Technical Writing and Communication 16, no. 4 (1986): 311–18. See also “Digging for Gould,” review of Understanding Scientific Prose, by Jack Selzer, Journal of Technical Writing and Communication 24, no. 4 (1994): 478–82. “The Uses of Metaphor in Citation Classics from the

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NOTES TO PAGES 246–249 Scientific Literature,” Technical Communication Quarterly 3, no. 2 (1994): 179–94, straddles the perturbation and the textual-features paths. 16. This research includes articles such as “The Literature of Enlightenment: Technical Periodicals and Proceedings in the 17th and 18th Centuries,” Journal of Technical Writing and Communication 17, no. 4 (1987): 397–405; “Structure of Scientific and Engineering Papers: A Historical Perspective,” IEEE Transactions, Professional Communication 32, no. 3 (1989): 132–38; and “Development of the Modern Technical Article,” Technical Communication 36, no. 1 (1989): 33–38. His intentions and his anxieties about a book on the evolution of scientific prose are expressed in “Understanding Scientific Communication,” 2–3. 17. “Understanding Scientific Communication,” 3. 18. Communicating Science, 27. 19. So far as I am aware, he took to the grave with him the secret of his displeasure with the titular preposition of. 20. Communicating Science, 5. 21. Isaac Newton, “A letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; containing his new theory about light and colors . . . ,” Philosophical Transactions of the Royal Society of London 6, no. 80 (1672): 3079–80. 22. Goodman and Rich, “Formation of a DNA-Soluble RNA Hybrid,” 2102; Gross, Harmon, and Reidy, Communicating Science, 23. 23. Goodman and Rich, “Formation of a DNA-Soluble RNA Hybrid,” 2108. 24. Approximately zero studies may seem hyperbolic in the face of such excellent rhetoric-of-science studies as Myers’s “Every Picture Tells a Story: Illustrations in E. O. Wilson’s Sociobiology,” Human Studies, 11, no. 2/3 (1988): 235–69, the several brilliant analyses in Fahnestock’s Rhetorical Figures in Science (New York: Oxford University Press, 1999), e.g., 65–69, 98–102, 108–12, and the work of—guess who?—Alan himself, both on his own in Rhetoric of Science (e.g., 36–38, 74–80, 114–16) and alongside—this one is an even easier guess—Joe, in Communicating Science 60–64, 104–11, 148–56, 200–211). But these are brief analyses, little more than descriptions in some cases, with only passing attention to, and little theorizing of, the verbal-visual interactions that crucially govern scientific tests. There was also a fairly large body of the visual and the verbal contributions to scientific communication outside rhetoric and linguistics, which Alan and Joe survey nicely in Science from Sight to Insight: How Scientists Illustrate Meaning (Chicago: University of Chicago Press, 2014), 7–10. But there was precious little that brought the visual and the verbal together, and nothing even close to the scale of attention Alan and Joe bring. 25. The Internet Revolution in the Sciences and Humanities (New York: Oxford University Press, 2016). 26. While the publication date is 2016, already very distant in the rearview mirror of digital technology, the primary draft was complete in the digital dark ages of 2013. Harmon, “Understanding Scientific Communication,” 9. 27. Alan’s edited collection with Jonathan Buehl is also an important contribution to understanding the influence of digital technologies on science. Science and the Internet: Communicating Knowledge in a Digital Age (London: Routledge, 2017). It is more robust in some ways than Internet Revolution because of the greater variety of approaches and topics, and the slightly higher recency of its composition; it includes a separate chapter by Alan and also one by Joe. 28. Alan and Joe were aware of this hopelessness, of course, which gives the project an air of nobility. See their prefatory notes, for instance; particularly xvii–xviii, where they acknowledge that even the form of their book (print) is inadequate to their mission and discuss its augmentation

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NOTES TO PAGES 249–253 by the companion website they had set up, but the very flux they were charting was also affecting the publishing industry, and they preferred to face the compromises of print than to deal with the instabilities and inadequacies of a digital book. (The choice was a good one. Oxford University Press’s digital platform is still ghastly, six years later.) 29. Both are from the University of Chicago Press, Scientific Literature in 2007, Craft of Scientific Communication in 2010. 30. David Lindsay, Scientific Writing = Thinking in Words (Collingwood: CSIRO, 2011), 20. 31. Craft of Scientific Communication, 3. 32. Craft of Scientific Communication, 11; the original they are quoting, “Super G-String,” is by V. Gate, Empty Kangaroo, M. Roachcock, and W. C. Gall, in Unified String Theories: Proceedings. Workshop on Unified String Theories (Institute for Theoretical Physics, Santa Barbara, July 29–August16), ed. M. B. Green and D. J. Gross (Singapore: World Scientific, 1986), 729–37. 33. While I think these track labels do characterize significant aspects of their partnership and of the books they wrote together, as an indication of how artificial this categorization of the two people whose names I am slinging around, consider Alan’s The Scientific Sublime: Popular Science Unravels the Mysteries of the Universe (New York: Oxford University Press, 2018), in which he samples and celebrates the evocative prose of scientists and science writers writing for a lay audience. Alan unquestionably had very strong aesthetic interests, and Joe has strong theoretical and analytical interests. 34. The category I have labeled “aesthetic grace,” our curators call “Writing with Style” (238), quite unaccountably—since they are among our most perceptive scholars of the linguistic and rhetorical dimensions of scientific texts—suggesting that style is absent from the other 117 passages in the collection. 35. Perhaps this is a rare experience. Joe and Alan call this contraption “an imaginary amusement park ride” (p. 000) and my own research failed to turn up any direct evidence of it beyond my small-town-on-the-coast-of-British-Columbia-in-the-1960s memory of traveling carnivals. But the 1893 Chicago World’s Fair had a “moveable sidewalk” that corresponds with Russell’s account. John Joseph Flinn, ed., Official Guide to the World’s Columbian Exposition in the City of Chicago (Chicago: Columbian Guide Company, 1893), 171–72, and John Robert Day reports on versions of the device in Paris and London at around the same time, describing their workings in considerable detail but never mentioning carnival rides. Day, More Unusual Railways (New York: Macmillan, 1960), 137–50. Russell mentions “exhibitions” (p. 29), which would have been more his style than carnivals, midways, or amusement parks; presuming he had personal experience with these spinning platforms, the most likely one would have been at the Crystal Palace in 1901 London, when Russell was in his late twenties. 36. “Understanding Scientific Communication,” 10.

