Quantum Profiles [2 ed.] 9780190056865, 019005686X

Table of contents :
Cover
Quantum Profiles
Copyright
Contents
Foreword
1. John Stewart Bell
2. John Wheeler
3. Albert Einstein
4. Wendell Furry
5. Philipp Frank
6. J. Robert Oppenheimer
7. Victor Weisskopf
8. Tom Lehrer
9. Max Jammer
10. Robert Serber
Notes
Index

Citation preview

Quantum Profiles

Quantum Profiles Second Edition J E R E M Y B E R N ST E I N

1

3 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2020 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging-in-Publication Data Names: Bernstein, Jeremy, 1929– author. Title: Quantum profiles / Jeremy Bernstein. Description: Second edition. | New York, NY : Oxford University Press, [2020] | Includes bibliographical references and index. Identifiers: LCCN 2019035270 (print) | LCCN 2019035271 (ebook) | ISBN 9780190056865 (hardback) | ISBN 9780190056889 (epub) | ISBN 9780190056872 (updf) Subjects: LCSH: Quantum theory. | Physicists—Interviews. | Physicists—Biography. Classification: LCC QC174. 12 .B464 2020 (print) | LCC QC174. 12 (ebook) | DDC 530. 12092/2—dc23 LC record available at https://lccn.loc.gov/2019035270 LC ebook record available at https://lccn.loc.gov/2019035271 1 3 5 7 9 8 6 4 2 Printed by Integrated Books International, United States of America

Contents Foreword

1. John Stewart Bell

vii

1

2. John Wheeler

75

3. Albert Einstein

115

4. Wendell Furry

131

5. Philipp Frank

139

6. J. Robert Oppenheimer

150

7. Victor Weisskopf

160

8. Tom Lehrer

163

9. Max Jammer

169

10. Robert Serber

190

Notes Index

195 199

Foreword Three of the profiles in this second edition appeared in modified form in the 1991 edition of this book. The John Wheeler profile was done at the request of the Princeton Alumni Weekly and appeared in a much shorter version in that publication on October 9, 1985. A profile of Besso appeared in a modified version in the New Yorker on February 27, 1989. I wrote the profile of John Stewart Bell with the New Yorker in mind, but it was not published there, and I took this opportunity to rewrite it. Most of the rest of this book has never been published.

Quantum Profiles

1 John Stewart Bell

John Stewart Bell and the author. I would like to thank Tullio Basaglia of CERN for supplying the photo.

In 1902, the Olympia Academy was founded in Bern, Switzerland. It had three members:  Maurice Solovine, Conrad Habicht, and Albert Einstein. Solovine, a young student, had answered a newspaper advertisement offering private tutoring in physics by Einstein for three Swiss francs an hour, while Habicht, who was studying mathematics with the idea of becoming a secondary-​school teacher, already knew Einstein. The three young men had regular evening “Academy” meetings over the next three years, at which they studied philosophy and discussed physics. Solovine recalled having eaten

2  Quantum Profiles caviar in his parents’ home in Romania, and on one of Einstein’s birthdays, he and Habicht treated Einstein to some expensive caviar, which he had never tasted. As luck would have it, that was the evening Einstein was scheduled to talk to the “Academy” about Galileo Galilei’s principle of inertia. He became so absorbed that he ate all the caviar without realizing what he was eating. In 1905, the group broke up when Habicht and Solovine left Bern. However, they began corresponding almost at once, and in one of his earliest letters to Habicht, written in the spring of 1905, Einstein described his program of research for the year in the sort of cheerful tone one might use to describe a little light reading. It was, however, this research program that laid the foundations of twentieth-​century physics. He wrote: I promise you four papers . . . the first . . . deals with radiation and energy characteristics of light and is very revolutionary. . . . The second work is a determination of the true size of the atom from the diffusion and viscosity of dilute solutions of neutral substances. The third proves that assuming the molecular theory of heat, bodies whose dimensions are of the order of 1/​1000  mm, and are suspended in fluids, should experience measurable disordered motion, which is produced by thermal motion. It is the motion of small inert particles that has been observed by physiologists, and called by them “Brown’s molecular motion.” The fourth paper exists in first draft and is an electrodynamics of moving bodies employing a modification of the doctrine of space and time; the purely kinematical part of this work will certainly interest you.

What is striking about this list—​apart from the fact that it was compiled by a then totally unknown twenty-​six-​year-​old physicist—​is that the first paper announces, it turns out, the invention of the quantum, while the last paper announces the invention of the theory of relativity, and of the two, it is only the former that is in the young Einstein’s view “revolutionary.” The theory of the light quantum, which Einstein initiated in 1905 and which is with us still, is certainly the most revolutionary development in the history of physics and arguably in the history of science. The creators of the theory, men such as Einstein, Niels Bohr, Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli, and Paul Dirac, were often struck by the apparent “absurdity”—​the utterly noncommonsensical aspects—​of the world depicted by quantum theory. Long after he had done his seminal work, Heisenberg recalled that

John Stewart Bell  3 an intensive study of all questions concerning the interpretation of quantum theory in Copenhagen finally led to a complete and, as many physicists believe, satisfactory clarification of the situation. But it was not a solution which one could easily accept. I remember discussions with Bohr which went through many hours till very late at night and ended almost in despair; and when at the end of the discussion I went alone for a walk in the neighboring park I repeated to myself again and again the question: Can nature possibly be as absurd as it seemed to us in these atomic experiments?

Unlike some of the other great intellectual revolutions of the twentieth century—​in art, music, literature—​until recently, at least, this one was not widely known, let alone understood, by the general public. Many physicists realized this, and a few of them tried to do something about it. For example, in 1953, J. Robert Oppenheimer delivered a very successful series of Reith Lectures over the BBC about subatomic physics. In one of them, he characterized the epoch of the discovery of quantum theory as follows: “It was a time of earnest correspondence and hurried conferences, of debate, criticism, and brilliant mathematical improvisation.” And then he added, with a touch of the baroque eloquence of which he was a master, “For those who participated, it was a time of creation; there was terror as well as exaltation in their new insight. It will probably not be recorded very completely as history. As history, its recreation would call for an art as high as the story of Oedipus or the story of Cromwell, yet in a realm of action so remote from our common experience that it is unlikely to be known to any poet or any historian.” Oppenheimer died in 1967, and while there has not yet arisen “an art as high as the story of Oedipus,” in the last few years, quantum theory has, much to the surprise of most physicists, entered into the popular culture. Fiction writers now cite, rightly or wrongly, the Heisenberg uncertainty principle as a basis for theories of literature. A New York Times book review said approvingly of a novelist that “she knows enough about Heisenberg to realize that the act of observation alters the object observed; or in literary terms, telling the story alters the story being told.” Tom Stoppard’s play Hapgood turns on the uncertainty principle; the printed text is preceded by a quote on the quantum theory of Richard Feynman. Even otherwise sober and non-​ science-​oriented magazines such as the Economist have felt an obligation to alert their readers that something odd has happened in physics. In a feature article in its January 7, 1989, issue titled “The Queerness of Quanta,” the

4  Quantum Profiles Economist notes that “many of this century’s most familiar technologies come with an odd intellectual price on their heads. The equations of quantum mechanics explain the behaviour of sub-​atomic particles in nuclear reactors and of electrons in computers and television tubes, the movement of laser light in fibre-​optic cables and much else. Yet quantum mechanics itself appears absurd.” Among the “absurdities,” the following are offered: “There are no such things as ‘things.’ Objects are ghostly, with no definite properties (such as position or mass) until they are measured. The properties exist in a twilight state of ‘super-​position’ until then.” “All particles are waves, and waves are particles, appearing as one sort or another depending on what sort of measurement is being performed.” Then, “A particle moving between two points travels all possible paths between them simultaneously.” And finally, “Particles that are millions of miles apart can affect each other instantaneously.” While most physicists would find these capsule descriptions of the quantum theory caricatural, there is enough truth in them to explain why people who seem to have an aversion to more conventional science are drawn to quantum theory. Quantum theory has become the basis of the New Age outlook, with its emphasis on Eastern religions and holistic medicine. This surely would have astonished Oppenheimer, who, incidentally, studied Sanskrit so that he could read the Upanishads in the original. Books such as Gary Zukav’s The Dancing Wu Li Masters—​quantum theory with a dash of Eastern mysticism—​abound, and no ashram, at least no Western one, can afford to be without its resident expert. In a health-​food store in Greenwich Village, I came across an announcement in the I Am News of the Ananda Ashram in Monroe, New York, which, under the heading “Quantum Dynamics,” read, “Spiritual Purification Program: Includes meditation, fire ceremony, rebirthing, sweat lodge and Quantum Dynamics initiation for those who haven’t had it; includes breathing techniques and mantra to dissolve upsets. This weekend we will work with Quantum Dynamics to dissolve past life karma all the way back to original cause.” Pace Robert Oppenheimer Although it is always somewhat dangerous to look for the cause of a complex sociological phenomenon in a single event, nonetheless, I believe that a case can be made for the proposition that the present widespread interest in quantum theory can be traced to a single paper with the nontransparent title “On the Einstein-​Podolsky-​Rosen Paradox,” which was written in 1964

John Stewart Bell  5 by the then-​thirty-​four-​year-​old Irish physicist John Stewart Bell. It was published in the obscure journal Physics, which expired after a few issues. Bell’s paper was, as it happens, published in its first issue. Bell, who began work in 1960 at CERN, the gigantic elementary-​particle physics laboratory near Geneva, used to claim that his paper involved only the use of “high school mathematics”; however, its six pages are dense with an extremely abstract set of arguments, which even professionals in the field must work hard to understand. In fact, for several years after its publication, few, if any, professional physicists bothered to try. This changed dramatically in 1969, when it was realized that “Bell’s theorem” (or “Bell’s inequality,” as it is often called) could actually be tested in the laboratory. What was at stake in such a test was nothing less than the meaning and validity of quantum theory. If Bell’s inequality was satisfied, it would mean that all of Einstein’s intuitions about the essential incompleteness of quantum theory had been right all along. If the inequality was violated, it would mean—​at least, many physicists believe—​that Bohr and Heisenberg had been right all along and that no return to classical physics was possible. By the early 1970s, such experiments were actually being carried out. They still are. With a few exceptions—​glitches, one thinks—​all these experiments show that Einstein was wrong. It was these experimental results that caused a new generation of physicists to confront just how peculiar and counterintuitive quantum mechanics really is. It is this realization that is being reflected in the growing popular interest in the theory. I knew John Bell for more than thirty years. When his tenure had just begun at CERN, in 1960, I had begun a series of visits to the laboratory. During that time, I talked to Bell about many things but very little either about his life or about his work in quantum mechanics. I also got to know his wife, Mary, who was also a physicist at CERN. The Bells, while charming company when one got to know them, tended to be very private people, keeping pretty much to themselves. “Mary and I are rather unsociable,” Bell once remarked to me in his lilting Irish brogue. (“Mathematics” is pronounced something like “mah-​ thah-​mahtics,” and “now” comes out sounding something like “nae.” Mary Bell is Scottish and has a fine burr. “Girl” sounds something like “gurrrle.”) Bell had a dry wit, and one had to pay attention when he spoke to see that he was not teasing. The Bells had no children but gave the impression of taking great and constant pleasure in each other’s company. I am quite sure that Bell would have been most willing to discuss his ideas about quantum theory if I had asked, but somehow I never did. I had, in fact,

6  Quantum Profiles never tried to read Bell’s 1964 article. But with all the mounting interest in the subject, I decided that I had been missing out on something and that I would educate myself. This process was aided no end when Bell sent me a copy of his book—​his collected papers on quantum theory, published in 1987 under the title Speakable and Unspeakable in Quantum Mechanics. It contains twenty-​ two essays, including his 1964 paper. Some of the essays are addressed to the educated layperson, including a celebrated one written in 1981 and with the unlikely title “Bertlmann’s Socks and the Nature of Reality.” (Reinhold Bertlmann is a real person.) I quote the opening paragraph because it is illustrative of Bell’s style: The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by Einstein-​Podolsky-​Rosen correlations. He can point out many examples of similar correlations in everyday life. The case of Bertlmann’s socks is often cited. Dr. Bertlmann likes to wear socks of different colours. Which sock he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the [Einstein-​Podolsky-​Rosen] business just the same?

That it is not—​a fact that brings us deep into the mysteries of quantum theory—​is the subject of the rest of this chapter and most of the other chapters in this book. Bell always talked over his ideas with Mary, and at the end of the preface, he wrote: “In the individual papers I have thanked many colleagues for their help. But here I renew very especially my warm thanks to Mary Bell. When I look through these papers again I see her everywhere.” Having studied the collection and an equally rewarding one titled Quantum Theory and Measurement, edited by physicists John Wheeler and Wojciech Zurek, I felt that I finally understood enough about the subject to at least carry on a sensible dialogue with Bell. I thought I would also use the opportunity to find out something about his and Mary’s lives. The odd twists of fate that determine the lives of young scientists have always fascinated me, and I could not imagine what circumstances had brought the Bells from Ireland and Scotland to Geneva.

John Stewart Bell  7 Bell had a very busy schedule, but we finally agreed upon a week in January. For a skier, this is an especially happy time to visit CERN, which is less than a half hour from the ski runs in the Jura. I did not think there would be much chance to persuade the Bells to go skiing on their lunch hours, since I knew that both of them had given up downhill skiing in favor of cross-​country some years earlier. They owned a modest apartment in Champéry, a ski resort not far from Geneva, where they could cross-​country ski in peace. But I thought I would spend alternate lunch hours downhill skiing in the Jura and eating in one of the CERN cafeterias with the Bells. As the plane landed in Geneva, I  saw that the Jura was brown—​hardly a trace of snow. It later turned out that there was no skiing at all. An informal tradition had developed at the laboratory, according to which “aristocrats” like theoreticians ate lunch late. one o’clock or so, while the more “plebeian” members of staff ate earlier. The Bells traditionally had lunch promptly at 11:45 and ate with the same small group consisting of, among others, a Dutch computer expert and a Norwegian in charge of laboratory safety. Both Bells were vegetarians, Mary since childhood and John since the age of sixteen. Since there was, at least in the past, no particular provision for vegetarian diets in the CERN cafeterias, Mary Bell would usually arrive at lunch with a satchel of fresh vegetables, which she and John would share. There is also the very pleasant tradition at CERN of after-​lunch espresso in the large lounge next to the main cafeteria or outside on the patio, from which one has a view of Mont Blanc, if the weather is nice. Gossip after lunch is another tradition at CERN. CERN is located on the French border, a few miles from Geneva. When I  first went there, it was entirely in Switzerland. As the giant elementary-​ particle accelerators that are the main business of CERN got larger and larger, the terrain of the laboratory spilled over into France. The tunnels that contain the evacuated pipes in which the beams of elementary particles run cross the border in several places. At the time of my visit in 1989, it had reached a kind of apotheosis in an accelerator called the LEP (Large Electron-​Positron Collider), whose construction was begun in 1981. By the time it was turned on in the summer of 1989, it had cost about a billion Swiss francs (nearly three-​quarters of a billion US dollars), which was provided by the thirteen European member states that ran CERN at the time (that number is now twenty-​three). The LEP tunnel had a radius of twenty-​seven kilometers. The tunnel contained electrons and their antiparticles, positrons, streaming in

8  Quantum Profiles opposite directions. From time to time, the beams collide, and the results were then the highest-​energy electron and positron collisions ever observed. Because of all this activity, the character of the laboratory had changed dramatically from what I remember of my first visit nearly thirty years earlier. This was not so long after World War II, and the European community had not yet rebuilt its scientific establishment; indeed, CERN was conceived to accelerate that process. Those days are long past. The Large Hadron Collider superseded the electron-​positron collider. It was turned on in 2008 and among other things was responsible for the discovery of the Higgs boson. While there was an enormous amount of construction at CERN by the time of my visit in 1989, the theoreticians still occupied part of the same compact-​looking four-​story building that they were in when I  first went there. I had no trouble finding Bell’s office, the same one I had been stopping in, on and off, for several decades. Like the rest of the laboratory, the theoretical division—​TH, as it is called—​had undergone an almost exponential expansion. When I had first been there, the entire division, including visitors like myself, consisted of something like thirty people. In 1989, there were about a hundred and forty. The signs on Bell’s door read “J. Bell” and “M. Bell.” I knocked and was invited in by Bell. He looked about the same as he had the last time, a couple of years earlier. He had long, neatly combed red hair and a pointed beard, which made him a somewhat Shavian figure. On one wall of the office was a photograph of Bell with something that looked like a halo behind his head, and his expression in the photograph was mischievous. Theoretical physicists’ offices run the gamut from chaotic clutter to obsessive neatness; the Bells’ were somewhere in between. Bell invited me to sit down after warning me that the “visitor’s chair” tilted backward at unexpected angles. When I had mastered it and had a chance to look around, the first thing that struck me was the absence of Mary. “Mary,” said Bell, with a note of some disbelief in his voice, “has retired.” This, it turned out, had occurred not long before my visit. “She will not look at any mathematics now. I hope she comes back,” he went on almost plaintively. “I need her. We are doing several problems together.” In recent years, the Bells had been studying new quantum-​mechanical effects that would become relevant for the generation of particle accelerators that succeeded the LEP. John had begun his career as a professional physicist by designing accelerators, and Mary had spent her entire career in accelerator design. A few years earlier, John Bell, like the rest

John Stewart Bell  9 of the members of the CERN theory division, had been asked to list his physics specialty. Among the more “conventional” entries in the division, such as “superstrings,” “weak interactions,” “cosmology,” and the like, Bell’s read “quantum engineering.” Bell thought we would be more comfortable in our discussions if we found a larger office. It turned out that the one next to his was temporarily free. Mary, he told me, would be glad to talk to me over the phone if I had something I wanted to ask her. We settled into the new office, and I asked if he would mind telling me a bit about his early life and how he got into physics. “I was born on July 28, 1928, in Belfast,” he began. “My parents were poor but honest. Both of them came from the large families of eight or nine that were traditional of the working-​class people of Ireland at that time. Both sides of the family have been in Northern Ireland for many generations. But we are from the Protestant tribe—​the British side—​so the real Irish people regard us as colonists.” I was curious, as I always am, about whether there had been any scientific or academic tradition in his family. He thought a moment and replied, “As far as I know, until the present generation, there was none. The kind of professions I had heard about in the family were carpenters, blacksmiths, laborers, farmworkers, and horse dealers. My father’s first profession was horse dealer. He stopped going to school at the age of eight—​his parents paid fines from time to time for that. He learned how to buy and sell horses instead. The nearest I heard of anyone in my family being educated was my mother’s half brother. He was a village blacksmith, but he taught himself something about electricity at a time when not many people knew about electricity. I was the only one of my siblings who reached high school. I have an older sister and two younger brothers, and they left school at about the age of fourteen. The normal thing would have been for me to get a job when I reached fourteen.” Encouraged by his mother, Bell applied for financial help to go to secondary school. At the time, there was no universal system of free secondary education in Britain. That would come a bit later with the Labor government. “I sat many examinations,” Bell recalled, “for the more prestigious secondary schools, hoping for scholarships, but I didn’t win any.” Some money did appear—​Bell was not sure from where—​so that he was able to attend the Belfast Technical High School, the least expensive. Bell remembered it with great affection. He did courses in bricklaying, carpentry, and bookkeeping, along with the more conventional curriculum.

10  Quantum Profiles Unlike many prominent theoretical physicists I have asked, Bell does not have any early memories of scientific or mathematical precocity. He did, however, recall that at the age of fourteen, he began a brief phase of reading Greek philosophers. “I was a bookish sort of child, much in the local public libraries. I was hostile to the idea of sports,” he said, laughing. “I regret it now. I’ve grown up to be a seven-​stone weakling. I was, you know, brought up in the Church of Ireland. I was even confirmed by a bishop. But in my adolescent years, I began to wonder if it was really true what they told you. Does God exist? Questions like that. So, like many children, I started looking for answers. One place to look, I thought, was philosophy. I was reading thick books on Greek philosophy. But very soon I became disillusioned with philosophy. I found that the business of the ‘good’ philosophers seemed mainly to refute the ‘bad’ philosophers. There didn’t seem to be much else. The next-​ best thing seemed to be physics. Although physics does not address itself to the ‘biggest’ questions, still it does try to find out what the world is like. And it progresses. One generation builds on the work of another instead of simply overturning it. In my secondary school, I was already beginning to get some idea that nature respects laws, like Newton’s laws of motion. I remember a big disappointment when we started our course in Newtonian mechanics. It was in a room with models of steam engines all around. The teacher said, ‘Next time, we are going to play with the machines.’ I thought he meant the steam engines. But it turned out that he meant things like levers. It was a great disappointment.” Because of the cost, the only university Bell could have considered going to after graduating from high school was Queen’s University in Belfast. But Bell had graduated from high school at sixteen, and the university would not admit anyone before the age of seventeen. So Bell looked for work. “I applied to be office boy in a small factory,” he recalled, “some starting job at the BBC—​things like that. But I didn’t get any of the jobs I applied for. One told me that I was overqualified; another didn’t tell me anything. It may be that I was resisting presenting myself as if I really wanted a job. I really wanted to continue on to the university, and the job I finally did get was in the university.” It turned out that a laboratory assistant was needed in the physics department, and Bell got that job. “It was a tremendous thing for me,” he said, “because there I met, already, my future professors. They were very kind to me. They gave me books to read, and in fact, I did the first year of my college physics when I was cleaning out the lab and setting out the wires for the students.”