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INDEX

Note: Page numbers in italics indicate figures. Ψ-function (wave function in Schrödinger equation), 81

planets by Herschels, 185–88; Galilean moons of Jupiter, 182–85, 183; gravitational wave detection, 200–5; Hubble’s velocitydistance relation of nebulae, 188–91; of NASA Hubble Space Telescope, 193–97; Penzias and Wilson and big bang, 191–93 Astrophysical Journal Letters, 59–60, 192 asymmetry, 15–16; Einstein’s radical solution to problem of, 16–17; between laws of electrodynamics and mechanics, 18 Atalla, Mohamed, 175–76 atomic bomb development, 201, 207–8, 224–25, 228, 235; first controlled chain reaction, 212–14; gadget development, 214–16; secret and open bomb debates, 219–22; secret pleas for action, 210–12; Trinity test site, 216–19. See also nuclear fission audience, 5, 8, 11–12, 23, 64, 111; general interest in science, 12, 31, 34, 44, 48, 57, 72, 85, 192, 203, 227, 273; specialized, 11, 31, 216; universal, 31

ABC of Relativity (Russell), 29–31, 234 absolute rest, 16, 17, 18, 26 absolute time and space, 14, 22, 48, 101 acknowledgment statement, 189, 202–3, 242 Adams, John, 217 Advanced LIGO, 202, 205 The Age of Entanglement: When Quantum Physics Was Reborn (Gilder), 237–38 Al-Khalili, Jim, 75–76, 85 Allen, Lew, 145–46, 195 Alpher, Ralph, 118 Alvarez, Luis, 224 ambivalence, Freud’s description of, 154 American Scientist, 171 analogy, 227; balloon example, 124, 132, 136, 157; communicative utility, 7; definitions of, 6–7; of Eddington’s thought experiment with swimmer, 28; in Einstein’s Relativity: The Special and General Theory, 20; importance to scientific discourse and argument, 6–9; limits of, 9; for multiverse, 133–35; in science writing, 61; for string theory’s nine-dimensions, 99–100; water bucket example, 41–43 Anaximander (Greek philosopher), 96 Anderson, Philip, 107, 253 Annalen der Physik, 14 Aristotle, 6–7, 242 Armstrong, Louis, 38 Aron, Jacob, 60–61 artificial atom. See quantum dot Ashoori, Raymond, 151 astronomical discoveries, 181; Cassini-Huygens mission to Saturn, 197–200; of comet and

Bacher, Robert, 224 Background Imaging of Cosmic Extragalactic Polarization (BICEP2), 128 Bacon, Francis, 103 Bahcall, John, 193–94 Bais, Sander, 15, 34–36 Ball, Philip, 239 Bardeen, Cooper and Schrieffer theory (BCS theory), 140, 14142, 146 Bardeen, John, 78, 140–41, 159–60, 167, 169–70, 171, 175 Barish, Barry, 201–3, 224 Barrett, Andrea, 237 Barsotti, Lisa, 224 Bayliss, William, 4 Bazerman, Charles, 241, 246, 271n10

289

INDEX Buehler, Ernie, 173 Buehl, Jonathan, 272n27 Burwell, Jennifer, 64, 76

BCS theory. See Bardeen, Cooper and Schrieffer theory A Beautiful Question: Finding Nature’s Deep Design (Wilczek), 103–4 BEC. See Bose-Einstein condensate Becker, Joseph, 165–66 The Beginning of Infinity (Deutsch), 153–54 Bell Telephone Laboratories, 165, 166, 180, 191–93, 236 Bethe, Hans, 207, 217, 223–24 Beyond Weird: Why Everything You Thought You Knew about Quantum Physics Is Different (Ball), 239 BICEP2. See Background Imaging of Cosmic Extragalactic Polarization big bang, 91, 94, 96, 113, 108, 116–17, 119, 125, 128–30, 136, 194, 203; discovery of, 191–93, 206; theory, 31, 118-24, 132–34, 157–58, 229–30, 232, 236, 238 Big Science, 201, 223–25 bits, 152–54 blackbody radiation, 66–67, 109 Black Holes & Time Warps: Einstein’s Outrageous Legacy (Thorne), 231–32 black holes, 11, 57–62, 58, 203, 231 Blagden, Charles, 186 Blitzer, Frank, 51 Bloch, Felix, 207 Blondin, Charles, 219, 219 Blundell, Stephen, 140–41 Bohr, Niels, 4, 67, 69, 82, 106, 151, 207, 208, 210, 235 Bondi, Hermann, 116 Borges, Jorge Luis, 135 Born, Max, 15, 23–26, 31, 36, 69, 76 Bose-Einstein condensate (BEC), 143–47 Bose, Satyendra Nath, 143, 144–45, 159 Bown, Ralph, 165 Brattain, Walter, 160, 162–63, 165–67, 169–70, 171, 175 Braun, Ernest, 164 A Brief History of Time (Hawking), 11, 57–59, 58, 62, 131–33, 231 Broken Genius (Shurkin), 179 Brookhaven National Laboratory, 89 Browne, Malcolm, 143 buckyballs (C60), 148, 149, 150–51

Campbell, John Angus, 241, 271n10 carbon: crystalline forms of, 148–50, 149; idiosyncratic behavior of, 148; tetrahedral arrangement, 150 Carnegie Mellon University, 175 Cassidy, David, 73 Cassini-Huygens mission to Saturn, 197–200, 206 Ceccarelli, Leah, 271n10 Century of Nature, A: Twenty-One Discoveries That Changed Science and the World (Garwin and Lincoln), 5 Chandrasekhar, Subrahmanyan, 103 circuit diagram, 168–69, 168, 172 classical computer, 154 classical entanglement, 84 COBE satellite. See Cosmic Background Explorer satellite Collins, Harry, 238–39 Communicating Science: The Scientific Article from the 17th Century to the Present (Gross and Harmon), 246, 247–49, 250 Compton, Arthur, 219 Compton effect, 68–69 conjectures, 112–13. See also cosmic conjectures Cooper, Leon, 140–41 Cooper pairs, 141, 142, 146 Copernicus, 82 core theory, 103–4 Cornell, Eric, 143–44 Cosmic Background Explorer satellite (COBE satellite), 123 cosmic conjectures: expanding universe, 116–25, 125; big-bell expanding universe, 124–27, 126; big brane universe, 127–30, 129; imaginary time universe, 131–33, 133; spherical universe, 113–16 The Cosmic Web (Gott), 191 Cosmology and Controversy: The Historical Development of Two Theories of the Universe (Kragh), 235–36 The Craft of Scientific Communication (Harmon), 249–50

290

INDEX Earhart, Amelia, 155 Eddington, Arthur, 15, 26–28, 27, 31, 36, 52, 54–56, 62, 137 Efros, Alexander, 152 Einspruch, Norman, 174 Einstein: His Life and Universe (Isaacson), 15 Einstein, Albert, 3, 4, 7, 14, 31, 38, 67, 69, 85, 106, 143, 144–45, 159, 207, 237; thought experiment against quantum theory, 80–81; energy equation, 127, 209; equivalence principle, 43–45, 45; gravitational wave prediction, 200; mathematical equations, 50–51; on special relativity for general public, 19–23; publishing paper on general relativity, 40; Relativity: The Special and General Theory, 14, 20, 23, 26, 31, 36, 43, 229; unification theory, 86; solar eclipse expedition, 52–55, 53; on special relativity for physicists, 15–19; static spherical universe theory, 113–16, 118, 135–36; using thought experiments, 14–16, 20–23, 43–48, 114–16, 226 Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc (Miller), 38–40 Einstein’s Clocks, Poincaré’s Maps: Empires of Time (Galison), 236–37 Einstein’s Theory of Relativity (Born), 23, 26, 31 Eisenhower, Dwight D., 222 Eldredge, Niles, 109–10 electrodynamics, 14–20, 23, 40. See also Maxwell, James Clerk electromagnetism, 86, 92, 96, 103, 205 Electronic Genie (Seitz and Einspruch), 174 Electrons and Holes in Semiconductors (Shockley), 179 The Elegant Universe (Greene), 97, 100, 232–33 Eliot, T. S., 38 Ellis, John, 104 Endeavour space shuttle, 196 Endless Universe (Steinhardt and Turok), 129–30 The End of Everything (Astrophysically Speaking) (Mack), 233–34 energy band theory, 162–64 entanglement, 153–54; classical, 84; quantum, 64, 83–84 EPR (Einstein, Podolsky and Rosen), 80–81 equations, as communicative tool, 5, 7, 19, 23, 40, 50–51, 64

Crystal Fire: The Invention of the Transistor and the Birth of the Information Age (Riordan and Hoddeson), 165–67, 236 Curie, Eve, 234–35 Curie, Marie, 235 Curie, Pierre, 155, 235 Curl, Robert, 148 cyclic universe, 127–30, 129 dark energy, 94, 127, 129–30 dark matter, 94, 104 Darwin, Charles, 6, 185; gradualism of, 109–10; Origin of Species, 6; The Structure and Distribution of Coral Reefs, 8; theory of evolution of atoll, 8, 8 Davidson, Charles Rundle, 54, 62 Davidson, Donald, 82 Davis, Raymond, Jr., 193 Dawid, Richard, 104 Dawkins, Richard, 109 Dearin, Ray, 6, 9 de Broglie waves, 69 definition, act of, 11–12, 57, 228, 229; black holes, 57–59, 62; Bose-Einstein condensate, 144; position of atomic particles, 68; scientific things, 139–40; simultaneity, 21–22, 25–26, 37; space-time, 47–48, 131–32; theories of everything, 104–5, 107–8 Derkatch, Colleen, 271n10 Deutsch, David, 107, 108–10, 111, 153, 159, 253. See also quantum computing Dialogue Concerning the Two Chief World Systems (Galileo), 17–18 diamond, 148–50, 149 Dicke, R. H., 192 Dirac, Paul Adrien Maurice, 63, 69, 156 The Discourses of Science (Pera), 6 The Discoveries: Great Breakthroughs in 20thCentury Science (Lightman), 4 Discovery space shuttle, 194 Disraeli, Benjamin, 185 Doctor Atomic (Adams), 217–18 Donne, John, 217–18 double-slit thought experiment, 77–80, 77, 79 Dreams of a Final Theory (Weinberg), 105–7 Du Pont Company, 214 Dyson, Frank Watson, 54, 62