John Stewart Bell  11 Among the professors who were especially helpful to him that year, Bell remembered Karl Emeleus and Peter Paul Ewald. Emeleus gave him two books to read: the classic freshman physics text Mechanics, Molecular Physics, Heat and Sound by Millikan, Roller, and Watson and an odd Victorian text on electricity and magnetism titled Elements of Electricity by the British physicist J. J. Thomson. It was Thomson who in 1897 had identified the first subatomic particle, the electron. He measured its charge and mass, and for this work he was awarded the Nobel Prize in 1906. His work seemed to show that the electron was a particle, a motelike billiard ball. Thomson was still alive when his son, G. P. Thomson, shared the 1937 Nobel Prize with C. Davisson for their independent experimental discoveries in the late 1920s that the electron can also act like a wave, one of the mysteries of the quantum theory. In any event, Bell found the senior Thomson’s book exceedingly difficult. While its donor, Professor Emeleus, was a rather formal character, Ewald, a very distinguished crystallographer who, in Bell’s words, “had been washed up on the shores of Ireland after the Nazis forced him to emigrate from Germany,” was just the opposite. “He’d discuss anything,” Bell noted. “He even declared that one of his assistants was mad.” By the time Bell graduated from Queen’s University in 1949, he had decided to make a career in theoretical physics. Ewald suggested that he continue his studies in graduate school with Rudolf—​later Sir Rudolf—​Peierls in Birmingham. Peierls was a physicist with an extraordinary breadth of interests. There is almost no branch of modern theoretical physics in which he had not made some very significant contribution. He was also a great teacher. While he was in Birmingham, several generations of young theoretical physicists came there to study with him. Some, like Freeman Dyson, even lived in the Peierlses’ house. Bell would have liked nothing better than to have gone off to Peierls, except, as he put it, “By that time I had a very bad conscience about having lived off my parents for so long [Bell had lived at home while he was in college], and I thought I should get a job. So I did get a job, at the Atomic Energy Research Establishment at Harwell. There I went, and I found myself soon sent off to a substation at Malvern in Worcestershire.” Bell was now twenty-​one. While he returned to Ireland regularly to see his family (and in June 1988, in a single week, he was awarded honorary degrees from Queen’s University in Belfast, his alma mater, and from Trinity College in Dublin), he never did return to live in Ireland. In the meantime, by an equally serendipitous route, Mary Bell had also arrived in Malvern. Mary Ross was born in Glasgow into what Bell called

12  Quantum Profiles a “slightly more bookish family than my own.” Her father began as a clerk in a shipyard and finally became a commercial manager specializing in the commerce of wood. Her mother was an elementary-​school teacher. Unlike John, Mary Bell recalled being especially fond of arithmetic problems as a child. Fortunately, as it turned out, the school she went to—​a comprehensive school with grades from elementary school through high school—​was coeducational, which meant it offered a physics course. “With girls alone,” she told me, “there very likely would not have been physics—​other sciences but not physics.” She did very well in school and, as her husband was fond of reminding her, won many prizes for “general excellence.” In 1941, she won a bursary competition, which enabled her to go to the University of Glasgow, where she majored in mathematics and physics. “It was during the war,” she reminded me, “and we all had to take courses in radio, circuits, and the like. At the end of my third year, I was drafted to work in the radar lab at Malvern, where, I must say, I didn’t do a lot.” After the war ended, she finished her degree in Glasgow and was, like John, hired by the Atomic Energy Research Establishment and soon sent to Malvern, where she joined the same accelerator design group that had hired John. As it happened, the Bells’ arrival in the accelerator group at Malvern more or less coincided with a revolutionary breakthrough in the design of accelerators, known as the principle of strong focusing, which was invented in the United States by Ernest Courant, M. Stanley Livingston, and Hartland Snyder and independently by a Greek physicist-​inventor named Nicholas Christofilos. A beam of charged particles that is being guided around the interior of an accelerator by electric and magnetic fields tends to try to “get away.” Unless it is focused by these fields, the beam squirts off uncontrollably in all directions. For a while, it appeared that this problem would be insurmountable for the new generation of machines being designed for the 1950s. But, as has happened so often in the accelerator business, there was an unexpected discovery that salvaged the situation. In this case, Courant, Livingston, and Snyder realized that if one used suitably varying electric and magnetic fields, rather than steady ones, as had previously been used to confine the beam, stability could be achieved. John Bell told me that prior to this discovery, a few designs had been generated in computer simulations that seemed to exhibit stability, but no one understood why. Bell very quickly became an expert on the mathematics of strong focusing. He is best known among theoretical physicists for his abstruse work on the theory of elementary particles and quantum mechanics, so he was very

John Stewart Bell  13 pleased to have in his curriculum vitae such “engineering” items as “Stability of Perturbed Orbits in the Synchrotron,” written in 1954. (Synchrotron is the generic term for the kind of accelerator that uses strong focusing.) As young as he was, Bell became a consultant to the British delegation that was beginning the design studies that would lead, in 1959, to the construction of the first accelerator at CERN—​the so-​called Proton Synchrotron. It was a landmark in postwar European science, as it was the first major scientific project carried out after the war by the European community as a whole. Bell began consulting for the project in 1952. That, as it happened, was also the year he got an unexpected job bonus—​“a bolt from the blue,” as he put it. It turned out that the Atomic Energy Research Establishment had the very enlightened policy of selecting some of their young people and sending them back to the universities for a year’s study. “It was proposed to me,” Bell recalled, still with a tone of surprise. “It didn’t come from me, that I might go back to university for a year. And so I said, ‘Fine,’ and off I went to Birmingham, and there I became a quantum field theorist.” In the meantime, the Bells had both moved from Malvern to Harwell and had gotten married. John went off to Birmingham, and Mary remained at Harwell. “Our marriage was a thing of weekends for a while,” he noted. In the British system at the time, there was in each department a single “professor” who functioned essentially as the chairman of the department. Peierls was the professor of theoretical physics at Birmingham, and he assigned the young people who came to work with him both problems to work on and junior members of the faculty to work with. Bell, having already worked as a professional physicist for three years, was somewhat older than the rest of the students. After noting that he did not intend to treat him as a “beginner,” Peierls suggested a general area for Bell to look into and assigned him an adviser, a young British theorist named Paul Matthews. It was not clear whether the work was meant to lead to a degree or even if a second year was possible. “I just didn’t open up that question,” Bell told me. “I thought a year was fine. I thought I was very lucky to get it. I just accepted that.” Within a few months, Bell discovered a very deep theorem in quantum field theory known as the TCP theorem. In this acronym, T stands for time reversal, C for charge conjugation, and P for parity. These are quantum-​ mechanical symmetries. The theorem states that the combined operation of these symmetries is a valid one even in theories where the individual symmetries may break down. It implies, among other things, that particles and antiparticles, such as electrons and positrons, have the same mass.

14  Quantum Profiles “Unfortunately for me,” Bell explained, “when I was writing that up, there appeared not just a preprint but a reprint from Gerhard Lüders, who had made the same discovery. So I was a year behind him. [Lüders’s work was later generalized by Wolfgang Pauli and is often referred to as the Lüders-​ Pauli theorem.] And I cannot exclude that there was some garbled rumor of Lüders’s work that had reached Birmingham and that Peierls had asked me to look into that. Anyway, I thought I could make a paper out of my stuff and also part of a thesis.” When his year was up, Bell returned to Harwell to a new group that had been formed to do fundamental research in areas such as elementary-​ particle physics. Bell was able to do a second problem, which completed his thesis. “From time to time,” he explained to me, “I had a remark to make to my old accelerator group. Mary was still there. I hadn’t given much thought to my future. When I went to Harwell at the age of twenty-​one, I already had a tenure position. I didn’t have to worry about anything. I just went along. So long as I was happy, I didn’t think of going anywhere. But towards the end of the fifties I began feeling uncomfortable because there was a growing soul-​searching at Harwell. What was that establishment supposed to be doing? They were not supposed to be doing nuclear weapons, though I believe now that there was some weapons work going on. Harwell had been set up to develop peaceful uses of atomic energy, but by that time, the nuclear power stations had already been built, and other, more applied-​research establishments had grown up to do that kind of work. Harwell had sort of lost its sense of direction. Although I was in a very particular corner of Harwell, doing relatively fundamental work, this malaise was felt everywhere. It also began to look as if the fundamental research would be one of the things that would disappear in a reorientation of the establishment. So I started to think about going somewhere else.” The “somewhere else” was CERN. CERN—​ which stands for Conseil Européen pour la Recherche Nucleaire—​had its formal beginnings in 1954. It was in 1989 a consortium of thirteen member states: Austria, Belgium, Great Britain, Denmark, France, Greece, Italy, the Netherlands, Norway, Spain, Sweden, Switzerland, and West Germany. Neither the United States nor the Soviet Union is a member, although both Americans and Soviets work in the laboratory. No classified work of any kind is done at CERN. In 1953, a referendum was held by the canton of Geneva, and voters ratified the decision of the Swiss government to give the nascent laboratory its site near the border. From the beginning, it was decided that CERN would have only a very small permanent staff of

John Stewart Bell  15 physicists compared with the visitors. For example, in the theory division, which consisted in 1989, the time of my visit, of about a hundred and forty people, less than 10 percent were staff members. Typically, a staff member is offered a three-​year contract with the understanding that as a rule, a second three-​year contract will be offered. Sometime during those six years, a decision is made about whether the staff member will be offered one of the few jobs with unlimited tenure. There did not seem to be any university in Britain that could accommodate both Mary Bell’s interests in accelerator design and John Bell’s growing commitment to research in elementary-​particle physics. CERN seemed ideal, except that they would be giving up the security of John’s tenured job for three-​year contracts. “I am amazed,” he commented, “at how easily we left a tenured situation at Harwell and went to an untenured one. I remember that Mary’s parents were a bit worried, but neither of us was worried. When we first got here in 1960, they already had the tradition that new people were more or less ignored and that you had to find your way to other people. Of course, when I first showed up in the theory division, they shook my hand and said, ‘Welcome,’ but after that, they left me alone. Nobody was coming into my office or anything. I got quite lonely for the first months. It’s my understanding that newcomers here can still feel like this for the first months. From time to time, we think that we must do something about it, and we have tried various schemes. But the trouble is that the staff members who are here are already so saturated that it is not easy to cold-​bloodedly say I must go and spend time with this person because he or she is new. In any case, Mary and I settled into Geneva very easily. We got to know people we work with in CERN, and we didn’t try to get to know many other people. So the fact that we were surrounded by Swiss rather than English and that they spoke French wasn’t very important to us. And of course, we were very happy with the new landscape around here. While we liked being in Berkshire, where Harwell is—​there are a lot of beautiful things in Berkshire—​the novelty of the high mountains here pleased us very much.” Except for a very occasional sabbatical leave, the Bells had not left Geneva since 1960. I once asked Bell whether during the years he was studying quantum theory it ever occurred to him that the theory might simply be wrong. He thought a moment and answered, “I hesitated to think it might be wrong, but I knew that it was rotten.” Bell pronounced the word rotten with a good deal of relish and then added, “That is to say, one has to find some decent way of expressing whatever truth there is in it.”

16  Quantum Profiles The attitude that even if there is not something actually wrong with the theory, there is something deeply unsettling—​rotten—​about it was common to most of the creators of quantum theory. Bohr was reported to have remarked, “Well, I think that if a man says it is completely clear to him these days, then he has not really understood the subject.” He later added, “If you do not get schwindlig [dizzy] sometimes when you think about these things then you have not really understood it.” My teacher Philipp Frank used to tell about the time he visited Einstein in Prague in 1911. Einstein had an office at the university that overlooked a park. People were milling around in the park, some engaged in vehement gesture-​filled discussions. When Professor Frank asked Einstein what was going on, Einstein replied that it was the grounds of a lunatic asylum, adding, “Those are the madmen who do not occupy themselves with the quantum theory.” Max Planck, whom one may consider either the father or the grandfather of quantum theory, depending on one’s analysis of the history, was hardly a “lunatic.” He was a conservative German, in the best sense of the term, from an ancient family of scholars, public servants, and lawyers. His father was a professor of law at Kiel, where Planck was born in 1858. Planck died in 1947, having lived with dignity in Germany during the Nazi regime. His son Erwin was executed by the Nazis after he took part in the July 1944 plot against Hitler. What appealed to Planck about physics was the possibility of finding absolute laws that would retain their meaning, as he once wrote, “for all times and all cultures.” One such law appeared to be the one governing what is known as black-​body or cavity radiation. A so-​called black body can be made with a hollow, thin-​walled cylinder of some metal such as tungsten. The walls of the cylinder are heated by, for example, passing an electric current through them. Radiation is then produced from the heated walls, and it collects within the hollow cylinder. If a small hole is drilled in the cylinder, enough of this radiation gets out that one can measure its characteristics. (Incidentally, if the cylinder is kept at room temperature, the hole looks perfectly black from the outside, since any radiation falling into it is trapped inside the cylinder—​ hence the name black body.) In particular, black-​body radiation has a very characteristic distribution of wavelengths—​colors. It turns out that this distribution depends only on the temperature to which the cylinder is heated and not on the material of which the cylinder is made. Cavities made of, say, tantalum or molybdenum will exhibit the same black-​body spectrum as

John Stewart Bell  17 cavities made of tungsten, provided only that all the cavities are heated to the same temperature. This was demonstrated theoretically in 1860 by Planck’s teacher at the University of Berlin, Gustav Kirchoff, using the newly discovered science of thermodynamics. He showed that if different materials had different black-​body spectra, one could construct a kind of perpetual-​ motion machine by connecting the cavities together. Kirchoff ’s result gave the black-​body spectrum the sort of absolute character that appealed to Planck. Moreover, in 1896, another German physicist, Wilhelm Wien, produced a simple formula that seemed to agree with both the thermodynamics and the empirical data. Planck set out to derive Wien’s formula from something like first principles. Indeed, by 1899, he thought he had found such a derivation. However, by October 1900, Planck realized that his derivation was wrong. Furthermore, the Wien formula was beginning to break down experimentally when confronted with new data that embraced a wider range of wavelengths. Planck then made a sort of inspired guess regarding what the correct formula was, and no sooner had he announced it than it was confirmed. He later wrote: The very next morning I received a visit from my colleague Rubens. He came to tell me that after the conclusion of the meeting [at which Planck had presented his formula], he had that very night checked my formula against the results of his measurements and found satisfactory concordance at every point. . . . Later measurements, too, confirmed my radiation formula again and again—the finer the methods of measurement used, the more accurate the formula was found to be.

And so it has remained. Planck tried to derive his formula. As he put it, “On the very day when I first formulated this law, I began to devote myself to the task of investing it with a real physical meaning.” To understand what is at stake, we can imagine the walls of the black-​body cavity as being made up of atoms that are set into oscillatory vibrations when heated. These oscillators emit and absorb radiation, and when they emit as much radiation as they absorb, an equilibrium situation is produced that is precisely that of a black body. In classical physics, there are no restrictions on how much energy an oscillator can emit or absorb in a single transaction; there are no minimal units. What Planck discovered was that he could derive his formula if he allowed the emission and absorption of radiation to take

18  Quantum Profiles place only in discrete units—​lumps of energy. (The use of the term quanta for these energy units was introduced by Einstein in 1905.) In Einstein’s homey image, it was like selling beer from a keg in pint bottles. As historians of science such as Thomas Kuhn have noted, the derivations Planck gave in his papers of 1900 and 1901 are sufficiently obscure that one cannot be sure whether Planck understood that he had made a radical new assumption or whether he thought he was still doing classical physics. Fortunately, Planck made an unjustified step in his derivation. If he had done it conventionally, it would have led not to the Planck formula (or to the Wien formula) but to the expression derived by Lord Rayleigh in 1905 that classical physics inexorably predicts. This expression, called the Rayleigh-​Jeans law because it was slightly amended by the British astrophysicist James Jeans, agrees with the Planck law for long wavelengths but then leads to disaster. It predicts that the total energy in the cavity is infinite, a nonsensical proposition that became known as the ultraviolet catastrophe. In short, by 1905 it was clear, if only to Einstein, that classical physics had broken down. A hint of Einstein’s state of mind at this realization is contained in his letter to Habicht that I quoted earlier. Of his 1905 papers, including the one on the theory of relativity, which modified our notions of space and time, it is only the paper on the black-​body spectrum that Einstein described as “revolutionary.” We will shortly see why. As in so many other aspects of physics, the quantitative attempts to study the nature of light begin with Isaac Newton. Newton spent at least as much time thinking about light as he did about gravitation; the same can be said about Einstein, although both men are best known for their theories of gravitation. Newton believed that light was a particlelike projectile emitted by a radiating object. In the English edition of his book Optiks, published in 1717, he described rays of light as being composed of “very small Bodies emitted from shining Substances.” However, to explain some of his observations, he supplemented this simple particle picture with the notion that these particles could incite wavelike disturbances in an all-​pervasive medium that became known as the ether. These disturbances he called “Fits of easy Reflexion and easy Transmission.” On the other hand, his less well-​known but almost equally great contemporary the Dutch physicist Christian Huygens, maintained that light was nothing but a wave disturbance in the ether. He worked out the mathematics of such wave propagation in a very sophisticated way that is still used.