291

INDEX universe, 121; liquid drop model, 208; Mr. Tompkins Explores the Atom, 75, 229–30; Mr. Tompkins in Paperback, 229; Mr. Tompkins in Wonderland, 229–30; visualization of Einstein’s thought experiment, 48–50, 49; visualization of Heisenberg’s thought experiment, 70–72, 71 Garwin, Laura, 5 gas, redefinition of, 142–45 Gates, S. James, Jr., 51 Geim, Andre, 150 Gell-Mann, Murray, 87, 88–90 general relativity, 38–40, 55–56, 61–62, 103, 113, 231; in cosmological theories, 113, 115, 118; Einstein’s equations, 50–51; equivalence principle, 43–45, 45; gravitational waves, prediction and detection of, 200–206, 238; relativity of circular motion, 41–43, 48–50; role in black hole creation, 57–59; in Science News, 59–61; solar eclipse and theory proof, 52–55; space-time warping, 46–50, 97; in unification theories, 84, 86–87, 96, 101–102, 110, 226, 227. See also special relativity George III (King of United Kingdom), 186–87, 188, 205 germanium element, 88. See also semiconductor Gilder, Louisa, 70, 237–38 Ginsparg, Paul, 60 Gold, Thomas, 116 Goodman, Allegra, 237 Goodman, Howard M., 246, 248, 271n11 Gott, J. Richard, 191 Gould, Stephen Jay, 109–10 grand unified theories (GUTs), 104, 157 graphite (graphene), 148–50, 149 gravitational field, 43–45 47–48, 52, 57, 62, 70 gravitational waves, 200; direct detection of, 204; LIGO project, 201–3, 205; primordial, 128–29 gravity, 51, 57, 94, 101, 103, 110 Gravity’s Kiss: The Detection of Gravitational Waves (Collins), 238–39 Great Experiments: Twenty Experiments That Changed Our View of the World (Harré), 4 Greene, Brian, 42, 96, 103, 110; string theory, 97–100; The Elegant Universe, 232–33; The Hidden Reality, 133–34; inflationary multiverse theory, 133–35

equivalence principle, 43, 45, 45, 46, 62 Eracleous, Michael, 59 Escherich, Theodor, 244 European Space Agency, 197 Evans, Christopher, 59 event horizon, 57, 59. See also black holes Everett, Hugh, 82–83, 155 The Fabric of Reality (Deutsch), 107–10 Fahnestock, Jeanne D., 241 Fairchild Semiconductor, 178 false vacuum, 121–23, 127–28 Faraday, Michael, 84 Fermi, Enrico, 104, 207, 212–13, 214, 216, 219 Fermi, Laura, 235 Feynman, Richard, 64, 97, 147, 216, 223, 252–53; Feynman diagram, 231; QED: The Strange Behavior of Light and Matter, 230–31; thought experiment about water, 137–39, 138; visualizations of wave-particle duality, 77–80, 77, 79 Finnegans Wake (Joyce), 104 The First Three Minutes (Weinberg), 119–21, 230, 232 Föppl, August, 16 Fowler, Wyche, 199 Franck-Hertz experiment, 69 Franck, James, 207 Franck Report, 222 Freud, Sigmund, 154 Friedman, Art, 72–74, 83–85 Frisch, Otto, 6–7, 207–9, 211–12 Fröhlich, Herbert, 141 Fuchs, Klaus, 235 Fuller, Buckminster, 148 fullerenes, 148–50, 149 Fussell, Paul, 220 Galchen, Rivka, 153–155 Galilei, Galileo, 181, 205, 235; Galilean principle in special relativity, 17–18, 19–20; refracting telescope, 182–85, 194; The Starry Messenger, 182, 184; thought experiments, 7, 17–18; Two World Systems, 9 Galison, Peter, 3, 223, 236–37 Gamow, George, 15, 31–34, 36, 70, 85, 118, 121, 127, 159, 236; conjecture on expanding

292

INDEX Higgs, Peter, 87, 90 Hiroshima, nuclear bombing in, 218, 220–21. See also atomic bomb development Hirschfelder, Joseph O., 216 Hitler, Adolf, 207 Hoddeson, Lillian, 165, 167, 236 Holmdel Horn Antenna, 191 Holmes, Richard, 188 Holt, Jim, 238 Holton, Gerald, 223 Hooker, John D., 188–89 Hooker telescope, 189 Hookham’s circus, 49 Hooper, Dan, 157 Hoyle, Fred, 116–18, 236 HST. See Hubble Space Telescope Hubble, Edwin, 115, 116, 181, 188–91, 205–6, 236 Hubble Space Telescope (HST), 193–97, 206, 228 Humboldt, Alexander von, 185 Huxley, Thomas, 105

Gross, Alan G., 6, 9, 240, 270n3, 271n10, 272– 73nn27–28, 273n35; Communicating Science, 246, 247–49, 250; The Internet Revolution in the Sciences and Humanities, 249; The Many Voices of Modern Physics, 246, 249, 251, 252, 253; The Rhetoric of Science, 241–44, 245, 247; Science from Sight to Insight: How Scientists Illustrate Meaning, 249–50 Groves, Leslie, 216, 219 Gutfreund, Hanoch, 20 Guth, Alan H., 121, 136, 155, 159, 192; contribution to quantum computing, 155; false vacuum, 121–23, 127, 128; inflationary theory, 123–24; The Inflationary Universe, 123–24, 192–93, 232; magnetic monopoles, 155–58; power of doubling time, 122 GUTs. See grand unified theories Hahn, Otto, 208 Halperin, William, 145, 147 Harmon, Joseph E., 240, 241, 245, 272–73n28, 273n35; Communicating Science, 246, 247–49, 250; The Craft of Scientific Communication, 249–50; The Internet Revolution in the Sciences and Humanities, 249; The Many Voices of Modern Physics, 246, 249, 251–53; Science from Sight to Insight: How Scientists Illustrate Meaning, 249, 250; The Scientific Literature: A Guided Tour, 249–50 Harré, Rom, 4 Hawking, Stephen, 11, 57, 62, 123, 159, 231; Brief History of Time, A, 57, 231; expanding balloon analogy, 119; imaginary time universe, 132–33; no-time-boundary theory, 131–33, 133; theory for black hole formation, 57–59, 58 hedging language, 9, 10–11, 56, 227 Heidegger, Martin, 137, 139, 158 Heisenberg, Werner, 38, 63, 64, 67, 85, 103, 159, 235. See also uncertainty principle helium, 117, 118, 142, 145–47 Herman, Robert, 118 Hermite, Charles, 103 Herschel, Caroline, 181, 185–88, 205 Herschel, William, 181, 185–88, 205 Hevelius, Johannes, 182 The Hidden Reality (Greene), 133–34 Higgs boson, 90–95, 110

The Inflationary Universe (Guth), 121–23, 192–93, 232 inflation theory, 121–24, 134–35, 157 internet, 9, 203, 249, 272 The Internet Revolution in the Sciences and Humanities (Gross and Harmon), 249 Isaacson, Walter, 15 Jack, Jordynn, 271n10 Johnson, Les, 161 Jordan, Pascual, 69 Joyce, James, 104 Kahng, Dawon, 175 Kaiser, David, 135 Kanon, Joseph, 218 Kapitza, Pyotr, 147 Kelly, Mervin, 165–66, 170 Kepler, Johannes, 103 Keränen, Lisa, 271n10 Ketterle, Wolfgang, 143 Kilby, Jack, 175 Kistiakowsky, George, 218 Klint, Hilma af, 38 Knocking on Heaven’s Door (Randall), 11, 91–96, 233

293

INDEX matrix theory, 69 Maxwell, James Clerk, 15–16, 19, 26, 84 McMillan, Edwin, 217, 224 Meany, Joseph, 161 Medici, Cosimo II de’, 184 Mehlenbacher, Ashley Rose, 271n10 Meitner, Lise, 6–7, 207–9 Mendeleev, Dmitri, 87–88, 88, 107 Mercury, deviation in orbit of, 52, 56 Merton, Robert, 207 Messier, Charles, 187 metal–oxide–semiconductor field-effect transistor (MOSFET), 174–78, 177 metal, redefinition of, 140–42, 228 metaphor, 6, 119, 136, 148, 151–52, 221, 229, 242, 244, 245 Michelson, Albert, 4 Michelson-Morley experiment, 28 Miller, Arthur I., 38, 62 Miller, Carolyn R., 241, 270n3 Minard, Charles Joseph, 127 Minkowski, Hermann, 24; graph for spacetime continuum, 24–25, 24; space-time diagrams, 36 Misener, Donald, 145–46 Mitchell, Peter Chalmers, 55–56 Moore, Gordon, 178 Moore, Henry, 212 Moore’s law, 178 Morley, Edward, 4 Morton, Jelly Roll, 38 MOSFET. See metal–oxide–semiconductor field-effect transistor Moss, Jean Dietz, 271n10 Mount Wilson Observatory, 188–89 Mr. Tompkins Explores the Atom (Gamow), 75, 229–30 Mr. Tompkins in Paperback (Gamow), 229 Mr. Tompkins in Wonderland (Gamow), 31–33, 229–30 multiverse, analogies for, 133–35 Musk, Elon, 242 Must Be Beautiful: Great Equations of Modern Science (Penrose), 50 Myers, Greg, 241, 246, 271n10 Mysterium Cosmographicum (Kepler), 103