John Stewart Bell  19 A pure wave theory of light makes predictions about optical phenomena that appear to be incompatible with any particle description whatsoever. For example, according to the wave theory, objects do not cast sharp shadows. Waves curl around objects, so their shadows are not sharply defined—​a phenomenon known as diffraction. A familiar example is a breakwater in a harbor. Water waves spread out behind a breakwater; a stream of particles, on the other hand, confronting such an obstacle would simply be deflected by it, and the obstacle would act like an ineluctable barrier to their transmission. At the heart of the distinction is the phenomenon of interference. When two waves encounter each other, they do not simply bounce off each other like colliding billiard balls. Rather, the two waveforms combine to produce a new wave pattern. Separate wave disturbances can reinforce one another to produce amplifications, or they can interfere destructively to produce areas of little or no wave activity. In the case of light waves, these would be dark regions; in the case of sound waves, these would be places where the sound is muted—​a problem that besets the designers of concert halls. Both the particle and the wave theories of light had their advocates until the beginning of the nineteenth century. However, in 1801, the British natural philosopher Thomas Young did an experiment that seemed to settle the matter once and for all in favor of the wave theory. He reflected sunlight from a set of parallel grooves cut into glass. He observed that the light coming through these grooves produced a pattern of alternating light and dark fringes, indicating interference effects. There was no doubt in Young’s mind what this meant; he concluded bluntly that “Radiant Light consists in Undulations of the luminiferous ether.” All of nineteenth-​century optics and electromagnetic theory was built on this discovery, including the grand synthesis created in the second half of the century by the Scottish physicist James Clerk Maxwell, whose theory of electricity and magnetism was to that subject what Newton’s theory of gravity was to that one. It was against this apparently overwhelming preponderance of evidence in favor of the wave theory of light that Einstein’s paper of 1905 was written. In contemplating the papers Einstein wrote in 1905, I  often find myself wondering which of them is the most beautiful. It is a little like asking which of Beethoven’s symphonies is the most beautiful. My favorite, after years of studying them, is Einstein’s paper on black-​body radiation. The paper has the mind-​numbing German title “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”—​in English, “Concerning a Heuristic Point of View about the Creation and

20  Quantum Profiles Transformation of Light.” It begins with a brief discussion of the difference between gases, and what Einstein calls “other ponderable bodies,” and light. The former appear to be made out of particulate elements—​Einstein mentions atoms and electrons—​while light is represented as a continuous medium. Mincing no words, Einstein states that the radiation in a black-​ body cavity, and elsewhere, pace the wave theory, may in fact have a particulate character. He writes: “According to the presently proposed assumption the energy in a beam of light emanating from a point source is not distributed continuously over larger and larger volumes of space but consists of a finite number of energy quanta, localized at points of space which move without subdividing and which are absorbed and emitted only as units.” In terms of Einstein’s previously quoted homey image, not only was the beer bought and sold in pint containers, but the beer in the keg could exist only in pint-​container  units. This having been said, in the second section of the paper, Einstein produces the formula for the black-​body distribution that Planck should have gotten if he had done the calculation correctly in classical physics—​the Rayleigh-​ Jeans law. Einstein arrived at it independently. He then points out that this law leads to an absurdity, namely, an infinite total energy in the cavity—​the ultraviolet catastrophe. It is in the fourth section of the paper that the true novelty begins. Having come to the conclusion in the first part of the paper that classical physics can correctly describe only the long-​wavelength parts of the spectrum—​the “graver modes,” in Lord Rayleigh’s wonderful terminology—​Einstein focused his attention on the opposite end of the spectrum, the short wavelengths, which must contain the new physics. Here the spectrum is described by the Wien law, so, Einstein reasoned, the new physics must be hidden there. Part of being a great scientist is to know—​have an instinct for—​the questions not to ask. Einstein did not try to derive the Wien law. He simply accepted it as an empirical fact and asked what it meant. By a virtuoso bit of reasoning involving statistical mechanics (of which he was a master, having independently invented the subject over a three-​year period beginning in 1902), he was able to show that the statistical mechanics of the radiation in the cavity was mathematically the same as that of a dilute gas of particles. As far as Einstein was concerned, this meant that this radiation was a dilute gas of particles—​light quanta. But, and this was also characteristic, he took the argument a step further. He realized that if the energetic light quanta were to bombard, say, a metal surface, they would give up their energies in lump

John Stewart Bell  21 sums and thereby liberate electrons from the surface in a predictable way, something called the photoelectric effect. Some evidence that this was true already existed in 1905, but it was not very convincing. It became convincing in the next decade, and when Einstein won the Nobel Prize in 1922, it was for this prediction and not for the theory of relativity. However, it must not be imagined that there was an epiphany among physicists after Einstein published this paper in 1905. In the first place, not many physicists were even interested in the subject of black-​body radiation for at least another decade. Kuhn has done a study that shows that until 1914, fewer than twenty authors a year published papers on the subject; in most years, there were fewer than ten. Planck, who was interested, decided that Einstein’s paper was simply wrong. He wrote a celebrated letter of recommendation for Einstein for his admission to the Royal Prussian Academy of Sciences in 1913, in which he said of Einstein, “that he may sometimes have missed the target in his speculations, as for example, in his theory of light quanta, cannot really be held against him.” One even wonders about Einstein’s attitude toward this work Three months after he finished the paper on the light quanta, he submitted his paper on relativity to the Annalen der Physik, the same journal that published the quantum paper. In the relativity paper, Einstein also deals with the theory of light; indeed, the propagation of light signals plays a central role. For the purposes of this paper, light is treated as a wave phenomenon. There is not a hint that it might have, under certain circumstances, a particle aspect. There is something almost schizophrenic about this separation of ideas in the two papers. It is a schizophrenia that haunted Einstein and has haunted quantum theory ever since. Two developments brought quantum theory to the center of physics. The first began in 1907, when Einstein wrote a paper that founded the quantum theory of solids, which we now call solid-​state or condensed-​matter theory. It is this discipline that lies behind much of modern technology, from the superconductor to the transistor. Einstein was concerned with how solid bodies absorb heat. He imagined that the atoms became agitated and oscillated when the substance absorbed heat. He applied the same quantum rules to these oscillators as Planck had used in his derivation of the black-​body law. This led to a new theory of heat absorption, which provided an explanation of some heretofore puzzling experimental results. That, in turn, aroused the interest of a community of scientists who had previously ignored quantum theory. For example, in 1910, the great German physical chemist Walther Nernst made a special trip to Zurich, where Einstein was teaching, to discuss

22  Quantum Profiles these matters with him. Nernst’s public endorsement of Einstein’s work influenced many other scientists to begin to take it seriously. But the real breakthrough came in 1913 with Bohr’s invention of the “planetary” model of the atom. The Bohr atom, with its electrons in circular orbits around a central nucleus, has become one of the defining pictorial images of the atomic age. Not until 1909 was it known that the atom had a nucleus. That year, the New Zealand–​born experimental physicist Ernest Rutherford directed his younger colleagues at Manchester University to do a series of experiments in which they allowed helium nuclei, which are emitted with substantial energies from certain naturally occurring radioactive substances, to impinge on a sheet of gold foil some fifty thousandths of an inch thick. Rutherford expected that these projectiles would pass directly through the foil. Instead, some of them bounced backward as if they had struck something hard in the interior of the gold atoms. Rutherford later described his astonishment. He wrote, “It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15 inch shell at a piece of tissue paper and it came back and hit you.” What the helium projectile had hit was the gold atom nucleus—​the tiny, and incredibly dense, part of the gold atom where most of its mass is located. (We now know that the nucleus is made up of protons and neutrons and that it is surrounded by a cloud of relatively light, electrically charged electrons.) At the time of this discovery, Bohr was still a student at the University of Copenhagen. After taking his doctoral degree in 1911, he went to Cambridge, hoping to work on electron theory with the discoverer of the electron, J. J. Thomson. Bohr and Thomson never quite hit it off, and after a short time, Bohr decided to go to Manchester with Rutherford. They made an odd but very well-​suited pair—​the shy Bohr and the enormously enthusiastic and totally self-​confident Rutherford. At Manchester, Bohr began the work that created the model of modern atom. The basic problem that Bohr confronted was what it was that kept the atom stable and why, when it was energized by electrical discharges or otherwise, it returned to stability by emitting beautiful patterns of spectral light. Classical physics taught that the electrons moving around the nucleus should radiate. As the electrons radiate, they lose energy and should then, according to classical theory, fall into the nucleus. Moreover, the classical energy radiated this way bears no resemblance to the beautifully ordered spectral lines given off in reality by excited atoms. Getting those harmonic patterns from a gas of chaotically collapsing electrons seemed about as likely as dropping a

John Stewart Bell  23 piano from a fourth-​floor window and having it play, as it hit the sidewalk, Beethoven’s Moonlight Sonata. To explain both the atomic stability and the spectral regularities, Bohr made the radical assumption that the electrons outside the nucleus were allowed to occupy only certain select orbits (these came to be known as the Bohr orbits) and no others. The Bohr orbit with the lowest energy, the “ground state,” was, he said, absolutely stable. On the other hand, electrons in the orbits with higher energies, the “excited” states, could make spontaneous transitions to the ground state with the emission of light quanta whose energies were determined by the energy differences of the electrons in the various Bohr orbits. No explanation was offered for these rules, and no accounting was given for what the electron did while it was making such a “quantum jump.” What persuaded everyone, including Einstein, who called the Bohr atom “one of the greatest discoveries,” that Bohr had done something of fundamental importance was that by using his rules, Bohr was able to derive a mathematical formula that gave the frequencies of the spectral lines in hydrogen to great accuracy. For the next decade, theoretical physicists tried to bring Bohr’s rules into some general context and to apply them to increasingly more complicated configurations of electrons. This enterprise now goes under the rubric of the “old” quantum theory. It was swept away by the “new” quantum theory, which was developed during a five-​year period beginning in 1923. That is the version of quantum theory that has endured to the present day. The first step in its creation came from a totally unexpected quarter, Louis de Broglie of Paris, who was born in 1892. It was a case of sibling rivalry. The older brother, Maurice, had become so enamored of physics while serving in the French navy that he contemplated resigning his commission in order to do research. This scandalized his family. His grandfather noted that science was “an old lady content with the attractions of old men.” As a compromise, a laboratory was set up for him in a room in the family mansion in Paris. Maurice de Broglie became a first-​rate X-​ray spectroscopist, and a generation of French experimental physicists after the First World War was trained in de Broglie’s mansion. The activity attracted his younger brother, Louis, who decided to have an equally distinguished career in physics. In the early 1920s, the brothers worked together studying various X-​ray phenomena. But in 1923, Louis de Broglie had an idea (it would become his PhD thesis) that transformed modern physics. He was familiar with Einstein’s early papers in which light had been given a particulate nature, and, largely

24  Quantum Profiles for reasons of symmetry, he proposed that particles such as electrons, which had previously been thought of as sort of billiard balls in miniature, should be given a wave nature. He referred to these waves as “fictitious,” since their relationship to the particulate electrons was unclear. But he was, nonetheless, able to give a kind of “explanation” for the location of the Bohr orbits by noting that their circumferences were just large enough that a whole number of electron wavelengths would fit into a given circumference. He pointed out that this speculation could be tested with the sort of diffraction experiments that Young had used to demonstrate the wave nature of light. However, de Broglie predicted that the electron waves would have wavelengths something like a thousand times smaller than those of visible light. Hence different techniques would have to be used to see the diffraction patterns. These experiments were carried out in 1927 by C. Davisson and L. Germer in the United States using crystals and by G. P. Thomson in Britain using thin films. (The electron microscope, developed in the 1930s, produces its high magnification by exploiting the shortness of the de Broglie waves.) At the time de Broglie made his speculation, he did not have his doctorate, so he submitted this work as his PhD thesis. His thesis adviser, Paul Langevin, was somewhat uncertain about what to make of it, so he sent a copy of the thesis to Einstein, who immediately grasped its potential importance. It is even possible that he had been thinking along similar lines. Einstein, in turn, sent a letter about this to the Dutch physicist Hendrik Lorentz, whom Einstein most admired among the physicists of the generation that preceded his own. Einstein wrote: “A younger brother of . . . de Broglie has undertaken a very interesting attempt to interpret the Bohr-​Sommerfeld quantum rules [this was the business of fitting the electron waves around the Bohr orbits]. . . . I believe it is the first feeble ray of light on this worst of our physics enigmas. I, too, have found something which speaks for his construction.” De Broglie won the Nobel Prize in 1929 for the work he did for his doctoral thesis. The next step was taken in 1925 by the young German physicist Werner Heisenberg. He, too, appears to have been inspired by Einstein, who hovers over this entire subject like some sort of magisterial ghost. Heisenberg had absorbed what he thought was the philosophical lesson of the theory of relativity, namely, that physics gets itself into trouble when it becomes based on metaphysical abstractions instead of concepts with direct links to experimental procedures. In the relativity theory, Einstein had replaced the metaphysical notions of “absolute” space and time by experimental procedures involving clocks and metersticks. Indeed, from this point of view space and

John Stewart Bell  25 time have no other significance than relationships measured by clocks and meter sticks. Heisenberg decided that Bohr’s emphasis on atomic electron orbits—​ despite their pictorial appeal—​had been misplaced. No one ever observed an electron actually circulating in an atomic orbit. What one did observe was the radiation emitted by these electrons as they lost energy—​the atomic spectra. The orbits were, from this point of view, a gratuitous remnant of classical physics. Heisenberg decided, therefore, to focus directly on the computation of the wavelengths of these spectral lines, even if this meant giving up the visualization in terms of electrons circulating in orbits. To this end, Heisenberg created a mathematical scheme known as matrix mechanics. Matrices, which were first studied in the nineteenth century, obey unconventional multiplication laws. The product of A times B is not, in general, equal to the product of B times A, whereas for ordinary numbers, 5 × 3 = 3 × 5 = 15. Heisenberg, who knew nothing about matrices, reinvented the subject by studying the properties of the atomic spectra. Once he had his matrix mechanics, Heisenberg was able to reproduce all the results of the old quantum theory and more. It was the first example of a kind of Faustian bargain that quantum theorists were to make with the spirit of visualization; namely, one would be allowed to predict experimental results with very high accuracy provided that one did not ask for a visualization of the phenomena that went beyond the rules themselves. Einstein followed Heisenberg’s work with interest, but it was the next step, taken by Heisenberg’s older contemporary, Erwin Schrödinger, that, at least initially, aroused his enthusiasm. Schrödinger, who was born in Vienna in 1887, was a fascinating man. I met him a few months before he died in 1961. All the inventors of quantum theory, as it happened, were men of very broad culture, perhaps attributable in part to their European gymnasium educations, but even in this group, Schrödinger stood out. He read very widely in a variety of languages, ancient and modern. He was a scientific polymath with a deep interest in Eastern religions. He was also a rather romantic figure who wrote poetry. I was told by Professor Frank that when Schrödinger appeared in 1939 at the Institute for Advanced Study in Dublin, where he had been offered sanctuary during the war, he did so with what Frank referred to as two “wives.” (This was the least of it. Schrödinger had several mistresses, with whom he fathered at least two daughters.) Schrödinger’s marvelous book What Is Life? written in Dublin in 1944, inspired a whole generation of young scientists such as Francis Crick to take up biology.

26  Quantum Profiles In 1918, Schrödinger thought he might get a chair of theoretical physics at the provincial university of Czernowitz. He was then thirty-​one. As he later wrote, “I was prepared to do a good job lecturing on theoretical physics . . . but for the rest to devote myself to philosophy.  .  .  . My guardian angel intervened: Czernowitz soon no longer belonged to Austria. So nothing came of it. I had to stick to theoretical physics, and, to my astonishment, something occasionally emerged from it.” In 1926, “wave mechanics” emerged from it. He later wrote that in discovering the equation that bears his name—​ which is the heart and soul of quantum theory—​he had been “stimulated by de Broglie’s thesis and by short but infinitely far seeing remarks by Einstein.” The Schrödinger “wave equation” describes how the de Broglie (or what Schrödinger insisted on calling the Einstein–​de Broglie) waves propagate in time and what their form in space is for all physical systems, from the electrons in an atom to the neutrons and protons in uranium. It is the basic tool of the modern theoretical physicist, to say nothing of the chemist and the electronics engineer. None of this was foreseen in 1926. The first reactions to wave mechanics were mixed, to put it mildly. Einstein was extremely enthusiastic and wrote to Schrödinger, “The idea of your article shows real genius.” Heisenberg, on the other hand, was severely critical—​polemical, in fact—​of wave mechanics. For him, it was a return to the kind of visualization of quantum phenomena in terms of classical pictures that went beyond the empirical data. It looked for a while as if there were two different quantum theories with radically different mathematical and philosophical underpinnings. That perception changed for two reasons. In the first place, Schrödinger and, independently, the British theoretical physicist Paul Dirac were able to show that wave mechanics and matrix mechanics were simply two equivalent ways of representing a common underlying mathematical structure, now simply called quantum mechanics. In the second place, it soon became evident that Schrödinger’s waves were no less abstract than Heisenberg’s matrices. The idea that they could be interpreted like, say, water waves on a pond, the sort of thing that appealed to Einstein, was an illusion. As I have mentioned, when de Broglie first introduced his waves, it was not clear how they were to be related to an object like an electron. Was the electron the wave, or did the wave attach itself to the electron and guide it, or what? De Broglie and Einstein certainly had the idea that the waves were physical objects that existed in ordinary, tangible three-​dimensional space—​ the kind we exist in. Einstein spoke of Führungsfelder (“pilot waves”) that

John Stewart Bell  27 guided the electrons and other particles. But it soon became clear that any such simple picture was impossible. To see the sort of thing that goes wrong, take as an example a free electron, one that is not confined to an atom. We know that we can measure its position as accurately as we would like. This means that the electron can be confined by this measurement to as small a region of space as we want. To describe this in a wave picture, it would mean that the wave describing the electron would have to be squashed down into this small region. This is quite possible, but then we can ask what happens to this squashed wave after the measurement. This question is answered by studying the Schrödinger equation. The results are dramatic. Suppose, for the sake of argument, we confine the electron to a region something like the size of an average atom. Then, once the measurement is over, the Schrödinger equation implies that the electron wave will spread out again very rapidly. Indeed, under the conditions I have just described, the electron wave would spread out over the entire solar system in only about four days. If the electron were really a three-​dimensional wave, this would mean that it had now become as big as the solar system. Clearly, something was wrong. A way out was suggested in a four-​page paper published by the German physicist Max Born. Recognizing these paradoxes, Born argued that the solutions to the Schrödinger equation—​which are called wave functions—​ should be thought of not as real waves attached to particles but rather as mathematical artifacts to be used (to take the example we have discussed) to compute the probability of finding the electron in a certain region of space. (In the body of his paper, Born suggests that the wave function itself is the probability, but in a footnote, he remarks that it really should be the square of the wave function that represents the probability. That, in fact, is the correct connection.) From this point of view, the bizarre behavior of the rapidly spreading electron described above is interpreted to mean that if we measure the electron’s position accurately by confining it to a minute region, then at later times, there is some probability of finding the same electron at a far distant place. According to this interpretation, the wave function does not tell us where the electron is but only where it is likely to be. Born was fully aware what a revolutionary step this was. In his paper he writes, “Here the whole problem of determinism comes up.” He briefly raises the possibility that in the future, one might find some “inner properties of the atom,” as he calls them (later “hidden variables” would be introduced for the same idea), whose discovery would restore the deterministic character of the

28  Quantum Profiles theory. But, he concludes, “I myself am inclined to give up determinism in the world of atoms.” A year later, Heisenberg quantitatively spelled out the limits to determinism in quantum mechanics in what became known as the Heisenberg uncertainty principle. A useful example is again provided by the attempt to measure the position of an electron. It is all very well to state, in the abstract, that one has performed an accurate measurement of the electron’s position, but how would one go about doing so in practice? In his paper, Heisenberg proposed using a microscope. Light shining on the electron will be reflected from it and will pass through the lenses of the microscope. To increase the accuracy, one must decrease the wavelength of the light. But the shorter the wavelength, the more energy and momenta the light quanta carry. When these energetic light quanta hit the electron, they knock it for a loop. The future position of the electron, along with its momentum, becomes more indeterminate the more accurately we insist on measuring the electron’s present position. Position and momentum are known in quantum mechanics as conjugate quantities—​the more accurately one quantity is known, the less accurately the other is known. A more precise statement of this conjugate uncertainty is given in terms of the Heisenberg relation

∆p∆q ≥ .

Here Δp and Δq stand for the uncertainties in momentum and position, respectively. The quantity ħ is related to Planck’s constant h by the equation

 = h / 2π = 1.054 × 10 −27 erg ⋅ seconds.

While this number involves dimensional quantities such as ergs (energy) and seconds (time), it is extremely small in the sense that this uncertainty relation plays no role in macroscopic physics. In a game of billiards, for example, we can ignore the Heisenberg relation. However, it is h that measures the departure from classical physics. If it had been zero, there would have been no quantum world. If quantum mechanics is right, there is no way to get around the uncertainty principle. The reason that the electron’s probability wave spread so

John Stewart Bell  29 much after we confined it, Heisenberg would argue, is that its momentum became almost completely indeterminate. In a manner of speaking, it headed off in all directions. There is something amusing about Heisenberg’s use of the microscope in his paper. A few years before it was written, he had taken his PhD qualifying oral examination and had been asked how a microscope works. He could not answer the question and nearly failed the oral. In fact, in his 1927 paper, he got it wrong again. In an addendum, he thanks Bohr for straightening the matter out. In 1926, even before Heisenberg’s paper, Einstein abandoned quantum theory. We know this because on December 4, 1926, he sent Born a letter that contains his most often quoted appraisal of the theory. He wrote: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the ‘old one’ [Einstein’s affectionate term for God]. I, at any rate, am convinced that He is not playing at dice.” Born was profoundly disturbed by this letter. When the letters were collected and published in 1971, Born wrote a commentary. Of this letter, he commented: “Einstein’s verdict on quantum mechanics came as a hard blow to me; he rejected it not for any definite reason, but rather referring to an ‘inner voice.’. . . It [the rejection] was based on a basic difference of philosophical attitude, which separated Einstein from the younger generation to which I felt that I belonged, although I was only a few years younger than Einstein.” Born also commented on the matter of the Nobel Prize. Heisenberg, who was Born’s junior colleague in Göttingen, received his in 1932, while, for reasons known only to the Swedish Academy, Born had to wait until 1954 to receive his for the work done in 1926, which had been the essential step leading to Heisenberg’s work. Born writes: “The fact that I did not receive the Nobel Prize in 1932 together with Heisenberg hurt me very much at the time, in spite of a kind letter from Heisenberg. I got over it, because I was conscious of Heisenberg’s superiority.” There are things one never gets over, and as the rest of the commentary shows, this was one of them. Born went on: It is not surprising that this acknowledgment [Born’s Nobel Prize] was delayed for twenty-​eight years, for all the great names of the initial period of the quantum theory were opposed to the statistical interpretation: Planck, de Broglie, Schrödinger, and, not least, Einstein himself. It cannot have been easy for the Swedish Academy to act in opposition to voices which

30  Quantum Profiles carried as much weight as theirs; there I had to wait until my ideas had become the common property of all physicists. This was due in no small part to the cooperation of Niels Bohr and his Copenhagen school, which today lends its name almost everywhere to the line of thinking I originated.

By the early 1930s, in fact, the statistical interpretation of quantum theory—​the wave function as probability—​was the “common property of all physicists.” Very little attention was being paid to the objections of the grand old men of the previous generation. The Swedish Academy has certainly done a number of strange things when it comes to the awarding of Nobel Prizes, and not giving one to Born until twenty-​eight years after his work was done is certainly one of them. Typically, Einstein sent Born a prompt letter of congratulations for the awarding of his “strangely belated” Nobel Prize. He added, “It was your . . . statistical interpretation of the description which has decisively clarified our thinking. It seems to me that there is no doubt about this at all, in spite of our inconclusive correspondence on the subject.” With typical Einstein humor, he noted, “And then the money in good currency is not to be despised either, when one has just retired.” When, in his Reith lectures, Oppenheimer referred to a recreation of history that “would call for an art as high as the story of Oedipus or the story of Cromwell,” there is little doubt that he had in mind the dialogues that took place about quantum theory between Einstein and Bohr. It is said that once these began in the 1920s, Einstein was never very far away from Bohr’s thoughts. Some sense of this is conveyed by an experience that the physicist Abraham Pais had in 1948, when he was helping Bohr prepare his account of these dialogues which was published in 1949 in the collection Albert Einstein: Philosopher Scientist. Bohr’s method of composition—​writing was always an agony for him—​was to find a younger colleague and dictate while pacing up and down. In 1948, Bohr was a visitor at the Institute for Advanced Study in Princeton. Einstein had a large office there and an adjacent office for an assistant. Since Einstein did not like the large office, he had moved into the assistant’s office, so the large office was available for Bohr. Bohr invited Pais into his office. Pais recounted: He then asked me if I could put down a few sentences as they would emerge during his pacing. It should be explained that, at such sessions, Bohr never had a full sentence ready. He would often dwell on one word, coax it, implore it, to find the continuation. This could go on for many minutes. At

John Stewart Bell  31 that moment the word was “Einstein.” There Bohr was, almost running around the table and repeating “Einstein . . . Einstein . . .” It would have been a curious sight for someone not familiar with Bohr. After a little while he walked to the window and gazed out, repeating every now and then, ‘Einstein . . . Einstein . . .” At that moment the door opened very softly, and Einstein tiptoed in. He beckoned me with a finger on his lips to be very quiet, his urchin smile on his face. He was to explain a few minutes later the reason for his behaviour. Einstein was not allowed by his doctor to buy any tobacco. However, the doctor had not forbidden him to steal tobacco, and this was precisely what he set out to do now. Always on tiptoe, he made a beeline for Bohr’s tobacco pot, which stood on the table at which I was sitting. Bohr, unaware, was standing at the window, muttering, “Einstein . . . Einstein . . .” I was at a loss what to do, especially because I had at that moment not the faintest idea of what Einstein was up to. Then Bohr, with a firm “Einstein,” turned around. There they were, face to face, as if Bohr had summoned him forth. It is an understatement to say that for a moment Bohr was speechless. I myself, who had seen it coming, had distinctly felt uncanny for a moment, so I could well understand Bohr’s own reaction. A moment later the spell was broken when Einstein explained his mission. Soon we were all bursting with laughter.

Although Bohr first met Einstein in Berlin in 1920, it was not until 1927 that the discussions began in earnest. Ever since 1911, the Belgian industrialist Ernest Solvay had been funding a series of international physics conferences. Einstein had been a frequent participant, and he and Bohr were both in attendance at the 1927 conference, which was held in Brussels. From this discussion, which I will describe shortly, one can see that Einstein’s objections to quantum theory, as they began to emerge in 1927, go far beyond the fact that quantum theory resorts to probabilities. However, the phrase “He is not playing at dice,” which Einstein used to describe God in his letter to Born, is the one that has stuck. As the postwar Born-​Einstein letters make clear, even Born did not understand that dice playing was not what ultimately bothered Einstein. Rather, it was the idea that there was nothing beyond dice playing, that quantum theory was the complete description of reality. The discussions of 1927 focused on what has come to be known as the double-​slit experiment. I have described how in 1801, Young “proved” that

32  Quantum Profiles light consisted of waves: sunlight, falling on a grating made up of parallel grooves cut in glass, makes patterns on the other side—​regions of light and dark. To see how this comes about in the wave theory, let us simplify the grating so that it consists of only two parallel slits through which the light can pass. If we cover one of the slits, so that all the light goes through the other, then what emerges is a diffuse beam of light with no especially interesting features. If we now open the second slit, the diffraction pattern appears. To understand this, let us concentrate on some specific location—​any location—​beyond the slits. In general, this location will be farther from one slit than from the other. Hence the waves from the two slits may arrive out of phase. The crests from one wave will not necessarily arrive in synchrony with the crests from the other. This is what produces the interference. For some locations, there will be synchrony, and there the light waves will reinforce each other, making a bright spot in the interference pattern. It is absolutely essential to have waves arriving from both slits to see anything interesting. This is how Young reasoned. But Einstein and Bohr knew that light in some circumstances appears to be made up of particles. How can this be reconciled with Young’s result? To make the situation as dramatic as possible, suppose, with Einstein and Bohr, we imagine reducing the intensity of the beam of light to such a low level that only one light quantum at a time is available to go through the slits. What will happen? We may suppose that we have put some sort of photosensitive screen behind the slits to detect the quanta as they come through, one after the other. Each time a quantum hits a spot on the screen, it blackens it, say. At first, nothing interesting will happen. The quanta that get through will blacken a few apparently random spots on the screen. But in the course of time, something remarkable happens. The spots on the screen will build up to make just the interference pattern that Young observed. From the point of view of a classical physicist, this is quite mad. A classical physicist would argue that if the light quantum is really a particle, it would have a well-​defined trajectory that would take it through one slit or another—​not both at once—​which would seem to be what is required if one is going to produce interference fringes. Einstein, with his years of experience in the patent office, even produced an imaginary modification of the double-​slit device that enabled it to measure the photon’s trajectory. Einstein imagined mounting the slits on springs so that they could jiggle when the photon passed through. That way, one could make a definite statement that the photon had gone through one slit or another on its way to the screen. If this modified device still produced an

John Stewart Bell  33 interference pattern, the quantum theory would be inconsistent. The particle properties and the wave properties of light, which are incompatible with each other, would have been forced to manifest themselves together in a single experimental arrangement. But Bohr pointed out that Einstein’s reasoning had neglected the Heisenberg uncertainty principle and therefore was not a valid criticism of quantum theory. It has assumed that the jiggling the photon produces—​which is a transfer of momentum from the photon to the structure holding the slits—​can be measured without limitation from the uncertainty principle. But, as Bohr pointed out, if the momentum is measured accurately enough to determine the trajectory, then the uncertainty principle implies that the position of the jiggled slits is sufficiently uncertain that no interference fringes can be produced. This was an extremely important observation. It was an example of something that Bohr elevated to a general principle that he called the principle of complementarity. In the case at hand, the complementary characteristics are the particle and wave aspects of light. The principle states that in this case, any experiment designed to reveal the particle aspect of light cannot reveal its wave aspect, and vice versa. Bohr enunciated this principle after analyzing a variety of examples such as the double-​slit experiment and seeing that in each example, the limitations on measurement imposed by quantum theory—​the uncertainty principle—​are just such as to prevent the theory from being self-​contradictory. Bohr was so impressed by this revelation that he began applying it to areas outside physics. He thought he saw echoes of this idea of complementary qualities in ethics (truth as opposed to justice), in psychology (thoughts as opposed to sentiments), in biology (mechanism as opposed to vitalism). He wrote and lectured extensively about these matters, but he had such difficulty in reducing his ideas to words that one wonders if any of it, quantum mechanics aside, will survive. The great value of this discussion for quantum theorists was that it forced them to confront, head-​on, the quantum-​mechanical nature of reality. Is light really a particle, or is it really a wave? The quantum theorist would answer that it really is neither. Light is just what it is revealed to be, in some given experimental arrangement. It was this aspect of quantum theory, and not the dice throwing, that profoundly bothered Einstein. There seemed to be a loss of objective reality. Pais recalls discussing these matters with Einstein on walks in Princeton. During one walk, Pais remembers, “Einstein suddenly

34  Quantum Profiles stopped, turned to me and asked whether I really believed that the moon exists only when I look at it.” The next confrontation between Einstein and Bohr took place at the Solvay Congress of 1930, also held in Brussels. Einstein had prepared a little surprise for Bohr. This was an imaginary device that Einstein thought violated the uncertainty principle involving energy and time. The more precisely an energy is measured, the less certain is the time at which that measurement takes place. Einstein’s imaginary contraption consisted of a box containing a clock along with some radioactive element. The clockwork was arranged so that it opened a hole in the box for a fraction of a second, just long enough to allow some radiation out but short enough so that the time when this happened could be precisely determined. One could imagine that the box was attached to a scale that could measure its weight before and after the release of the radioactivity. In this way, one could, Einstein claimed, determine the energy of the released radioactivity, which corresponded to the weight lost by the box, along with the precise time at which the energy was released—​a violation of the energy-​time uncertainty principle. Bohr was stunned. His reaction was later described by Leon Rosenfeld, the Belgian physicist who was a close associate of Bohr. Rosenfeld wrote, “It was quite a shock for Bohr . . . he did not see the solution at once. During the whole evening he was extremely unhappy, going from one to the other and trying to persuade them that it couldn’t be true, that it would be the end of physics if Einstein were right; but he couldn’t produce any refutation. I shall never forget the vision of the two antagonists, Einstein, a tall majestic figure, walking quietly, with a somewhat ironical smile, and Bohr trotting near him, very excited. . . . The next morning came Bohr’s triumph.” During the night, Bohr had realized that Einstein had left out of his argument an important consideration involving his own general theory of relativity and gravitation. A clock in a gravitational field runs more slowly than a clock not influenced by gravity. (This remarkable prediction of the theory has now been confirmed experimentally by very accurate atomic clocks flown in satellites and airplanes.) This effect plays a role in Einstein’s imaginary device, because, as Bohr realized, the position of the clock was somewhat uncertain owing to the uncertainty principle. Since the gravitational field varies from place to place, this affected the rate of the clock, which was therefore uncertain to the extent that the clock’s location was uncertain. When that was taken into account, the uncertainty relation between energy and time was restored.

John Stewart Bell  35 The fact that Einstein had not realized this consequence of his own theory gives an indication of the depths of his feelings about quantum theory. He wanted to destroy it. Nonetheless, Einstein nominated Heisenberg and Schrödinger for the Nobel Prize in 1928 and again in 1931. In 1931, his nomination proposal said of quantum mechanics, “I am convinced that this theory undoubtedly contains a part of the ultimate truth.” After this encounter with Bohr, Einstein’s attitude toward quantum theory seems to have changed. He apparently accepted its logical consistency but refused to believe that it was any more than “a part of the ultimate truth.” This attitude resulted in the publication in 1935 of what has become the most enduring residue of the Einstein-​Bohr debates, Einstein’s paper written with two young Princeton associates, Boris Podolsky and Nathan Rosen. (Einstein had emigrated to the United States in the summer of 1933.) The paper, which has the title “Can Quantum-​Mechanical Description of Physical Reality Be Considered Complete?” was, unlike most of Einstein’s previous papers, written in English and published in the Physical Review, the professional journal of the American Physical Society. Once again, it deals with an imaginary experiment, but like so many other works of the imagination, this one has surpassed the intentions of its creators. In the first place, it is unlikely that they thought that the experiment they were proposing, or any facsimile, would ever be carried out. This, thanks largely to the work inspired by Bell, has now happened. Indeed, our physics journals are now resplendent with new and ever more ingenious versions of the Einstein-​Podolsky-​Rosen experiment, along with increasingly accurate experimental results. In the second place, and this is also an aftermath of Bell’s work, the Einstein-​ Podolsky-​Rosen experiment has made its way into much of the popular folklore about quantum theory. (It is usually referred to in the literature, familiarly, as the EPR experiment.) This has much to do with an aspect of the experiment that was not even mentioned in the original paper, namely, its use of what Einstein would later call “spooky actions at a distance” (spukhafte Fernwirkung in the German original). This concerns influences of one part of a system on another even when the two parts are widely separated in space. I will come back to this matter shortly. The EPR experiment has to do with the kind of inferential knowledge we make use of all the time correlating some event taking place in front of us with some event at a distant place beyond our ken because we know some relationship between the objects involved. I have already mentioned Bell’s fetching example of Bertlmann’s socks. Here is another equally fetching

36  Quantum Profiles example provided by Bell. “Suppose,” he wrote, “I take from my pocket a coin and, without looking at it, split it down the middle so that the head and tail are separated. Suppose then, still without anyone looking, the two different pieces are pocketed by two different people who go on two different journeys. The first to look, finding that he has a head or tail, will know immediately what the other will subsequently find.” In the language of Einstein, Podolsky, and Rosen, the observation by the first person that he has, say, a tail confers “reality” on the head that the second observer will inevitably find. In the somewhat formalistic language of the EPR paper, the authors proposed the following definition (the italics are theirs): “If without in any way disturbing a system we can predict with certainty . . . the value of a physical quantity [the head, in the example above] then there exists an element of physical reality corresponding to this physical quantity.” According to this definition, the observation of the tail makes the head real even though it is not directly observed. Einstein, Podolsky, and Rosen went on to apply the same logic to quantum mechanics. For this purpose, they supposed that two particles have approached each other from a great distance, interacted, and then separated once again to a great distance. By an ingenious arrangement, they set things up so that if measurement of the position of one particle was done, this immediately told them the position of the other, far distant particle. This then, according to their definition, conferred “reality” on the position of the second particle. Likewise, by modifying their setup, they could measure the momentum of the first particle in such a way that this told them the momentum of the second particle. This conferred “reality” on the second particle’s momentum as well—​that is to say, both the position and the momentum of the second particle were given “reality.” But quantum mechanics tells us that no quantum-​mechanical description is possible in which both position and momentum are precisely specified. Hence, in this arrangement, it looks as if we have conferred “reality” on something that quantum mechanics cannot describe. Thus, their answer to the question in the title of their paper “Can Quantum-​Mechanical Description of Reality Be Considered Complete?” was a clear-​cut no. The EPR paper took Bohr completely by surprise. Rosenfeld recalled later that “this onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable.” They were in the middle of exploring some puzzles that had arisen in the applications of quantum theory to electromagnetism. Rosenfeld went on:

John Stewart Bell  37 A new worry could not come at a less propitious time. Yet, as soon as Bohr had heard my report of Einstein’s argument, everything else was abandoned: we had to clear up such a misunderstanding at once. We should reply by taking up the same example and showing the right way to speak about it. In great excitement, Bohr immediately started dictating to me the outline of such a reply. Very soon, however, he became hesitant: “No, this won’t do, we must try all over again we must make it quite clear. . . .” So it went on for a while, with growing wonder at the unexpected subtlety of the argument. Now and then, he would turn to me: “What can they mean? Do you understand it?” There would follow some inconclusive exegesis. Clearly, we were further from the mark than we first thought. Eventually, he broke off with the familiar remark that he must sleep on it. The next morning he at once took up the dictation again, and I  was struck by a change in the tone of the sentences:  there was no trace in them of the previous day’s sharp expressions of dissent As I pointed out to him he seemed to take a milder view of the case, he smiled. “That’s a sign,” he said, “that we are beginning to understand the problem.” And indeed, the real work now began in earnest; day after day, week after week, the whole argument was patiently scrutinized with the help of simpler and more transparent examples. Einstein’s problem was reshaped and its solution reformulated with such precision and clarity that the weakness in the critics’ reasoning became evident, and their whole argumentation, for all its false brilliance, fell to pieces. “They do it ‘smartly,’ ” Bohr commented, “but what counts is to do it right.”

The whole process took six weeks, Rosenfeld recalled, a kind of speed record for Bohr. Some indication of Bohr’s eagerness to get his message out was the fact that prior to the publication of his rebuttal of the EPR paper in the Physical Review, he sent a letter to the British journal Nature announcing his forthcoming paper and assuring people that everything was really all right. Despite Rosenfeld’s—​and implicitly Bohr’s—​characterization of the EPR paper, there is nothing really “wrong” with it in the sense of a mistake by its authors in either the physics or the mathematics, of the kind that Einstein had done when he tangled with Bohr in 1930. If one could construct an EPR apparatus, there is no reason to think that it would not do just what its inventors said it would—​namely, one could use it first to measure implicitly the exact position of a particle at a distant place. One could then modify the apparatus to

38  Quantum Profiles measure the exact momentum of the distant particle. What the EPR paper did not state clearly is that these measurements are separate and distinct, and involve different modifications of the apparatus. In no single measurement can one measure both the position and the momentum with arbitrary precision. If one uses the EPR setup to measure the position, then the momentum becomes completely uncertain, and vice versa. In one insists on using the EPR language, one can say that one measurement has conferred “reality” on the position and the other has conferred “reality” on the momentum, but no experiment can confer “reality” on both if one believes in the correctness of quantum mechanics. For Einstein, this was what was intolerable about the theory. He seemed to feel that once reality was conferred on something, this reality should be an enduring aspect of that thing, not to be removed because the experimenter had chosen to measure something different. For Bohr, on the other hand—​ and this was the burden of his response to Einstein—​all of this was just another illustration of the principle of complementarity. A particle in reality has neither a position nor a momentum. It has only the potential to manifest these complementary properties when confronted by suitable experimental apparatus. For Einstein, this was an incentive to look for a deeper theory. The EPR paper ended: “While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.” For Bohr, the matter had been settled. The deeper theory was quantum mechanics. It is clear that these views were irreconcilable. While Bohr continued to write about these matters after this exchange, the EPR article was the last, as far as I know, that Einstein ever published in a technical journal about quantum theory. But he thought about it incessantly; his correspondence with Max Born reflects that. Something of his state of mind can be seen from a letter he wrote to Born on September 7, 1944. He ended it by writing: We have become Antipodean in our scientific expectations. You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture. I firmly believe, but I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of the quantum theory does not make me believe in the fundamental dice-​game, although I am well aware that our younger

John Stewart Bell  39 colleagues interpret this as a consequence of senility. No doubt the day will come when we will see whose instinctive attitude was the correct one.