Kragh, Helge, 235–36 Kroto, Harold, 148 Kuhn, Thomas, 3, 67, 82, 109 Laguna, Pablo, 59, 60–61 Lamé, Gabriel, 103 language of physics, 11–12 Large Hadron Collider (LHC), 91–92, 147, 233. See also Higgs boson Laser Interferometer Gravitational-Wave Observatory (LIGO), 201–6, 204, 228, 238 Lawrence, Ernest, 219, 224 Leibniz, Gottfried, 12 Lemaotre, Georges, 118, 121 Les Demoiselles d’Avignon (painting of Picasso), 39, 39–40 Levin, Janna, 200–1 LHC. See Large Hadron Collider Libby, Leona Marshall, 235 Library of Babel, 135 Lightman, Alan, 4, 237 LIGO. See Laser Interferometer GravitationalWave Observatory Lincoln, Tim, 5 Linde, Andrei, 238 Lippershey, Hans, 182 liquid drop model, 208–9 liquid, redefinition of, 145–47 Lofgren, Edward, 224 Longinus, Cassius, 7–8 loop quantum gravity theory, 87, 100–2, 102, 110 Lorentz, Hendrik, 18, 26 Lorentz transformation, 18–19, 30 Los Alamos (Kanon), 218–19 The Los Alamos Primer (Serber), 214–16 Mach, Ernst, 41 Mach’s principle, 41–42, 47 Mack, Katie, 124–25, 233–34 Madame Curie: A Biography (Eve Curie), 234–35 magnetic monopoles, 155–58 Maimon, T. H., 5 The Making of the Atomic Bomb (Rhodes), 235–36 Manhattan Project. See atomic bomb development The Many Voices of Modern Physics (Gross and Harmon), 246, 249, 251–53 Maskelyne, Nevil, 186

294

INDEX Perelman, Chaïm, 6, 11, 242 periodic table of element, 86–88, 88, 90, 92, 94–95, 103, 107, 110, 118, 127, 149, 227. See also Standard Model table of particles Perkin-Elmer Corporation, 195–96 persuasion, use of, 185, 193, 228, 244–46 Pessl, Marisha, 237 Philosophical Transactions of the Royal Society, 186–87 Physical Review Letters (Brattain and Bardeen), 167–69, 172, 180, 203 Picasso, Pablo, 38–40, 39, 62 Pickering, Andrew, 3 Pines, David, 141 Planck, Max, 3–4, 19, 65, 109; Planck’s constant, 65–67, 69, 75; reluctant revolutionary, 67, 84–85, 109; support of relativity theory, 19, 65; thought experiment with quanta, 65–67 Podolsky, Boris, 80 Poincaré, Henri, 237 Polyakov, Alexander, 156 Popper, Karl, 109, 128 postulates, use of: in general relativity, 43–48; in special relativity, 17–18, 26, 34 Pound, Ezra, 38 Powers, Richard, 237 practical military weapon, 215–16, 219 Prelli, Lawrence J., 241, 246 primordial gravitational waves, 128–29 Principia Mathematica (Newton), 41

Nabokov, Vladimir, 231–32 Nagasaki, nuclear bombing in, 218, 220–21. See also atomic bomb development Nambu, Yoichiro, 174 narrative, 10, 237–38; in cosmology communications, 112–13, 116, 118, 121, 123–26, 127–30, 132, 230–32; in story thought experiments, 33–34, 75, 112 National Air and Space Museum, 220 National Science Foundation (NSF), 200–2 Nature magazine, 5, 145, 152 The Nature of the Universe (Hoyle), 116–17 The New Rhetoric (Perelman and OlbrechtsTyteca), 6, 70–71 Newton, Isaac, 41, 84, 112, 159, 185 New York Review of Books, 105 Nichols, Kenneth, 216 Niebuhr, Reinhold, 221 no-time-boundary theory, 131–32 Nobel, Alfred, 174, 179 Norton, John, 9 NSF. See National Science Foundation Nuclear Energy (Moore), 212 nuclear fission, 208–10; chain reaction, 209–10, 212-15; liquid drop model, 7, 208–9, 224. See also atomic bomb development Octet Rule, 161–62 Oerter, Robert, 94 Ogin, Gregory, 224 Ohl, Russell, 165–66, 169 Olbrechts-Tyteca, Lucie, 6, 11 omega minus particle (Ω-), 89–90, 90 Onnes, Heike Kamerlingh, 140, 145 Oppenheimer, J. Robert, 217–19, 222 Origin of Species (Darwin), 6 Owen, Wilfred, 52–53

QED: The Strange Theory of Light and Matter (Feynman), 97, 230–31 qualifications, use of, 9, 10–11 quanta, 66–67, 101, 104, 227 quantum computing, 152–55 quantum dot, 151–52 The Quantum Dot (Turton), 152 quantum materials, 139, 228; Bose-Einstein condensate, 142–45; magnetic monopoles, 155–58; superconducting metal, 140–42; superfluid, 145–47; super small objects, 147–51; quantum bit, 152–55; quantum dot, 151–52 Quantum Mechanics: The Theoretical Minimum (Susskind and Friedman), 72–74, 83–84 quantum mechanics, 84–85, 97, 131, 144;

Pale Fire (Nabokov), 232 Panofsky, Wolfgang, 224 passive voice, 196 Pauli, Wolfgang, 69 Peebles, P. J., 192 Peierls, Rudolf, 207, 210–12 Penrose, Roger, 50–51, 57, 230 Penzias, Arno, 119, 181, 191–93 Pera, Marcello, 6

295

INDEX Schoenberg, Arnold, 38 Schrieffer, Robert, 140 Schrödinger, Erwin, 38, 67, 74, 85, 159; Schrödinger’s cat, 81–82, 85, 153, 155; waveparticle duality equation, 74–76 Science from Sight to Insight (Gross and Harmon), 8, 9, 249, 250 Science News, 60 Science of Mechanics (Mach), 41 Scientific American, 127, 171 scientific articles, 7, 11–12, 31, 165, 174, 176, 179, 250 The Scientific Literature: A Guided Tour (Harmon), 249–250 scientific things, 137, 151, 158, 179, 228 Segal, Judy, 271n10 Segrè, Emilio, 207 Seitz, Frederick, 174 Sekula, Stephen Jacob, 51 semiconductor, 160–61; band gap diagram for, 162; doping, 161–62; energy band theory, 162–64; germanium based, 169, 172–74; n- and p-types, 162, 169–72, 177; silicon based, 161–62, 164, 165–67, 172–74, 176–77 Serber, Robert, 214–15 Shiota, Kikue, 218 Shockley, Bill, 173–74 Shockley, William, 160–61, 164, 170, 175; bipolar junction transistor, 170–72; Shockley Semiconductor, 178 silicon element, 88. See also semiconductor simile, 16, 245 simultaneity, 20–22, 21; definition of, 11; visualization of, 23–26 singularity, 59. See also black holes six-dimensional Calabi-Yau manifold, 99–100, 100 Slater, John C., 107 Smalley, Richard, 148 solar eclipse expedition, 52–55 solid-state theory, 163 space-time, 131; in Hawking’s no-boundary universe, 132, 133; space-time-story graphic, 126, 127; warping, 46–48, 51, 61 Space, Time and Gravitation: An Outline of the General Relativity Theory (Eddington), 26–28, 31 Sparks, Morgan, 173

Feynman’s visualizations of wave-particle duality, 77–80; Gamow’s visualization of Heisenberg’s thought experiment, 70–72; Heisenberg’s uncertainty thought experiment, 67–70; problem in explaining, 63–64; quantum dot, 151–52; quantum entanglement, 83–84; quantum spin, 72–74, 84, 89–90, 93, 108; quantum strangeness, 89, 89, 103; quantum superposition, 64, 82, 85, 142, 153, 154; Schrödinger’s equation, 74–76; thought experiments against quantum theory, 80–83; wave-particle duality, 74–76, 77–80, 85, 142, 239 qubits, 153–55 Randall, Lisa, 11, 91–92, 94–96, 233 Rawls, John, 220–21 The Realm of the Nebulae (Hubble), 189–91 Relativity: The Special and General Theory (Einstein), 14, 20, 23, 26, 31, 36, 43, 52, 55, 114, 115, 229 relativity theory, 19–20, 26, 97. See also general relativity; special relativity Renn, Jürgen, 20 retrograde motion, 9, 256n19 rhetoric, 6, 7, 11, 50, 57, 101, 196, 242; in science, 40, 148, 242–50, 270–73 rhetorical questions, 104–106 The Rhetoric of Science (Gross), 241–44, 245, 247 Rhetoric Society Quarterly, 241 Rhodes, Richard, 235–36 Rich, Alexander, 246–47, 271n11 Ride, Sally, 197–98 Riordan, Michael, 165, 167, 173, 236 Roll, P. G., 192 Roosevelt, Franklin Delano, 210–11 Rosen, Nathan, 80 Rotblat, Joseph, 207 Rothman, Tony, 41–43 Roundtree, Aimee Kendall, 271n10 Rovelli, Carlo, 100–102, 110 Royal Astronomical Society, 53, 55 Royal Society of London, 53, 55 Rudberg, Erik G., 159–60, 163 Russell, Bertrand, 15, 36, 252, 273n35; ABC of Relativity, 29–31, 234; thought experiments for special relativity, 29–31

296

INDEX 53, 56; Galileo’s refracting design, 182, 205; the Herschels’ reflecting designs, 185–88, 205; Holmdel Horn Antenna, 191-93, 206; Hubble Space Telescope, 193–97, 206, 228; Hooker telescope in Mount Wilson Observatory, 188–91, 205–206 Teller, Edward, 207 tensors, symbols for, 50 Texas Instruments, 175 theory of everything, 13, 87, 104–108, 110–111, 227; unified theory for fabric of reality, 108–9, 111. See also unification theories Thirty Years That Shook Physics (Gamow), 70–72 Thomson, J. J., 56, 84 Thorne, Kip, S., 57, 202–3, 205, 224, 231–32 ‘t Hooft, Gerard, 156 thought experiments, 4, 7, 9, 12, 36–37, 61–62, 63–64, 226–27, 230–32, 234; in children’s story by Gamow, 31–34; on constant speed of light, 26–28, 29–30, 252; in Einstein’s published works, 14–15, 18–19, 22–23, 40, 229; on evolution of universe, 112; on equivalence principle, 43–45, 45; on gravitational waves, 200–201; on incompleteness of quantum mechanics, 80– 82; on power of doubling; 155; on quantum entanglement, 84; on quantum of energy, 65–67; on relative motion, 15–18, 28, 41–43; on relative time, 28, 34–36; on simultaneity, 20–22, 23–26; on static spherical universe, 114; on superconductivity, 140; on theory of everything, 104–7; on uncertainty principle, 67–76; on warping of space-time, 46–50, 49, 51, 52, 56; on water as scientific thing, 137–39; on wave–particle duality, 77–80 Townes, Charles H., 5 transistor, 179–80, 228, 236; applications for, 160; bipolar junction, 170–72; commercial exploitation, 161, 178–79; effects of, 159–160, 178; on power of doubling; 155; inventors of first silicon-based transistor, 172–74; Moore’s law, 178; patenting MOSFET transistor, 174–78, 177; precursor, 165–67; point contact, 167–70; semiconductor triode, 168. See also semiconductor Trinity test site, 216–19. See also atomic bomb, development of