While it is unlikely that Einstein’s younger colleagues went so far as to characterize him as being “senile,” it is certainly true that few of them paid much attention to the issues raised by the EPR paper. This had largely to do with the ever-​increasing practical success of the theory. By the 1930s, Linus Pauling and others had explained chemical bonding using quantum mechanics. Around the same time, Heisenberg, Enrico Fermi, and others had shown that the theory, which had originally been invented to deal with atomic phenomena, had validity even at nuclear dimensions, which are some one hundred thousand times smaller than atoms. Dirac had made a marriage of quantum theory and relativity in the late 1920s. Its offspring was the prediction of antimatter, which was confirmed in 1932, when the American physicist Carl Anderson found positrons—​antielectrons—​in cosmic rays. It is true that there were some puzzles to clear up in the applications of quantum theory to electricity and magnetism, but the optimism of the day is well reflected in Dirac’s aphorism that even then, quantum theory explained “most of physics and all of chemistry.” That a few elderly physicists were squabbling about the foundations of the theory seemed all but irrelevant. This attitude was reflected in quantum mechanics textbooks, not only in the ones written before the war but even until fairly recently. In the early 1980s, before the impact of the work initiated by Bell had found its way into textbooks, I  made a survey of seventeen standard textbooks on quantum theory. I discovered that only one of them, David Bohm’s Quantum Theory, published in 1951, made any reference at all to the paper of Einstein, Podolsky, and Rosen. (I will have more to say about Bohm’s book shortly.) Even Dirac’s great text, Quantum Mechanics, which Einstein had called the “most logically perfect presentation” of the theory, has no mention of the paper or of any of the issues it raises. Bell told me that in the 1950s, a colleague of Dirac’s asked him why none of this was discussed in his book. Dirac answered, in his usual elliptic way, “I think it is a good book, except for the absence of several introductory chapters.” These were, presumably, the chapters in which Dirac might have discussed the foundations of the theory. He seems to have decided that these questions were too far removed from resolution and of too little relevance to application to merit inclusion in his book. Bell began reading popular books on quantum theory while he was still in high school. He began taking courses in it during his last two years at

40  Quantum Profiles Queen’s University in Belfast. This was in the late 1940s, and none of the texts discussed the more philosophical aspects of the theory. Bell remembered, with some distaste, a course he took on atomic spectra—​bread-​and-​butter quantum mechanics. “It went into what I thought at the time was a lot of unnecessary detail,” he said. “All the atoms in the periodic table. I think that atomic spectra were something of a speciality at Belfast because they were interested in the physics of the upper atmosphere. We learned a lot of stuff about the Bohr atom. That might make you wonder what was happening while the electron was jumping from one orbit to another as the atom is radiating. But still, there are rules. You learn about the periodic table of elements—​all the practical aspects of the theory. Then the puzzles start.” Bell recalled being particularly perplexed by the Heisenberg uncertainty principle. “It looked as if you could take this size and then the position is well defined, or that size and then the momentum is well defined. It sounded as if you were just free to make it what you wished. It was only slowly that I realized that it’s not a question of what you wish. It’s really a question of what apparatus has produced this situation. But for me it was a bit of a fight to get through to that. It was not very clearly set out in the books and courses that were available to me. I remember arguing with one of my professors, a Dr. Sloane, about that. I was getting very heated and accusing him, more or less, of dishonesty. He was getting heated, too, and said, ‘You’re going too far.’ But I was very engaged and angry that we couldn’t get all that clear.” I can imagine Bell at nineteen, with his red hair and his Irish temper flaring because Dr. Sloane could not explain the uncertainty principle clearly enough. It was at this time that Bell had begun thinking about the problem that would always bother him: where does the quantum world leave off and the classical world begin? In our everyday lives, we do not directly experience any of the bizarre effects described by quantum theory. Does that mean that quantum theory does not apply to us but only to our individual atoms? How many atoms does it take before we have a system that is large enough so that it becomes classical? In 1935, Schrödinger invented a paradox that shows the conundrums one can get into if one supposes that quantum mechanics applies to systems as big as ourselves or, in his case, as big as cats. He imagined a dastardly arrangement in which, as he put it, “a cat is penned up in a steel chamber, along with the following diabolical 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 one hour one of the atoms decays, but also with equal probability perhaps

John Stewart Bell  41 none; if it happens, the counter tube discharges and through a relay releases a hammer which 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 atom decay would have poisoned it.” If one insisted on using quantum mechanics to describe this entire system, then one would have to say that prior to observing the cat, by opening the steel box, it would be neither dead nor alive but in some weird quantum-​mechanical mixture of life and death, which seems like an absurdity. I asked Bell if he had, as a student, taken up reading people such as Bohr, especially about questions like these. He said that he had and went on, “I disagree with a lot of what Bohr said. But I think he said some very important things which are absolutely right and essential. One of the vital things that he always insisted on is that the apparatus [the measuring instrument] is classical. For him there was no way of changing that. There must be things we can speak of in a classical way, and for him that was the apparatus. For him it was inconceivable that you could extend the quantum formalism to include the apparatus. [If you did, you would confront all sorts of Schrödinger-​cat-​like paradoxes.] “It is very strange in Bohr that, as far as I can see, you don’t find any discussion of where the division between his classical apparatus and the quantum system occurs. [How many atoms does it take to construct a classical apparatus?] Mostly you will find that there are parables about things like a walking stick—​if you hold it closely it is part of you, and if you hold it loosely it is part of the outside world. He seems to have been extraordinarily insensitive to the fact that we have this beautiful mathematics, and we don’t know which part of the world it should be applied to. “Bohr seemed to think that he had solved this question. I could not find his solution in his writings. But there was no doubt that he was convinced that he had solved the problem and, in so doing, had not only contributed to atomic physics, but to epistemology, to philosophy, to humanity in gen­ eral. And there are astonishing passages in his writings in which he is sort of patronizing to the ancient Far Eastern philosophers, almost saying that he had solved the problems that had defeated them. It’s an extraordinary thing for me—​the character of Bohr—​absolutely puzzling. I like to speak of two Bohrs: one is a very pragmatic fellow who insists that the apparatus is classical, and the other is a very arrogant, pontificating man who makes enormous claims for what he has done.”

42  Quantum Profiles I asked Bell where he thought disciples of Bohr such as Heisenberg and Pauli stood on these questions. After a little thought, he answered, “In the beginning Heisenberg and Pauli felt very close to Bohr. Those three were the Copenhagen trio, the Three Musketeers of the Copenhagen interpretation. In later years, Pauli seems to have decided that Bohr himself was not a complete supporter of the Copenhagen interpretation. He reproached Bohr along the following lines: Bohr insisted that there was this division between the quantum-​mechanical system and the classical apparatus. He explicitly repudiated the idea that the human mind was somehow an important element in quantum mechanics—​that is, that the division was between the interior world [mind] and the outer world [matter]. But Pauli was attracted to that idea, and at the end of his life [Pauli died in 1958 at the age of fifty-​eight] he became increasingly religious. He felt that it was wrong to separate science from religion; it was wrong to separate psychology from physics. He felt that the real Copenhagen interpretation did insist that the mind was something that you could not avoid referring to in formulating quantum mechanics. Pauli thought, as far as I can judge, that the division between system and apparatus was ultimately between mind and matter. “It is perfectly obscure to me what Heisenberg thought. As I said, Bohr thought it was between big objects and little ones and seems to have been remarkably insensitive to the need to make that distinction more precise. For me, it was a big risk that I would get hung up on these questions once I learned about them. When I was not quite twenty-​one, I rather deliberately walked away from them, and toward accelerator physics. I  had the feeling then that getting involved in these questions so early might be a hole I wouldn’t get out of.” In the early 1950s, while Bell was working on accelerators, there were two important advances in the interpretation of quantum mechanics, both made by the American physicist David Bohm. Just as there were, it seems, two Bohrs, there were apparently two Bohms: a 1951 Bohm and a 1952 Bohm. The 1951 Bohm, who was then in Princeton, published the influential textbook I mentioned above, Quantum Theory. It is the only serious textbook on quantum theory that I have ever seen in which there are more words than equations. Unlike all its predecessors and most of its successors, in it, Bohm went into great detail about the interpretation of the theory. All of this was done from the orthodox Bohr point of view. He presented a novel version of the EPR experiment, one that is much easier for someone trying to learn the subject to visualize. It has become the basis of most of the modern discussion.

John Stewart Bell  43 It is this version, especially following the work of Bell, that has lent itself to actual laboratory experiments. The purpose of Bohm’s discussion of the EPR experiment was to argue, along the lines of Bohr’s refutation, that the experiment, properly interpreted, was simply another example of the principle of complementarity. Toward the end of the book, Bohm presented an extensive discussion of the “hidden variable” question. This is important for understanding Bell’s work, so I will say a few words about it here and come back to it later. When Einstein spoke of “completing” quantum theory, it was never entirely clear what he meant. It probably could not have been made completely clear unless he had succeeded in carrying out the program, whatever that turned out to be. One possibility for what he meant—​and there is support for this in his writing—​would be “hidden variables.” The paradigmatic example of the introduction of hidden variables into physics was the use of the atomic theory of matter by such nineteenth-​century physicists as James Clerk Maxwell and Ludwig Boltzmann to explain the laws of thermodynamics, such as the conservation of energy, which had been discovered earlier in the century. It would have been perfectly consistent to take these laws at their face value without searching for a deeper meaning. However, people like Maxwell and Boltzmann argued that these laws could be “explained” if one supposed that, say, a heated gas consisted of chaotically moving atoms and that heat, for example, was nothing but a manifestation of the random motion of these atoms. To us, this seems almost obvious, but in the nineteenth century, no one had ever seen an atom. One was proposing to explain observed macroscopic regularities by introducing another, apparently hidden domain of unobserved and possibly unobservable microscopic phenomena. Many physicists, even some of Planck’s caliber, resisted the atomic hypothesis as an unnecessary complication. Two of Einstein’s 1905 papers dealt with just this question. As he wrote to his friend Habicht, in the letter I quoted above, he used what he called the “molecular theory of heat” to account for the disordered motion of small particles suspended in liquids, so-​called Brownian motion. These small particles were visible, at least in a microscope, whereas the molecules were not. In this sense, the molecules represented the hidden, or uncontrollable, microscope variables that governed the destinies of the observed macroscopic particles. Could there not be something similar going on in quantum theory? Indeed, in a 1948 article, Einstein put the matter in just these terms. He wrote: “Assuming the success of efforts to accomplish a complete physical

44  Quantum Profiles description, the statistical quantum theory would, within the framework of future physics, take an approximately analogous position to the statistical mechanics within the framework of classical mechanics. I am rather firmly convinced that the development of theoretical physics will be of this type; but the path will be lengthy and difficult.” When quantum mechanics was first invented, other members of the older generation (apart from Einstein), including de Broglie and Schrödinger, had misgivings about the developing interpretation of the theory. In late 1926, as Heisenberg afterward recalled, Schrödinger paid a visit to Copenhagen. He was still trying to defend the idea that the Schrödinger waves were oscillations in actual space. Bohr was relentless. The discussion went on night and day, until finally Schrödinger, exhausted, retreated to his bed. Bohr felt that this was no reason to end the discussions and followed him into the bedroom. Heisenberg reported that “the phrase ‘But Schrödinger, you must at least admit that . . .’ could be heard again and again.” Finally, in desperation, Schrödinger said, “If we are going to stick to this damned quantum jumping, then I regret that I ever had anything to do with quantum theory.” The irrepressible George Gamow, who was in Copenhagen a few years later, drew a cartoon that showed a similar scene with the Russian physicist Lev Landau bound and gagged, with Bohr hovering over him and saying, “May I get a word in?” By the early 1930s, with the exception of Einstein and Schrödinger, most of this opposition had died down. In 1932, the remarkable Hungarian-​born mathematician John von Neumann published a book titled Mathematische Grundlagen der Quanten-​ mechanik (Mathematical Foundations of the Quantum Theory). He presented quantum theory as if it were a branch of pure mathematics, like Euclidean geometry, derivable from a set of formal axioms. It was an immensely influential book and greatly clarified the mathematical foundations of the theory. In it, von Neumann presented what purported to be a formal proof that no hidden-​variable theory could reproduce the results of quantum mechanics. On its face, this argument would seem to have ruled out any attempt along the lines that Einstein apparently had in mind. I am not aware that Einstein ever commented on von Neumann’s proof. Perhaps he did not know about it, or—​and I think this is more likely—​he had a certain mistrust when it came to mathematical proofs of things being impossible in physics. In any event, Bohm presented a version of this proof in his text and drew the conclusion,

John Stewart Bell  45 in agreement with von Neumann, that hidden-​variable theories were impossible. That was the Princeton Bohm. Bohm had come to Princeton in 1947 from Berkeley. He had been a student of Robert Oppenheimer, and after Oppenheimer moved to Princeton, Bohm followed him to the university. During the war, he had wanted to go to Los Alamos but had been turned down for security reasons. In 1949, just before his text came out, he became the subject of an investigation by the House Un-​American Activities Committee, before which he appeared in the spring of 1949. He pleaded the Fifth Amendment and was indicted for contempt of Congress. Despite the fact that he was acquitted, the president of Princeton refused to reappoint him, and he was unable to find another job in this country. However, helped by a strong letter of recommendation from Einstein, in 1951, he was offered a job at the University of São Paulo in Brazil. He had been there only a few weeks when he was summoned by the American consul, who removed his passport. He was informed that the passport would be stamped “Valid Only for Return to the United States.” The consul apparently feared that Bohm would visit the Soviet Union. Bohm’s concern was that he would become scientifically isolated in Brazil. Hence, he applied for and obtained Brazilian citizenship so that he could travel. In 1955, he left Brazil and spent two years in Israel before settling in England, where he ultimately retired from Birkbeck College of the University of London. He died in 1992. Thus, the United States had lost the services of one of the best American physicists of the postwar generation. When he was in Brazil, Bohm published two papers, one of which ended with an acknowledgment thanking Einstein for “several interesting and stimulating discussions.” In the course of these discussions, Einstein seems to have persuaded Bohm to look again at the interpretation of quantum mechanics. Murray Gell-​Mann, who saw Bohm frequently at this time, remembers Bohm crediting his conversion to discussions with Einstein. Be that as it may, the content of Bohm’s Brazil papers was just to exhibit a specific model of exactly the sort of hidden-​variable theory that the Princeton Bohm had “proven” to be impossible. Clearly, something very murky was going on. I will return to these matters shortly. Before I do so, I would like to discuss Bohm’s version of the EPR experiment, the one that is given in his textbook and is used as the basis of the modern treatments of the subject. To do this, I have to introduce the notion of “spin,” a remarkable quantum-​mechanical attribute that elementary

46  Quantum Profiles particles can have and a fascinating subject in its own right. Spin is a form of angular momentum. First, then, what is an angular momentum? When, say, a pair of stars—​ double stars—​orbit around each other, the ordinary momentum of the system is zero. But their circular motion is evident. Physicists introduced a second kind of momentum, angular momentum, to characterize this kind of motion. The angular momentum of the double stars is called “orbital” angular momentum, and it has the property that it vanishes when the orbiting object is brought to rest. The “old” quantum theory used orbital angular momentum as one of the characterizations of the different Bohr orbits of the electrons orbiting around an atomic nucleus. By 1925, it became apparent that not all the atomic spectral lines could be accounted for if the only characterization of the orbits was the orbital angular momentum. Hence the notion arose that the electron should be allotted an additional angular momentum, which became known as its spin. This angular momentum, which has no classical counterpart, persists even after, say, the electron is brought to rest. The image, which does not really do justice to the quantum-​mechanical abstraction, is of the spinning electron as a tiny top whose spinning persists even if the electron is brought to rest. The concept of spin was invented in 1925 by the young American theoretical physicist Ralph Kronig. Unfortunately for him, he was talked out of publishing it by Pauli, who at first thought that the idea was nonsense. He used to refer to it as Irrlehre (“heresy”). So it had to be independently reinvented by two equally young Dutch physicists, Samuel Goudsmit and George Uhlenbeck, also in 1925. They were at Leiden and were working under the general guidance of Einstein’s friend Paul Ehrenfest. Ehrenfest advised the young men to write up their work so that it could be shown to the great senior theoretical physicist at Leiden, Hendrik Lorentz. Uhlenbeck recalled many years later that in a few days, they got back a long manuscript, filled with equations, from Lorentz. The burden of the manuscript was also that spin was nonsense. Lorentz took the picture of the spinning electron quite literally. He thought of it as a sort of classical particle with a certain extension and argued that if it were spinning as fast as Goudsmit and Uhlenbeck claimed, its surface would be spinning faster than the speed of light, which would have violated the basic principle of the theory of relativity that nothing can move faster than light in a vacuum. A modern quantum theorist thinks of the electron, in a certain sense, as a point particle, so this objection is irrelevant.

John Stewart Bell  47 At the time, Goudsmit and Uhlenbeck were crushed. Uhlenbeck wrote: “Goudsmit and myself both felt that it might be better for the present not to publish anything; but when we said this to Ehrenfest, he answered, ‘Ich habe Ihren Brief schon längst abgesandt. Sie sind beide jung genug um sich eine Dummheit leisten zu können!’ [‘I sent your paper off long ago. You’re both young enough that you can afford a stupidity!’]” A classical angular momentum can have any value at all. Spin, however, can have only the values 0, 12 , 1, 23 , 2, 25 . . . and so on (in suitable units). A  classical angular momentum can point in any direction, and there are no limitations on the accuracy with which that direction can be measured. With spin, there are limitations, and these are given by a variation of the Heisenberg uncertainty principle. Let us take spin 12 as the simplest illustration. If we pick an axis that defines a direction and measure (I will explain how this is done shortly) the direction of the spin with respect to that axis, then we will discover that the spin can point only along the axis or in the opposite direction. In the first instance, we say that the spin is “up,” and in the second, we say that the spin is “down.” Having chosen an axis, and having made our measurement, we can then change axes and make a new set of measurements. Once again we will find that the spin points up or down with respect to the new axis. This is reminiscent of the situation with position and momentum. As we have seen, at least in the usual interpretation, a quantum-​mechanical particle has neither a position nor a momentum. It has the potential for exhibiting a position, say, when confronted by a measuring instrument designed to measure positions. In the same sense, a spin has no direction, but it has the potential for pointing up or down in a measurement designed to measure directions. Remember that Bohr warned that one could get schwindlig (dizzy) thinking about quantum mechanics. Spin may be a case in point. The fact that spin can point only in a restricted number of directions with respect to a given axis (two for spin 12 , 3 for spin 1, and so on) was called space quantization, although it is not space that is quantized but rather the directions in which the spin can point. In actual fact, space quantization was discovered experimentally before the invention of spin. In 1922, the German physicists Otto Stern and Walter Gerlach discovered space quantization in an experiment involving silver atoms. They heated silver atoms in a furnace and extracted a beam of these atoms, which they allowed to pass through a strong magnetic field. The direction of this field is what defines the spatial axis of which mentioned earlier.

48  Quantum Profiles Not knowing anything about spin, they made use of the Bohr model of the atom, which seemed to imply in this case that the angular momentum could point in one of two directions. They expected that the silver atoms, after their encounter with the magnet, would have had their trajectories bent in one of two directions. To test this, they allowed the atoms to deposit themselves on a plate of glass. They discovered that they deposited themselves into two fine lines separated by a fraction of a millimeter. Nowadays, having absorbed the lessons of quantum theory, we would say that this was a perfect demonstration that silver atoms have spin ½. The atoms could move only up or down in the magnetic field, so half of them moved up and half moved down—​hence the two fine lines. However, to most physicists at the time, this result was absolutely astounding. The late I. I. Rabi, who was entering physics at about the time of the Stern-​Gerlach experiment and who a few years later went to Germany to work with Stern, once said to me, “I thought the old quantum theory was stupid. I thought one might be able to invent another model of the atom which had the same properties. But you can’t get around the Stern-​Gerlach experiment. You are really confronted with something quite new. It goes on in space, and no clever classical mechanism would do, would explain it.” In the Bohm version of the EPR experiment, we imagine that we have at our disposal two Stern-​Gerlach-​like magnets located at different places, far enough apart that they have no contact with each other. We may imagine that near one of the magnets, we have a supply of molecules, the analog of the silver atoms in the original Stern-​Gerlach experiment. These molecules, we suppose, are composed of two atoms each, and each of these atoms has spin ½. It is possible to arrange things so that, loosely speaking, the spins of the atoms in these molecules point in opposite directions, so that the net molecular spin is 0. The resultant molecule is spinless. Now, imagine, with Bohm, that the molecules spontaneously split up—​a kind of radioactivity—​into their constituent atomic components. When any given molecule splits up, its two atoms fly off in opposite directions into the waiting Stern-​Gerlach magnets. An observer at one of the magnets records whether the atom that enters that magnet has spin up or down. If the answer is spin up, then that observer can be 100 percent certain that the observer at the other magnet would record a spin down. This reflects the correlations of the atomic spins in the original molecule. If we now use the criterion of EPR, we would say that this experiment has conferred “reality” on the direction of the spin of the second atom.

John Stewart Bell  49 Now we may imagine rotating both magnets by, say, ninety degrees and doing the experiment again. According to EPR, this will confer “reality” on a different direction of the spin. But the Heisenberg principle, in this case, tells us that no experiment can measure the components of a given spin in more than one direction. Hence, EPR would conclude that quantum mechanics does not offer a complete description of reality, while Bohr would argue that this setup is just another illustration of the principle of complementarity. In this case, the complementary aspects are the components of the spins in more than one direction. All of this is clearly spelled out in ­chapter 22 of Bohm’s book. There are at least two virtues to the Bohm version of the EPR experiment as opposed to the original. In the first place, one can begin to imagine how one might do a real EPR experiment, since measuring spins with Stern-​Gerlach-​like experimental techniques has become, over the years, common practice for experimenters. I will come back to this shortly. The second virtue is that this setup makes it graphically clear just how bizarre these distant quantum-​ mechanical correlations are. To make things as graphic as possible, let us suppose that one Stern-​ Gerlach magnet is in Princeton and the other one is on the moon, or even farther away. And again, let us suppose that there is no contact between the two observers. Let us suppose that before departing for the moon, the observers agree to set their magnets so that the field directions are at right angles to each other. Each observer makes a tape that shows whether the spin is up or down when each atom arrives at its respective magnet. Afterward, the tapes are compared event by event to see if there are any correlations between the spin measurements made at the different magnets. If the magnets are actually set at right angles, quantum mechanics predicts that there are no correlations. A spin up at one magnet is just as likely to be associated with a spin up at the other as it is likely to be associated with a spin down. But suppose that while the atoms are traveling through space, one of the observers changes his or her mind and does not rotate the magnet, so the magnets remain parallel. After the experiments are done and the tapes are examined, what the observers will now find is perfect correlation between the events. Every time a spin up is recorded by one observer, a spin down will have been recorded by the other. These correlations manifest themselves according to the rules of quantum mechanics even though there is no contact, until long after the fact, between the two observers. This is surely what Einstein had in mind when, in connection with quantum theory, he

50  Quantum Profiles spoke of spukhafte Fernwirkungen, “spooky actions at a distance.” Someone not trained in quantum theory looking at these experimental results would surely conclude that the atoms must be carrying with them some kind of program—​some kind of hidden variable—​that instructs them in some sort of causal fashion how to respond when confronted with the magnets in their various settings. Bell was often called upon to lecture on these subjects to groups of people, such as secondary-​school teachers, who had no special scientific training. To help them understand the oddness of these distant correlations, he compared them to the situation of those rare pairs of identical human twins who have grown up in separate environments with no knowledge of each other. The twins correspond to the two atoms, which are “born” in the same decay and then lose contact with each other. If one followed the behavior of one of the twins with no reference to the other, there would be no suggestion of anything in that behavior that the person was a twin. In the same way, an individual atom arriving at one of the magnets will move up or down in an apparently random way. It is only when the tapes are compared for the two atoms that the correlations emerge. Likewise, it is only when twins finally meet, if they ever do, that remarkable correlations in their behavior appear. Bell was fond of one specific example he turned up while perusing the annals of an entity called the Institute for the Study of Twins. He noted with some astonishment that the Institute had “found two people, identical twins, who had been separated as babies. There was an amazing list of coincidences between them. They both bit their nails. They both smoked the same brand of cigarette. They had both bought the same model of car. They bought it in the same color. They went to the same resort in Florida for their holidays with their families. They had married on the same day. They both had dogs, and the dogs had the same names. In my lecture I show a picture of them.” In the case of the twins, we have what we think of as a “scientific” explanation of these coincidences. These twins have identical genes. Genes, we think, are an important factor in determining behavior. Hence this pair of identical twins is a beautiful illustration of genetic determinism. According to the conventional quantum theorist, it is here that the analogy between the twins and the atoms breaks down. Such a theorist would argue that nothing “explains” the EPR correlations; they are simply a fact of life. Indeed, the theorist would say more. As Bell put it, “If this theorist was one of the more dogmatic members of the Copenhagen school, he would say, ‘It’s naive to demand an explanation. I give you the rule for the correlation and that’s enough.’ ” This

John Stewart Bell  51 is the attitude that is brilliantly defended in Bohm’s textbook. It is also the essential implication of von Neumann’s theorem. Bell first heard about the theorem when he was a university student in Belfast. “I read about it,” he told me, “in a book by Max Born called Natural Philosophy of Cause and Chance. I was very impressed that somebody—​von Neumann—​had actually proved that you couldn’t interpret quantum mechanics as some sort of statistical mechanics.” In statistical mechanics, remember, the atoms act as hidden variables whose causal behavior accounts for the laws of thermodynamics. However, as I  have mentioned, in 1952, Bohm (who was then at the University of São Paulo) published two papers in the Physical Review titled “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables”—​exactly what von Neumann had “proved” was impossible and what Bohm had echoed in his 1951 text. In the introduction to the first of these papers, Bohm explained their intent. He wrote: Most physicists have felt that objections such as those raised by Einstein [to quantum theory] are not relevant, first, because the present form of the quantum theory with its usual probability interpretation is in excellent agreement with an extremely wide range of experiments, at least in the domain of distances larger than 10–​13 centimeters, and secondly, because no consistent alternative interpretations have as yet been suggested. The purpose of this paper . . . is, however, to suggest just such an alternative interpretation. In contrast to the usual interpretation, this alternative interpretation permits us to conceive of each individual system as being in a precisely definable state, whose changes with time are determined by definite laws, analogous to (but not identical with) the classical equations of motion. Quantum mechanical probabilities are regarded (like their counterparts in classical statistical mechanics) as only a practical necessity and not as a manifestation of an inherent lack of complete determination in the properties of matter at the quantum level.

In other words, Bohm claimed to have reduced quantum mechanics to a new form of classical physics free of probabilities, indeterminism, and all the rest. (Since Bohm wrote this, the validity of quantum mechanics has been shown to extend down to much shorter distances. The length 10−13 centimeters is known as the Fermi, after Enrico Fermi. It is roughly the size of the smallest nucleus, the nucleus of hydrogen, known as the proton. The

52  Quantum Profiles interior of the proton has now been explored and is well described by the quantum mechanics of quarks.) Bell was smitten by Bohm’s papers. When he described his reaction, even after nearly forty years, he was still excited. “I couldn’t read von Neumann’s book,” he told me, “because it was only available in German, and I couldn’t read German. Then Bohm’s papers came out in 1952. I  was enormously impressed with them. I saw that von Neumann must have been just wrong. At that time, I discussed these things with a colleague of mine at Harwell, Franz Mandl. Franz was of German origin, so he told me something of what von Neumann was saying. I already felt that I saw what von Neumann’s unreasonable axiom was.” It turned out that von Neumann had made what appeared to be an innocuous technical assumption for which there was no justification. No one had paid any attention to this until Bohm produced his model. Of course, Bohm was aware that his model contradicted von Neumann’s theorem. At the end of his second paper, he discussed this. Having read this discussion several times, I think it is fair to say that it is, to put it charitably, obscure. The matter was clarified only a few years later by Bell, who isolated the specific unreasonable mathematical assumption von Neumann had made. I myself was studying quantum mechanics as a student at Harvard in 1952 when Bohm’s papers were published. I  can recall mixed—​indeed, largely negative—​reactions to them. Part of the problem was that they did not seem to contain any new physics. Bohm was perfectly aware of this. After all, the idea of his papers were to demonstrate that quantum mechanics could be reinterpreted as a deterministic theory with hidden variables. The validity of quantum mechanics was assumed. As I have mentioned, Bohm felt that quantum mechanics had been tested only down to distances as small as 10-​ 13 centimeters. He thought that quantum mechanics might break down at smaller distances and that new physics would reveal itself. Possibly, he felt, this new way of looking at quantum mechanics would play a role in this new physics. But, as I have also mentioned, we have now explored distances much smaller than this, with no sign that the theory is going to break down. One might naively have thought that Einstein, with whom Bohm had discussed these matters, would have been enthusiastic about Bohm’s new way of looking at things. Not at all. He ended a letter written to Born on May 12, 1952, with the following comment: “Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret

John Stewart Bell  53 the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I.” I was so surprised when I came across this reaction of Einstein’s to what, offhand, I would have thought was the kind of development he would have liked that I asked Bell what he thought it meant. Before replying directly, Bell said with some heat that among the books he would like to write—​“I would like to write a half a dozen books, which means I won’t write any”—​would be one tracing the history of the hidden-​variable question and especially the psychology behind people’s peculiar reactions to it. “Why were people so intolerant of de Broglie’s gropings and of Bohm?” he asked me. Without waiting for an answer, he went on, “For twenty-​five years people were saying that hidden-​variable theories were impossible. After Bohm did it, some of the same people said that now it was trivial. They did a fantastic somersault. First they convinced themselves, in all sorts of ways, that it couldn’t be done. And then it becomes ‘trivial.’ I think Einstein,” Bell went on, “thought that Bohm’s model was too glib—​too simple. I think he was looking for a much more profound rediscovery of quantum phenomena. The idea that you could just add a few variables and the whole thing [quantum mechanics] would remain unchanged apart from the interpretation, which was a kind of trivial addition to ordinary quantum mechanics, must have been a disappointment to him. I can understand that—​to see that that is all you need to do to make a hidden-​variable theory. I  am sure that Einstein, and most other people, would have liked to have seen some big principle emerging, like the principle of relativity, or the principle of the conservation of energy. In Bohm’s model one did not see anything like that.” When Bell went to Birmingham in 1953 to work with Peierls, he experienced firsthand this attitude on the part of physicists like Peierls, who had grown up with the conventional interpretation of quantum mechanics. All the students were asked to give a talk about what they had been doing. Bell gave Peierls a choice of two topics: the foundations of quantum theory or accelerators. Peierls made it quite clear that he preferred accelerators. To give an idea of how they had changed in recent years—​owing in many ways to Bell’s work—​in 1979, Peierls published a book titled Surprises in Theoretical Physics, in which he discussed some of the surprising things he had learned in a lifetime of doing theoretical physics. One of the surprises was the fact that von Neumann’s theorem had not settled the matter of the hidden variables, which, he noted, had finally been clarified by Bell.

54  Quantum Profiles When the Bells took one of their rare leaves from CERN, they tended to go to California, to the Stanford Linear Accelerator. This may account for the fact that Hawaiian shirts seem to have been one of Bell’s sartorial preferences. Like nearly everyone else at CERN, both Bells dressed very informally at work. Seeing Bell at CERN wearing a tie is a great rarity and usually signals some official function such as the visit of the Dalai Lama. In any event, in late 1963, the Bells went to Stanford, where they had been invited to spend a year. As it happened, they arrived in the United States the day after John F. Kennedy was assassinated. “It was the worst possible moment to have come,” Bell commented. Nevertheless, they were welcomed at the laboratory, where, as Bell remembered, “Mary was quickly integrated into the accelerator team at Stanford, and I into the theory group. Not long before I  came over, I  had once again begun considering the foundations of quantum mechanics, stimulated by some discussions with one of my colleagues, Josef Jauch. He, it turned out, was actually trying to strengthen von Neumann’s infamous theorem. For me, that was like a red light to a bull. So I wanted to show that Jauch was wrong. We had gotten into some quite intense discussions. I thought that I had located the unreasonable assumption in Jauch’s work. Being at Stanford isolated me, and gave me some time to think about quantum mechanics. My head was full of the argument of Jauch, and I decided that I would get all that down on paper by writing a review article on the general subject of hidden variables. [It did not appear until 1966, two years after Bell’s theorem had been published.] In the course of writing that I  became increasingly convinced that ‘locality’ was the center of the problem.” “Locality,” in the sense that physicists now use the term, is something that came into physics quite recently, although its roots go back as far as the seventeenth century—​the age of Newton. Prior to Newton, the forces that physicists dealt with were the tangible forces of pushing and pulling. The object exerting the force was in direct contact with the subject of the force. Newton introduced the force of gravitation, which acted over long distances between objects that were not in any apparent physical contact. For example, the earth, Newton claimed, acted on the moon with the force of gravitation, although the earth and the moon do no appear to have any direct physical contact with each other. It should be noted that prior to Newton, René Descartes had also introduced a theory of gravitation. In his theory, space was filled with a medium called the ether, and the forces of gravitation were transmitted through the

John Stewart Bell  55 ether in the same sort of way that water waves can transmit a force from one part of a body of water to another—​by direct physical contact. When he was young, Newton also seemed to seek an explanation of gravitation in terms of an ether, but in his later years, he took the position that the mathematical law of gravitation—​the fact that the force of gravity falls off as the inverse square of the distance between two masses—​did not need an explanation. This is the meaning I attach to his celebrated dictum that “the main Business of Natural Philosophy is to argue from Phaenomena without feigning Hypotheses.” If I may be pardoned the anachronism, I would call this the Copenhagen interpretation of gravitation. In the nineteenth century, the attention of physicists turned from gravitation to electricity and magnetism. At the end of the eighteenth century, the French physicist Charles-​Augustin de Coulomb discovered that electric charges attracted or repelled each other also by an inverse-​square law. This created the science of electrostatics. Electrodynamics, the study of how electrical phenomena can vary in time and space, was created in the middle of the nineteenth century by Maxwell. One of Maxwell’s accomplishments was to show that electricity and magnetism were related phenomena; a moving electric charge, for example, generates a magnetic field. His greatest contribution was providing the equations that relate electric and magnetic fields. He also showed that light was an electromagnetic phenomenon, a special kind of electric and magnetic field that oscillated in space and time. Maxwell and the rest of the physicists of his generation believed that these oscillations took place in a material medium—​again, the ether. The counterintuitive idea that electric and magnetic waves could propagate in empty space was not, as far as I know, considered at all. The first person in modern times to raise the question of the speed of this propagation was Galileo. In 1638, Galileo published his final scientific work, entitled Discourses and Mathematical Demonstrations concerning Two New Sciences. The discourses are in the form of dialogues among three fictitious characters called Salviati, Simplicio, and Sagredo. (Sagredo probably represents Galileo himself.) One of the dialogues concerns the speed of light. Simplicio says: “Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired, at a great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.” To this, Sagredo-​Galileo responds, “Well, Simplicio, the only thing I  am able to infer from this familiar bit of experience is that sound, in reaching our ear, travels more slowly than light; it does not inform me whether the

56  Quantum Profiles coming of light is instantaneous or whether, although extremely rapid, it still occupies time.” Sagredo proposes a method for deciding. He and an assistant will each have a lantern and will go to separate locations. Sagredo will then uncover his lantern, and when the assistant sees the flash, he will in turn uncover his own lantern. By measuring the time lapses involved, one could in principle measure the speed of light. With modern electronics, this experiment, or something like it, can be done and the speed of light measured this way. But light is much too fast—​the elapsed times are much too small—​for Galileo to have concluded in the seventeenth century anything except that the speed of light was very great. However, in 1674, the Danish astronomer Ole Roemer actually measured the speed of light using the moons of Jupiter, which are periodically eclipsed by the planet, as the distant lantern. The great distance to Jupiter makes this time lapse measurable. He found a value of 214,000 kilometers per second. This can be compared with the present value, obtained using the best modern techniques:  299,792.458 kilometers per second. Roemer was not that far off. To the nineteenth-​century physicists, the speed of light was no different from any other velocity. For example, for them, it was quite conceivable that, given suitable propulsion, one might travel at the speed of light—​or faster. This notion was completely altered after Einstein’s special theory of relativity, in one of his 1905 papers, became a generally accepted part of physics. (Incidentally, his theory of relativity was accepted much more rapidly than his ideas on quantum theory.) In the theory of relativity, the propagation of light is singled out. In the first place, the theory predicts that no material object can move faster than the speed of light. All the experiments ever done on rapidly moving particles (especially those in large accelerators, which move at speeds very close to that of light) bear this out. In the second place, the speed of light appears the same to all observers. To see how odd this is, suppose we have two observers, one at rest and the other moving in a spaceship at speeds close to that of light. Suppose the observer at rest has a flashlight, which he turns on. Both observers are then invited to measure the speed of propagation of the light emitted by the flashlight. The theory of relativity predicts that both observers will get exactly the same answer, even though the second observer is in rapid motion with respect to the first. This is possible only because space and time appear different to the two observers, and the distortions are just such as to maintain the absolute character of the speed of light.

John Stewart Bell  57 The fact that no signal can propagate faster than the speed of light—​no force and no influence—​is what physicists call locality. It means that to influence some event in the future, at some other place, there must be enough time allowed for the signal to propagate to that place. The notion of locality also gives us another view of the present instant. As I write this, I imagine the universe at exactly the same instant. I believe it exists. But I can never be quite sure. What reach me at the present instant are only signals from the past, propagating at the speed of light—​or less. The speed of light is so fast that, for most practical purposes, I ignore this delay. I act as if these past events are really present. Astronomers, on the other hand, confront the limitations imposed by locality all the time. When they say, for example, that a supernova has exploded in a distant galaxy, they speak as if that is a contemporary event What is happening now is really only that a signal from the past has arrived at our telescopes now. By “now,” that galaxy may have disappeared. If we construct a theory, quantum-​mechanical or otherwise, that is consistent with the theory of relativity, then it has this locality property built into it. Some attempts have been made to construct theories that have particles in them that always move faster than light, objects that the physicist Gerald Feinberg called tachyons. There is no evidence that any such particles exist, and there has been much discussion of whether such a theory is really compatible with relativity. In general, physicists believe that any theory that is compatible with the theory of relativity—​and hence with our experimental knowledge—​must be local. While it is true that Bohm’s theory reproduced the results of quantum theory, there was a price to pay (most physicists would even say an intolerable price): it was nonlocal. In one of our conversations, Bell once referred to it, more with remorse than anything else, I thought, as being “hideously nonlocal.” The theory involves the instantaneous transmission of what Bohm called “quantum-​mechanical forces”—​new forces characteristic of his theory. In fairness to Bohm, he never claimed that his theory described rapidly moving particles, for which the theory of relativity would be essential. His theory was quite explicitly nonrelativistic, giving it, at best, a limited domain of validity. Its nonlocality casts doubts on whether it could ever be extended to include relativity. Perhaps that was another reason Einstein did not like it. Bell put the position to me. “While Bohm had disposed of von Neumann,” he said, “his theory was nonlocal. Terrible things happened in the Bohm

58  Quantum Profiles theory. For example, the trajectories that were assigned to the elementary particles were instantaneously changed when anyone moved a magnet anywhere in the universe. I decided to find out if this was a defect of his particular picture or is somehow intrinsic to the whole situation [the situation of finding a hidden-​variable theory that could reproduce the results of quantum mechanics]. I  knew, of course, that the Einstein-​Podolsky-​Rosen setup was the critical one, because it led to distant correlations. They ended their paper by stating that if you somehow completed the quantum-​mechanical description, the nonlocality would only be apparent. The underlying theory would be local [unlike Bohm’s]. So I explicitly set out to see if in some simple Einstein-​Podolsky-​Rosen situation I could devise a little model that would complete the quantum-​mechanical picture and would leave everything local. I started playing around with the very simple system of two spin-​½ particles [the example in Bohm’s textbook], not trying to be very serious, but just to get some simple relations between input and output that might give a local account of the quantum correlations. Everything I tried didn’t work. I began to feel that it very likely couldn’t be done. Then I constructed an impossibility proof.” If one were not worried about locality, one could imagine a mechanism that would reproduce the quantum-​ mechanical correlations without “spooky actions at a distance.” One could introduce a new force that would be sensitive to the orientations of both magnets. Hence, after the electrons were “born” in the radioactive decay, this force would keep track of the orientations of the respective magnets and adjust the spins of the electrons in just such a way as to reproduce the observed correlations. This arrangement is nonlocal, because in order to keep up with the changes in orientations of the magnets, before the particles arrive at them, it must keep ahead of the particles. If one magnet is on the moon, say, and the other is close at hand, then the force must get to the moon faster then the electron that is heading in that direction, no matter how close that particle is to the moon. Thus, the force responsible for this mechanism must be transmitted instantaneously. Bell’s impossibility proof comes down to showing that this is the only kind of mechanism that can account for the correlations. No local mechanism of this type will work. We cannot have Einstein’s local realism and quantum theory. We can have only Einstein’s local realism or quantum theory. As Bell put it in his paper, “In a theory in which parameters [such as might correspond to new forces] are added to quantum mechanics to determine the results of individual measurements, without changing the statistical

John Stewart Bell  59 predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that the theory could not be Lorentz invariant [this is another way of saying that it could not be consistent with the theory of relativity].” Furthermore, Bell’s theorem is quantitative in the sense that the distinction between Einstein’s local realism and quantum theory becomes a testable proposition. The local realistic theories lead to correlations that are different from those of quantum theory. This difference is known as Bell’s inequality, and it is something experimenters could test. As Bell remarked in his paper, “It requires little imagination to envisage the measurements involved actually being made.” It is usually much easier for a theorist to “envisage” a measurement than it is for his experimental colleagues to carry it out. In the case of Bell’s inequality, it was five years before the matter was taken up by the experimenters. Part of the reason for this delay certainly had to do with the fact that at the time, studying the foundations of quantum mechanics was not a fashionable thing to do. While Bell was a very highly regarded elementary-​particle theorist, this side of his work was regarded with some indulgence—​Bell’s violon d’Ingres—​something that, as far as I could tell at the time, he accepted cheerfully. Perhaps he felt, instinctively, that the tide would turn. To compound matters, Bell published his paper in a relatively obscure journal, Physics, which did not survive much after 1964, the year his paper appeared in it. In 1964, the Physical Review, published by the American Physical Society, was the leading physics journal in the world. It would have been the natural place to publish any paper to ensure maximum exposure. The problem was that the Physical Review had, and has, page charges. At the time, even an article of only a few pages could cost the author (or, much more likely, his or her institution) a hundred dollars or so. Bell felt himself to be a guest at Stanford, and as he told me, “I was embarrassed to ask them to pay for my article.” On the other hand, Physics actually paid authors to publish in it. “I thought,” Bell said, “that I would submit my paper to Physics and that that would be a good way to avoid embarrassment. I didn’t make much money on it. It turned out that, although they paid for the article, they didn’t give you any free reprints. What they paid me was just enough to buy some reprints.” How much more quickly Bell’s paper would have been noticed if it had been published in the Physical Review is impossible to say, but it certainly