special relativity, 11, 14–15, 36–37, 61, 101, 231; Einstein’s popular science book on, 20–23; Einstein’s scientific article on, 15–19; Gamow’s children’s story about, 31–34; thought experiments on constancy of speed of light, 26–28, 29–31; thought experiments on relative space, 28; thought experiments on relative time, 28, 29–31; thought experiments on simultaneity, 23–26, 24; thought experiments on twin paradox and time travel, 34–36. See also general relativity Spitzer, Lyman, 193 Standard Model table of particles, 11, 86, 90, 92–94, 93, 227; Higgs boson, 90, 91, 92–95; supersymmetric versions, 94–96, 103 Standard Model theory, 11, 86, 87, 100, 103, 106–107, 110, 127 Starling, Ernest, 4 Starring the Text: The Place of Rhetoric in Science Studies, 243 The Starry Messenger (Galilei), 182, 184 steady state theory, 116–18, 236 Stein, Gertrude, 38 Steinhardt, Paul, 115–16, 127–29 Stern, Otto, 4 Stimson, Henry, 219–20 Strauss, Lewis, 222 Stravinsky, Igor, 38 string theory, 87, 96–100, 102, 104, 110, 130, 227, 232–33 The Structure and Distribution of Coral Reefs (Darwin), 8 super-bomb, 211–12 super atom, 143. See also Bose-Einstein condensate superconductivity, 140, 142, 145–47 superfluidity, 145–47, 146 super small objects, 147–51, 149; buckyballs (C60), 148, 150–55; graphene, 148–50, 149; single-walled carbon nanotube, 149 Susskind, Leonard, 72–74, 83–84, 85 synecdoche, 50 Szilard, Leo, 207, 209–10 Tanenbaum, Morris, 173–74 Teal, Gordon K., 174 telescopes, 181; confirming general relativity;

297

INDEX weak nuclear forces, 86, 104 Weiler, Edward J., 196–97 Weinberg, Steven, 105, 110–11, 253; The First Three Minutes, 119–21, 230, 232; reductionist thought experiment, 105–7 Weiss, Rainer, 200, 202, 224 Wells, H. G., 209 Westfall, Richard S., 183 Weyl, Hermann, 103 Why Does the World Exist? An Existential Detective Story (Holt), 238 Wieman, Carl, 143, 144–45 Wigner, Eugene, 106–7, 207, 210, 253 Wilczek, Frank, 103–4, 123 Wilkinson, D. T., 192 Wilson, Alan, 164 Wilson, Robert, R., 119, 181, 191–93, 224 Winkler, Clemens, 88 Woolf, Virginia, 38 The World Set Free (Wells), 209 wormholes, 84, 203, 231 written communication types, 4–5, 179, 228; congressional testimonies, 193–94, 196; declassified reports, 5, 208, 214-15, 219-20; historical accounts, 165–66, 173–74, 188, 235–37; lectures, 46, 70, 72, 77–80, 137–39, 143–44, 148–50, 159–61, 178–79, 202–4, 214–16, 224; news, 19–20, 55–56, 60–63, 143; patents, 165, 170, 174–78; personal letters, 81, 184, 184–87, 208, 210–12, 237; poem, 217–218; popular science articles, 41–42, 127–28, 171-72; popular science books, 5, 7, 11–15, 31, 91, 113, 140, 160, 217, 227, 229–39; press releases, 192, 238; scientific articles, 7, 11–12, 31, 165, 174, 176; technical memoranda, 195–96, 211–12.

True Genius (Bardeen), 178 Truman, Harry S., 219 Tufte, Edward, 127 Turing, Alan, 108–9 Turok, Neil, 115–16, 127, 129–30 Turton, Richard, 152 twin paradox, 34–36, 35. See also special relativity Two World Systems (Galileo), 9 Ulam, Stanislaw, 207 uncertainty principle, 64, 79, 85, 142, 144, 231, 239; Gamow’s visualization of, 70–72, 71; Heisenberg’s thought experiment, 67–70; quantum spin thought experiment, 72–74, 73. See also Heisenberg, Werner unification theories, 86, 110, 227; loop quantum gravity theory, 87, 100–102, 102, 110; string theory, 87, 96–100, 102, 104, 130, 232–33; Weyl’s gauge theory of gravitation, 103; Wilczek’s core theory, 103–4 unified theory for fabric of reality, 107–11 universal luminescent ether, 17, 26 universe, theories about, 112–13, 135–36, 227; big brane, 127–30, 129; divine creator, 113, 121, 238; end of, 233–34; expanding after big bang, 116–17, 118–21, 132, 136; expanding with big bang and inflationary period, 113, 121–27, 125, 126, 157, 232, 238; expanding steady state, 116–18; imaginary time in, 131–33, 133; multiverse, 84, 128, 133–35 Uranus, discovery of, 185, 186 Van Helden, Albert, 182 velocity-distance relation, 189–91, 190 Very Special Relativity: An Illustrated Guide (Bais), 34–36 Vilenkin, Alex, 238 viscosity, 145–47, 146 visualization of science, 7–9, 70, 227, 248–49

Yamamoto, Isoroku, 223 Zeitschrift für Physik journal, 88 Zeleny, Enrique, 30 Zweig, George, 90

Walzer, Art, 241, 242 Walzer, Michael, 220 wave-particle equation, 64; Feynman’s visualizations of, 77–80; Schrödinger’s work on, 74–77

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