60  Quantum Profiles could not have received less notice. Bell does not remember anyone paying any attention to it at all until 1969. That year, he received a letter from a physicist name John Clauser, who was at the University of California at Berkeley. Clauser and some colleagues, it turned out, had invented a generalization of Bell’s inequality that could be tested using correlated pairs of light quanta rather than electrons—​a good thing, since precision experiments using properties of light quanta are much easier to carry out than similar experiments using electrons or other spin-​½ particles. The property of light quanta that these experiments take advantage of is called their polarization. This is the photon’s equivalent of the electron’s spin. In classical terms, when a light wave propagates, the wave oscillates at right angles to the direction of propagation. Imagine making a wave motion in a rope by agitating the rope up and down. The wave propagates along the rope, but the wave motions of the rope are up and down, perpendicular to the direction of propagation of the rope. In the experiment that Clauser was suggesting, the spin-​0 molecule radiates two light quanta, rather than two spin-​½ atoms. The polarizations of these light quanta, it turns out, are correlated according to quantum mechanics. This is just Bohm’s version of the EPR experiment again, in which light quanta and their polarizations have replaced atoms and their spins. Clauser, along with Michael Home, Abner Shimony of Boston University, and Richard Holt of the University of Western Ontario, published these ideas in 1969 in a paper titled “Proposed Experiment to Test Local Hidden-​Variable Theories.” This paper was published in the Physical Review Letters, the rapid publication journal of the American Physical Society. This journal is probably the most tightly refereed physics journal in the world. It is reserved for the rapid publication of very significant new work. The fact that this paper was accepted for the Letters was an indication of a change in attitude toward reopening what had previously been assumed to be settled questions on the foundations of quantum mechanics. In 1972, Stuart Freedman and Clauser published, again in the Letters, the result of the first precision experiment that tested Bell’s inequality. The result agreed with quantum mechanics and seemed to rule out all local hidden-​variable theories. This work began an era of the precision testing of the foundations of quantum theory that continues to the present day. One of the most frequently cited examples of this work was a series of experiments carried out in Paris by a group led by Alain Aspect. A novel feature of the Aspect experiments is that the angle between the polarization detectors is switched every hundred millionths of a second while the photons are in flight. This rules out

John Stewart Bell  61 the possibility of communication between the detectors while the polarized light quanta are moving toward them. These experiments and the ones that have succeeded them also agree with quantum mechanics. The evidence is now overwhelming that Einstein’s program to “complete” quantum theory with a local deterministic theory was misguided. Local realism simply does not work. Confronted with these results, many physicists react the way Pauli did to the earlier discussions of Einstein’s qualms about quantum theory. In 1954, in a letter to Born, he commented, “As O.  [Otto] Stern said recently, one should no more rack one’s brain about the problem of whether something one cannot know anything about exists all the same, than about the ancient question of how many angels are able to sit on the point of a needle. But it seems to me that Einstein’s questions are ultimately always of this kind.” In the present context, the results of these experiments have persuaded many physicists that the matter is settled and no longer worth discussing. However, a growing number of physicists, confronted by just how odd quantum mechanics is, have begun to wonder whether something is missing after all—​perhaps not local hidden variables but something. No one has ever expressed this feeling better than Richard Feynman. In 1982, he said in an interview, “We always have had a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I’m an old enough man that I haven’t got to the point that this stuff is obvious to me. Okay, I still get nervous with it . . . you know how it always is, every new idea, it takes a generation or two until it becomes obvious that there’s no real problem. It has not yet become obvious to me that there’s no real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.” One of the more puzzling things about all of this, at least to physicists, and not least to Bell, is how rapidly these very abstruse ideas, however garbled, have entered into general popular culture. An astonishing number of people who have no apparent interest in science in general seem to have heard of the EPR experiment and Bell’s theorem. It is difficult to figure out how exactly this happened, but certainly books such as Zukav’s The Dancing Wu Li Masters from 1979 (after the first round of experiments involving Bell’s theorem had been carried out) played an important role. The last part of Zukav’s book centered around Bell’s theorem. At one point, Zukav even noted that “some physicists are convinced that it is the most important single work, perhaps in the history of physics.” When I tried this sentence out on Bell, he replied,

62  Quantum Profiles his lilting Irish accent sounding even more musical than usual, that Zukav’s book was “too breathless. It gives the wrong impression of what is happening in physics institutes. People are not all desperately discussing Buddhism and Bell’s theorem and the like. A precious few are doing that, whereas his book gives the impression that that’s what we’re doing all the time. On the other hand, it is a book in which some of the biggest questions that physicists discuss were brought before the public. I don’t resent its success.” What seems to have excited Zukav, and others, is a train of reasoning that runs as follows: EPR correlations, acting over great distances, require an explanation. Bell’s theorem and the resulting experiments show that no explanation is possible with local physics. Therefore, relativity or not, there must exist nonlocal physics. In short, there must be “superluminal” phenomena—​ that is, phenomena that propagate at speeds greater than that of light. The lure of superluminal phenomena for the minds of the susceptible is difficult to exaggerate. It has become the late twentieth century’s equivalent of the elusive perpetual-​motion machine. Something of the genre is exemplified by a letter quoted in an article by Cornell physicist David Mermin, who has written a number of particularly lucid semipopular articles explaining Bell’s theorem to both the general public and his colleagues. Mermin reported that the following communication was sent from the executive director of a California think tank to the undersecretary of defense for research and engineering: If in fact we can control the faster-​than-​light nonlocal effect, it would be possible . . . to make an untappable and unjammable command-​control-​ communication system at very high bit rates for use in the submarine fleet. The important point is that since there is no ordinary electromagnetic signal linking the encoder with the decoder in such a hypothetical system, there is nothing for the enemy to tap or jam. The enemy would have to have actual possession of the “black box” decoder to intercept the message, whose reliability would not depend on separation from the encoder nor on ocean or weather conditions.

It is not without irony that the only actual military work that Einstein did during either world war was a brief stint during World War II working for the US Navy on submarine detection. Bell felt a sense of responsibility about the impact his work made on nonscientists. He was very concerned that such people did not get the

John Stewart Bell  63 impression that quantum mechanics has implications in areas such as holistic medicine or telepathy, where there is no evidence that it does. For this reason, he took time, something that not every physicist would do, to answer questions from laypersons about such matters. While I was at CERN, he showed me a published exchange of letters that he had with University of Pittsburgh biologist R. A. McConnell, a proponent of parapsychology. In response to an inquiry, Bell wrote: As I understand your letter, you would like me to express an opinion on the relevance or irrelevance of quantum nonlocality for parapsychology. Of course it is easy to see why people have felt there might be some connection. What has been brought out in the theoretical and experimental study of quantum nonlocality is that nature is much more curiously connected up than could have been envisaged by classical physicists, and even more so than was realized by many quantum physicists. But it must be stressed that what has been brought out here is just a feature of orthodox quantum mechanics—​which fully predicts the classically inexplicable correlations which experimenters have found. Now while orthodox quantum theory is less well formulated theoretically than I would like, it is rather unambiguous in practice. And it implies rather clearly that these queer correlations do not enable us to act at a distance, for example signal faster than light. So it seems to me that, strange as quantum mechanics is, and strange as psychokinesis is, the first does not help to explain the second. Such phenomena would require, I think, the revision of quantum mechanics as well as classical physical theories.

Bell ended his letter to McConnell on a conciliatory note: But I  remember how as a student in Ireland I  was required to attempt experiments in electrostatics—​and formed the opinion that electrostatics could never have been convincingly discovered in my home country—​ because of the damp. It may be that parapsychological phenomena are erratic only because of some factor analogous to damp which remains to be identified and controlled. However that may be, I would not think it sensible to ignore evidence simply on the ground that the phenomena in question would not be explicable, as far as I could see, in the context of contemporary physics and physiology. I am inclined to think that even physics is in its infancy, and that entirely new things will be found, if there is time.

64  Quantum Profiles Bell also occupied himself, on occasion, with exploring the connection (if any) between quantum theory and Eastern religions, something discussed, for example, in Zukav’s book. Many of the founders of quantum theory, such as Bohr, Pauli, and Schrödinger, had deep interests in Eastern religion. Schrödinger, in fact, wrote a brief book titled My View of the World, in which he described his rather mystical Eastern beliefs. However, he took great pains in the preface to point out that those beliefs had nothing to do with quantum theory. He said: “I do not think that these things [quantum mechanics and the rest of modern physics] have as much connection as it is currently supposed with a philosophical view of the world.” Bell had the chance to discuss these connections, whatever they are, with two of the most prominent contemporary representatives of Eastern religions, the Dalai Lama and the Maharishi Mahesh Yogi, although in the case of the latter, discuss may not be quite the appropriate word. On August 30, 1983, the Dalai Lama visited CERN. As Bell explained, “CERN is now one of the monuments of Europe, so from time to time, important people come to pay their respects, and if they’re important enough, they are received in state. And the Dalai Lama was one of those.” In his book Seven Years in Tibet, Heinrich Harrer, who was the Dalai Lama’s tutor when the latter was fourteen, observed that as a boy, the Dalai Lama was fascinated with the workings of technological devices, such as movie projectors. He learned, for example, with no instruction from Harrer, to take apart and reassemble the one Harrer found for him in Lhasa. After his visit, the CERN Courier, the laboratory’s house journal, ran a delightful photograph of the Dalai Lama seated at the controls of one of the huge CERN particle detectors with an impish smile on his face. I asked Bell whether, in that vein, he thought that the Dalai Lama might have been aware of some of the connections people had been making recently between quantum physics and Buddhism. “I think that might have been an element in it,” Bell answered. “When he came there was in his party an Englishman named David Skitt. He clearly knew about these things and was interested in them. He is some kind of a curator of a Tibetan-​Buddhist monastery near Vevey, on Lake Geneva. That brings him to this area several times a year. I wonder, now that I think of it, if he was the one who originated the idea of the visit. In any event, the Dalai Lama came to see what was here and to learn a bit about the work. And then there was this lunch. All the important people of CERN were there to meet him. Because of this idea

John Stewart Bell  65 that maybe quantum mechanics and Buddhism have some connection, I was asked to join the party.” Bell went on to describe this extraordinary encounter. “There were thirteen or fourteen Buddhists [robed] on one side of the table and thirteen or fourteen CERN people [in business suits] on the other side of the table, and we chatted. A somewhat formal chat, in that the Dalai Lama did not admit that he spoke English on this occasion. I suspect that was in order that he would have time to think about everything. Such a man must be careful of what he says. I have heard him on television speaking English fluently, but on this occasion he insisted on doing everything through an interpreter, both listening and speaking. He raised some very interesting questions in that they came from such a different angle—​so they are odd questions. For example, he said that he could not believe in point elementary particles, because he did not see how if you put together a lot of points you could ever make an extended object. It didn’t seem to have occurred to him that there could be spaces in between the points. Curious things like that,” Bell shook his head and went on, “He was also very interested in the Big Bang theory, according to which the world had a start and probably will have an end. This appears to be somewhat contrary to Buddhist scripture, which emphasizes eternal recurrence; things happen again and again. I pressed him on that. Of course, I insisted that the Big Bang was a fashion in science that could change. But if science did become committed to a one-​time universe, how could that be reconciled with Buddhist scriptures? He listened through his interpreter and replied, ‘Well, it is perhaps not part of the Buddhism to which we are completely committed. We would have to study our scriptures very carefully, and, usually, there is some room for maneuver.’ ‘Some room for maneuver’ was the phrase the translator used. I liked that very much. “Another thing I  brought into the conversation was the question of whether Buddhism and science really go together historically. If you read the books of Joseph Needham on science and civilization in China, you find that Needham tends to insist that Buddhism is hostile to science, and that science had a hard time taking hold in countries that were dominated by Buddhism. I have the impression that that is true. Buddhism is an inward-​looking religion, concerned with personal salvation. Once you decide that that is the really important question, then questions of how stones accelerate as they fall, and so on, are ones to which you are not going to give much attention. I  brought this up. To my surprise, most of the Buddhists had apparently not heard of Needham. It was a difference of perspective. For me, he is the

66  Quantum Profiles great bridge between Eastern and Western science. And they did not know about this great work of scholarship. But the Englishman, David Skitt, knew about it. He maintained that Needham was consistently wrong in his view of Buddhism. Skitt and I got together afterwards, and we have become great friends. I see him whenever he comes to Switzerland. We carry on this discussion, but we don’t force it to a conclusion. I don’t know whether he would still insist that there is nothing in what Needham says, because it seems clear to me that there is.” I asked Bell if he and the Tibetans discussed the putative connections between Buddhism and quantum theory. “We didn’t discuss that too much,” Bell answered regretfully. “I had the impression that they were not all that interested. They were very hazy about any kind of physics and especially about modern quantum mechanics. I think, for them, these analogies are just not very important. Physics is a subject which changes rapidly and is concerned with a very limited set of phenomena in the world. I think it would be a bit absurd to try to find the support for some big philosophy, or religion, in anything so ephemeral and specialized as that. I doubt that they have analyzed it to that degree. I think that they have just not paid attention to physics very much. They don’t feel they need any support for their system. They are not looking around, grasping for straws. They are quite self-​confident in their tradition. I don’t think they were particularly interested in seeing me. On the other hand, I was particularly interested in seeing them, because I wanted to know what Buddhists think about these things. And especially people who have grown up in Buddhism, rather than people from the West who are going around, looking for a solution, and have decided to try this one.” “It must have been an amazing occasion,” I  said to Bell, wishing I  had been there. “It was,” he answered. “The only parallel in my experience was the time I met the Maharishi. He has an international university, and they sponsored a little symposium in a place called Vegas, near Lake Lucerne. The symposium was on physics, and the implications of physics for religion, and so forth. I was invited, among other people. “The Maharishi was a much more regal figure than the Dalai Lama. He sat on a sort of white throne, in his white robes, surrounded by about thirty acolytes, mostly ladies, also in white robes—​ forming a kind of audience—​looking very sweet, but saying nothing. In the middle of the gathering—​which for a scientist is quite an uncomfortable atmosphere of adulation—​were the handful of people who had been invited to discuss

John Stewart Bell  67 these problems. We all made little speeches, and so I made a little speech. My speech was, of course, very skeptical in character. He had, at that time, as head of his physics department a man called Larry Domash. Domash was trying to see some analogy between the state of lowest energy of a superconductor and the state that people reach in meditation. I expressed great skepticism about that also. Domash would occasionally ask the Maharishi for his view—​invited pronouncements. There was no discussion. For me he was just a figure on the throne making pronouncements. “I was shocked to learn in the course of that, that he thought he could make rain. ‘The sky is blue,’ he said. ‘There is no cloud anywhere. Then you relax, and a little cloud appears. It grows and grows, and soon there is rain.’ “I liked the Maharishi setup,” Bell concluded, “because it was vegetarian. The meals were very good.” While many physicists take comfort from the fact that the experiments have vindicated quantum mechanics and ruled out Einstein’s local reality, Bell did not. For him, it only deepened the mystery. As he explained it to me, “The discomfort that I feel is associated with the fact that the observed perfect quantum correlations seem to demand something like the ‘genetic’ hypothesis [identical twins, carrying with them identical genes]. For me, it is so reasonable to assume that the photons in those experiments carry with them programs, which have been correlated in advance, telling them how to behave. This is so rational that I think that when Einstein saw that, and the others refused to see it, he was the rational man. The other people, although history has justified them, were burying their heads in the sand. I feel that Einstein’s intellectual superiority over Bohr, in this instance, was enormous; a vast gulf between the man who saw clearly what was needed, and the obscurantist. So for me, it is a pity that Einstein’s idea doesn’t work. The reasonable thing just doesn’t work.” For Bell, the problem remained just what it was when he first began learning about quantum theory in Belfast some forty years earlier. Where does the quantum world stop and our world begin? “What worried me then,” Bell reminisced, “was how to get rid of that division. I was looking for some reformulation of the theory that would permit its elimination. It was clear to me then that the hidden-​variable approach would be one such formulation. If you gave definite properties—​hidden variables—​to the elementary quantum particles, you don’t have to be concerned that the classical apparatus has definite properties. Everything has definite properties. It is just that they are more under our control for big things than for little things. It was

68  Quantum Profiles clear to me that that was one line of possible development. I am not really looking for revisions in the standard quantum-​mechanical calculations. I think that when we have solved the problem of the interface between the classical and the quantum-​mechanical worlds, there will be something different in the theory. On the other hand, I am not like many people I meet at conferences on the foundations of quantum mechanics. There are many people there who have not really studied the orthodox theory. They have devoted their lives to criticizing it, and to thinking of revisions of it. I think that that means that they haven’t really appreciated the strengths of the ordinary theory. I have a very healthy respect for it. I am enormously impressed by it. So I’m not thinking it will be swept away. But I am thinking that, nevertheless, some aspects of it may be changed.” Bell got up from his chair and walked around a bit. Then he said, “Doing quantum mechanics may be something like riding a bicycle. I am not sure that there is anybody who knows how to ride a bicycle. From time to time I come upon quite complicated papers on the stability of a bicycle. When you read them, you find that the situations they treat are highly simplified—​ like having no rider on the bicycle. Nonetheless, bicycles are rideable. I suspect that the complicated interactions that you have in bicycle riding between man, machine, and mind are maybe a bit like what we do when we do quantum mechanics. We don’t quite know what we are doing, yet we can do it. We get on, and after a time we find that we can stay up, and write papers, and so on. Part of the reason is that we tackle suitable situations where the division between the quantum and classical worlds is clear. We select our problems so that the division is plain. No one would be so crazy as to regard one atom, in a hydrogen molecule, as a classical apparatus, observing the atom. The division between the quantum system and the classical apparatus has to be placed with good taste.” When he finished his pacing, Bell sat down and said, “Perhaps I did something to rekindle interest in these questions. People who are younger than me now tend to agree that there are problems to be solved. Of course, most of them don’t tackle these problems. They’d rather work on lines in elementary-​ particle physics like string theory. But they are generally more open to the idea that there are problems with the foundations of the quantum theory than their teachers were.” On a bright, sunny early-​winter morning, Bell and I  decided to take some time off from discussing quantum mechanics and go visit the huge electron-​positron collider known simply by the acronym LEP, for Large

John Stewart Bell  69 Electron-​Positron Collider. Mary Bell wanted to come along as well. She had been involved in designing one of the components of the machine, the so-​ called electron-​positron accumulator—​a little ring in which the electrons and positrons are accumulated and stored before they are swept by electromagnetic fields into the big machine. She had not yet seen the whole machine, which was then nearing completion. So Mary drove out from Geneva to meet us. As it happened, another old CERN friend of mine, an Italian physicist named Emilio Picasso, was the director of the LEP. When I called to ask if we could have his permission to visit the machine, he said he would be delighted but was too busy to show us around himself. He would arrange, however, for the senior administrator of the project, Manfred Buhler-​Broglin, to be our guide. We all agreed that we would meet at ten in the morning in front of the CERN cafeteria. A little before ten, Bell and I went down to the cafeteria for an espresso, and a little later Mary joined us. Both Bells were wearing whitish ski parkas and slacks, and John had on what looked like an Icelandic fisherman’s sweater with brown snowflake designs. I had not seen Mary since her retirement. After we greeted each other, I remarked that I had heard from John that she would not look at any more mathematics. “He is exaggerating,” she said with a hearty laugh. He looked relieved. After a few minutes, Picasso and Buhler-​Broglin appeared. Picasso introduced me to Buhler-​Broglin, who had a serene round face and was the only man wearing a tie. One of his most important jobs, I later found out, was community relations. The construction, which had gone on for several years, had been quite disruptive to the lives of the small French communities near which the twenty-​seven-​kilometer LEP tunnel ran. Buhler-​Broglin had attended all sorts of community meetings to try to ease the relations between the laboratory and these communities and to make sure that the completed machine left as little impact as possible on the environment. The ring through which the electrons and positrons ran was buried deep underground—​in places some five hundred feet—​so there was no significant problem with radioactivity. Our intention was to visit a couple of the sites where access to the buried tunnel was possible. Winding through the entire twenty-​seven-​kilometer tunnel was the metal evacuated pipe, within which the electrons and positrons would run in opposite directions. The pipe had a complicated, roughly elliptical shape, with dimensions of something like six by two inches.

70  Quantum Profiles The beams of electrons and positrons within it had dimensions roughly the size of one’s thumb. Shafts had been sunk into the ground at a few locations so that people (technicians, experimenters, visitors like us) could go down into the tunnel. As it happened, these locations were in France, several miles from the main CERN laboratory, so Buhler-​Broglin went to get a CERN staff car to take us over the border. When he came back, we bundled ourselves into the small car and headed for the customs checkpoint, which was just outside the entrance to CERN. I had forgotten to get a French visa, which was then necessary, but fortunately, the lab was able to provide special temporary visas for visitors to the LEP. The electrons and positrons, crossing the border several times on each circuit around the tunnel, had no such problem. After driving for some time in the delightful French countryside, we left the main road and stopped at something that looked, at first sight, as if it might have been the surface operation of a mining company. This impression was reinforced when Buhler-​Broglin produced three yellow plastic mining helmets for us to wear. Mary Bell got her abundant curls under her helmet, while John Bell’s red beard protruded from his, giving him a slightly nautical look. Buhler-​Broglin had an official-​looking blue helmet. We were then taken to an elevator. It descended five hundred feet into the earth. My only comparable experience was when, a couple of years earlier, I had visited what is known as the IMB (for Irvine, Michigan, and Brookhaven) detector at the Fairport mine in Painesville, Ohio. It was located two thousand feet down a working salt mine owned by the Morton Salt Company. It was this detector, a tank of ultrapurified water, that detected the neutrinos that came from the supernova explosion of February 1987. In the case of the LEP, the detectors were huge electronic scanning devices, the size of a three-​story house, which could be wheeled in and out of the beam on railway tracks. Using detectors like this and a lower-​energy proton-​ antiproton collider, the experimenters at CERN in 1982–​1983 made one of the most important discoveries in contemporary elementary-​particle physics: they found the carriers of the weak force that is responsible for radioactivity. Unlike the light quantum, which carries the electromagnetic force and is massless, these quanta are very heavy on the scale of elementary particles, the electrically neutral specimens weighing something like ninety times the mass of the proton—​as much as a sizable atomic nucleus. To find these carriers, the CERN experimental teams, which had typically a hundred

John Stewart Bell  71 and fifty or so people in them, had to scan a billion collisions in a thirty-​ day period in order to find five—​just five—​usable events. When the LEP was fully implemented with its complement of superconducting magnets, it produced a thousand of these events an hour. This opened up a whole new era of high-​energy experimental physics. We reached the bottom of the elevator shaft. Several groups of neatly dressed scientists and engineers were going about their jobs, speaking the many languages of the people who make up the CERN community—​French, German, Spanish, Italian, the Scandinavian languages, Russian, English, Chinese, and Japanese. The whole thing, even the languages, gave me a great sense of order. I could see the LEP tunnel. It was so long that when one looked down it, one did not have any sense that it was curving. So much human effort spent to uncover—​to reveal to us—​this beautiful, austere quantum world. Somewhere that world stops, and ours begins. But where? My visit to the LEP with John and Mary Bell took place in January 1989. The machine was officially scheduled to be turned on on Bastille Day the following summer. Bastille Day had been chosen as a gesture to the French, who had donated much of the land. As it turned out, because of objections by Margaret Thatcher (Britain had contributed a share of the money), the official opening took place a little later. The machine worked perfectly and continues to do so for over a decade. The experimental groups, whose building-​sized detectors we had visited, began taking data soon afterward and by the late summer announced results on the mass and “width” of the Z0. The fact that the Z0 has a width is something one can trace back to the Heisenberg uncertainty principle that connects energy and time. The Z0 is an unstable particle with a lifetime of less than 10​−24 seconds. Since the accuracy of an experiment in which energy is measured is limited by the Heisenberg relation ΔE Δτ ≈ ħ (where ħ is Planck’s constant), this means that an unstable particle can never have a precisely determined rest energy or mass. In the present instance, each production of a Z0 in an electron-​positron collision produces a Z0 with a slightly different mass. The spread of these masses is what is known as the width of the Z0. This width can be calculated from quantum mechanics if one knows the decay mechanisms. The Z0 has several possible decay modes. About 10 percent of the time, it decays into particles such as electron-​positron pairs of neutrinos, and the rest of the time, it decays into quarks.

72  Quantum Profiles The experimenters chose a convenient decay mode in order to measure the width. Quantum mechanics tells us that any mode will manifest the same width as any other. The particle has a single, unique lifetime. By comparing the observed width with the theory, one can learn about decay modes that cannot be directly measured. For example, it is not possible in these experiments to directly measure the decay of a Z0 into, say, a pair of neutrinos (these interact so weakly that they simply escape from the detector). But one can tell that the Z0 does decay into neutrinos, because if one leaves out neutrino decays in the theoretical calculations, the predicted width is too small. It disagrees with the experimental result. Moreover, one can also learn how many different types of neutrinos the Z0 decays into, because the number of types determines the width. The CERN groups found that the Z0 can decay into only three types or “families” of neutrinos. This was both a very mysterious and a very satisfying result. It was satisfying because the cosmologists have been telling us for some time that the amount of helium produced in the early universe is also determined by the number of neutrino families. The cosmodynamics of the early universe is related to the energy density in the early universe, and this in turn is related to the number of neutrinos that were present. These same cosmologists have been insisting that having more than three families would have produced an uncomfortably large amount of early-​universe helium. Thus, the fact that the terrestrial accelerator experiments also limit the number of families to three is very satisfying. But it is also very mysterious. Why precisely three families, and not four, or seven? No one has a good explanation. Perhaps the explanation will take us into the interweavings of quantum mechanics and cosmology.

Epilogue On my visit in 1989 to CERN, I had two missions, one overt and one covert. The overt mission was to work on a physics problem I had been working on for some time with limited success. I thought that being free of academic responsibilities and with some new people to talk to, I  might make some progress. The covert reason requires some explanation. Beginning in the early 1960s, I had been writing scientific profiles for the New Yorker magazine. The first one was about the Chinese-​American Nobel Prize winners T. D. Lee and C. N. Yang. Then I had written about Marvin

John Stewart Bell  73 Minsky, one of the creators of artificial intelligence, the physicists Hans Bethe and I. I. Rabi, the science fiction writer Arthur C. Clarke, and finally Einstein. Now I had the idea of writing a profile of Bell. Bell was not then widely known among nonscientists. Now that has totally changed, and any philosopher of science you happen to meet in the street will give his or her view of the Bell inequalities. My goal was to explain all of this to the readers of the New Yorker. I therefore began my series of interviews with Bell in his office. I tape-​recorded them. Eventually, I turned these tapes over to CERN. I then returned to New York to write my profile. What happened next requires a bit of New Yorker history to understand. When I joined the magazine, it was being edited by the legendary William Shawn. Unusually, I later learned, he had chosen to edit my Lee and Yang profile himself. I cherish a set of forty questions and suggestions he wrote for me. Here is question 18: Now, here we have the crucial meeting of Lee and Yang, in 1946, so it may be the time for me to bring up the suggestion that somewhere along the line—​before you come to the meeting—​something more (and I don’t mean a great deal) should be woven in on the two men’s backgrounds; their parents, their brothers and sisters (if any). Their childhoods, their education. Perhaps held down to a minimum but still enough to touch on the essentials. Also, at this point you might, I’d suggest, take a little time out to describe the two young men: again, just a minimum on their physical appearance and personal characteristics. Not going any further than you feel you can go without detracting from their dignity or the dignity of the piece.

I think that my profile reflects these suggestions. When I joined the New Yorker and for nearly twenty years after that, it was a semiprivate company. I had to get permission to buy a few shares. But that all changed. The magazine was acquired by Advance Publications, the media company owned by Samuel Newhouse, in 1985 for $200 million when it was earning less than $6 million a year. Newhouse realized that the problem was in the demographics. The New Yorker readers were very loyal, but they were aging. To liven up the magazine, he fired Shawn and brought over the book editor Robert Gottlieb. Gottlieb introduced photography and had articles about celebrities. It was to Gottlieb that I handed in my profile, and he turned it down. His comment about the Bells was “Who are these people?” I realized that nothing I could do to change it would work, so I published it in a

74  Quantum Profiles collection called Quantum Profiles (the first edition of this book), which first appeared in 1991. By this time, my profile was already out of date. In 1990, I had raised enough money to invite John Bell and his wife, Mary, to come to New York to give a lecture on the first of October. The audience had already begun to gather when I received a phone call from Mary that John had just died of a cerebral hemorrhage. I found this almost impossible to believe. He seemed like the kind of person who was destined for a very long life. He was trim and fit. He cross-​country skied and rode a bicycle. He had a very happy marriage. He had been a vegetarian since the age of sixteen. If you wanted to have lunch with John at CERN, you would have to go to the cafeteria at about a quarter to twelve, when Mary would arrive with the daily harvest of fresh vegetables. Later she told me that John had been having some headaches, but knowing him, he probably took a few aspirin. My profile was written before he died, and none of this was in it. There were also things that are now out of date, so in this new version, I have brought them up to date. One thing that is out of date is the recognition by the scientific community at large of his work on the foundations of quantum theory. I learned after his death that he had been short-​listed for a Nobel Prize.

2 John Wheeler

John Wheeler. Photograph by Allison H. Speckman, courtesy of AIP Emilio Segrè Visual Archives, Wheeler Collection.

In the fall of 1983, I audited one of the most remarkable and idiosyncratic physics courses I have ever encountered. It was called Foundation Problems of Physics and was open to graduate students only, so a solid background in advanced physics was assumed. It was taught by John Archibald Wheeler, then (like me) an I. I. Rabi Visiting Professor at Columbia University. (At the time, Rabi was still alive, and Wheeler and I were able to tell him how much we enjoyed occupying his “chair.”)

76  Quantum Profiles Wheeler was then seventy-​two but extremely active. He was the full-​time director of the Center for Theoretical Physics at the University of Texas at Austin. That semester, he commuted back and forth between New  York City and Austin, with numerous stops elsewhere to fulfill various lecture commitments—​Wheeler was a very popular lecturer. When I  asked him about his almost incredible energy, he attributed it partly to the fact that he managed to swim a quarter of a mile a day in a small enclosed pool by his house in Austin. A few years after he gave the course, I had several lengthy conversations with Wheeler about his life and work, and I took the opportunity to ask him how the course had come about. He told me that the title had been invented by Gerald Feinberg, then chairman of the Columbia physics department, who had invited Wheeler to visit the university. The only trouble was that Feinberg neglected to explain what the course was to be about. So, Wheeler explained, when it began, he had no clear idea of how to go about teaching it. However, halfway through the first hour, Wheeler recalled, “I got this idea.” He asked each of the twenty-​odd students to turn in, after each lecture, a single summary sentence that he or she felt best summarized the lecture, along with what Wheeler characterized as a single “pregnant” question. Wheeler would study these papers carefully and in the next class would hand out neatly handwritten mimeographed notes with the class’s contributions and his own responses. The class became a little like the “surprise” version of the game Twenty Questions, in which the participants have no preset object in mind, but rather the object is created by the questions as the game proceeds—​an image, incidentally, Wheeler sometimes uses in characterizing the quantum theory of measurement. Many of the questions had to do with relativity and cosmology, subjects closely identified with Wheeler’s work. Typical were questions like “Why did the Big Bang occur?”—​to which Wheeler responded, “Physicists’ standard way to avoid misunderstanding of the word why:  translate to ‘How did it come about that there was a Big Bang?’ ” To which Wheeler added, “A wonderful question, worthy of thought every day.” Some of the questions had a philosophical bent, which did not seem to faze Wheeler. For example, one student asked, “Where is the barrier between solipsism and objective reality in a physical theory?” Wheeler responded to this in the slightly skewed way that sometimes characterized his discourse: “The Los Angeles girl locked from babyhood to age thirteen (when the neighbors found out and called the police) in an attic room, given food but never

John Wheeler  77 spoken to, had by that time lost the power not merely to speak, but even to think. There is not a word we utter, a concept we use, an idea we form, that does not directly or indirectly depend on the larger community for its existence. ‘Meaning’—​and what else is ‘objective reality’ if it is not meaning?—​is the joint property of those who communicate.” A few of the questions were beyond Wheeler. One student asked, “Does the similarity between different equations of physics mean the consistency of the physicist’s picture of the world (which is exciting to us) or merely the heredity of physical ideas (which is less exciting)?” To this, Wheeler responded, “I am too stupid to know how to analyze this question.” To me, the most interesting questions concerned the interpretation of quantum theory. These students were just confronting the theory afresh. Like most gifted students, they found the mathematics straightforward. It is not the mathematics that is the problem (something that is difficult to communicate to the layperson for whom anything involving mathematics is, almost by definition, difficult); it is what the mathematics is supposed to mean—​the sort of thing that so much bothered John Bell when he was a student. In the questions these students asked, one saw all the difficulties in understanding quantum theory, and in Wheeler’s answers, one saw all the difficulties in responding to these questions. Here are a few samples quoted at some length. The first question had to do with what is meant when one claims in quantum mechanics that one knows—​can predict in advance—​the “state” of, say, an atomic electron. In responding, Wheeler attempted to clarify for the student what is meant by the “state of an electron” and what is meant by its determinability. He wrote, “Ψ7(x), the wave function of an electron in, say, the seventh quantum state, we can know perfectly from our calculations based on Schrödinger’s equation, and in a common and generally accepted way of speaking, this means that we know the ‘state’ of the electron.” In other words, the solutions to the Schrödinger equation—​the wave functions—​are just as causally deterministic as the orbits of classical mechanics. But these wave functions describe only the probable outcomes of experiments to be performed. As Wheeler went on to explain, “What we do not know and ordinarily cannot know [in quantum mechanics] is ‘the value’ of a dynamical variable [such as position or momentum] until (1) we or, better, our apparatus decides which of one or another complementary variables to measure, and (2) ‘nature,’ in the shape of an ‘irreversible act of amplification,’ gives us an answer. Only then do we know the position of the electron or through which slit the photon came, etc. But the use of [the term] ‘state’ to describe that

78  Quantum Profiles information, while understandable among friends who make allowances for slurring of terminology, is truly dangerous in the larger world, where people have such a tendency, an understandable tendency, to misunderstand!” In this answer, Wheeler made use of a phrase taken from his teacher Niels Bohr, a phrase that he was to repeat often during the course—​namely, Bohr’s dictum that “no quantum phenomenon is a phenomenon until it has been registered by an irreversible act of amplification.” Sometimes Wheeler illustrated this with three baseball umpires discussing their craft. No. 1: “I calls ’em like I see ’em.” No. 2: “I calls ’em the way they are.” No. 3: “They ain’t nothin’ till I calls ’em.” In a homey way, No. 2 (Einstein) and No. 3 (Bohr) are a perfect summary of the issue in that great debate. It was interesting to me that the students did not find Bohr’s formulation entirely satisfying. Many of them wanted to know what words like “amplification” and “irreversible” really meant. One student asked, “What exactly is the meaning of ‘registered’? ‘Irreversible act of amplification’? ‘Indelible’? And why does quantum mechanics need such a classical process, whereas classical theory is only a limiting case of quantum theory?” Wheeler’s answer—​which was, in its entirety, “Bohr: To be able to tell one another what we found”—​would have driven the young Bell, or even the older Bell, to distraction. To a second student, who asked, “What is the definition of ‘registered’? How without it can one properly define elementary quantum phenomena?” Wheeler responded that it meant “Brought to a close ‘by an irreversible act of amplification’ (blackening of a grain of photographic emulsion, click of Geiger counter, etc.), which was Bohr’s version. That it is ‘open-​ended’ is an inspiring indication that there’s something great yet to be learned!”—​a sentiment that would certainly be endorsed by Bell. As this course and my subsequent conversations with Wheeler made clear, he thrived on students. As he once remarked to me, “I am one of those retarded learners . . . one of those people who can’t learn except by teaching.” He has an unusual lecture style. It features diagrams that appear to grow organically as the lecture proceeds. One has the feeling that they will continue to evolve on their own after everyone has left the room. They are at once enormously dense and yet very clear—​like Salvador Dalí drawings. Perhaps this can be attributed to Wheeler’s early training in engineering drawing at Johns Hopkins University or to an even earlier course in drawing he took when he

John Wheeler  79 was still a high school student in Youngstown, Ohio. Wheeler thought, and had always thought, in a very pictorial way. He remembered as a young child being given a book by his father called Ingenious Mechanisms and Mechanical Devices. “Each page,” he told me, “was absolutely marvelous to look at—​an illustration of cleverness. I  can remember lying in bed thinking of those pictures. It wouldn’t be words. It wouldn’t be equations. It would be pictures of how one thing would fit together with another.” Wheeler’s ambition then was to make a clock with little actors that would emerge when the hours chimed, but he settled for making a machine that solved algebraic equations and a sewing-​machine cabinet for his mother with hinges that did not show. “That was a very fancy doing—​my own design,” he told me. “It had a tulip-​ leaf pattern at each corner. I turned most of it out on a lathe that I made out of an electric motor with a rod at the other end.” In the fifty years that Wheeler had been teaching physics—​there was a substantial hiatus during the war—​he had produced some fifty PhDs (the most famous of whom was no doubt Richard Feynman). This is an enormous number of doctorals for a theoretical physicist. An experimental physicist, by contrast, can often have several PhD students working together on a single experiment. For a theorist, each PhD represents at least one publishable idea, and fifty is a lot of publishable ideas. In his memoir “Surely You’re Joking, Mr. Feynman!” Feynman, who took his degree at Princeton with Wheeler in 1942 and won the Nobel Prize in 1965, had a chapter called “Monster Minds”—​ an affectionate reference to Wheeler. He said that when he was a student, he came to Wheeler with a calculation that Wheeler, after a cursory inspection, said was wrong. Feynman wrote, “What bothered me was, I thought he [Wheeler] must have done the calculation. I only realized later that a man like Wheeler could immediately see all that stuff when you gave him a problem. I had to calculate, but he could see.” In addition to supervising students, Wheeler did an incredible amount of original research. His papers, dozens of them, were bound in several volumes, which he kept for handy reference on a shelf near his desk in Austin. Nearby were the bound theses of many of his students. He worked successfully in almost every branch of physics, from nuclear fission—​his paper written with Bohr in 1939 was the first successful theoretical treatment of fission—​to black holes. The terms black hole, ergosphere, geon, Planck length, and stellarator were all invented by Wheeler. The Wheelers trace their heritage in this country back to seventeenth-​ century New England. They came with the migration of the “dissenters”

80  Quantum Profiles from the southeast of England. Wheeler told me that in 1645 there were forty-​five families named Wheeler in Concord, Massachusetts. He was descended from one of them—​Sergeant Thomas Wheeler. The Archibalds, Wheeler’s mother’s side, migrated from Nova Scotia to Kansas just before the Civil War. John Christy Archibald, Wheeler’s great-​grandfather, was one of the founders of Lawrence, Kansas. Kansas was a free state, while Missouri was not. In a pre–​Civil War skirmish, Quantrill’s Raiders—​the Confederate “border bandits” under the command of William C. Quantrill—​came over the border into Kansas and burned down the houses in Lawrence. They lined up Wheeler’s grandfather and some other men in front of a barn door and were about to shoot them. Wheeler’s great-​grandmother threw herself in front of her son, crying, “Don’t shoot him. He’s just a boy!” and Wheeler’s grandfather escaped. During the Civil War, he was nearly done in when a cannonball hit the ground in front of him, ricocheted, and grazed him in the head. He was rescued on the battlefield by a woman who took him into her house, where he revived in a couple of days. After the war, Wheeler’s grandfather matriculated at the University of Kansas in Lawrence, where he met Wheeler’s future grandmother, who came from Ohio. Her family had run an underground abolitionist “railway station.” Wheeler told me that “in the family we have two silver spoons. They came from a Negro woman who had lived in Louisiana as a slave and had arrived in Ohio on the underground railway to stay. She was ill, and the family looked after her for several weeks. When she left, she wanted to give my family something, so she gave them two silver spoons she had taken from the household in Louisiana. After all those years of service she thought she was entitled to take those spoons.” Wheeler’s father’s grandfather, Ezekiel Wheeler, was a Seventh-​Day Adventist minister. Wheeler’s father recalled visiting them and listening to heated theological discussions after they thought he had been safely tucked into bed. After Wheeler’s Archibald grandparents married, they moved to a ranch near Trinidad, Colorado. Besides running the ranch, Grandfather Archibald taught school. Wheeler remembered that when he was very young, his grandfather taught him some mathematics. In all, five children were born on the ranch; Wheeler’s mother was the youngest. He did not count any scientists among his ancestors. However, he told me, his mother, who often walked a ten-​mile round trip along the railroad tracks to school, was very gifted in arithmetic. When standing in line in a grocery store, she could look at the figures upside down on the sales receipt of the customer in front of her

John Wheeler  81 and add them in her head before the sales clerk could add them right-​side up. As a Civil War veteran, Wheeler’s grandfather had some sort of priority with respect to government jobs, so when Wheeler’s mother was eighteen, the Archibald family moved to Washington, D.C. Meanwhile, on the other side of the family, Wheeler père was working his way through Brown University, partly as a sign painter and partly as a librarian. Wheeler told me, “He fell in love with libraries.” As a result, he studied to be a librarian at the State University of New York at Albany. After graduation, the senior Wheeler got a job in the public library in Washington, where Wheeler’s mother had also taken a job. The couple met and fell in love. “Those were the days,” Wheeler explained, “when everybody would gossip about everybody, so at the end of the day they would exit the library by separate exits. They would meet in Rock Creek Park and read Keats and Shelley and Byron and Wordsworth. So I was a gleam in their eye at that time.” The couple married in October 1910 and moved to Jacksonville, Florida, where Wheeler was born on July 9, 1911. A  few months later, Wheeler’s father took a position with the Los Angeles public library, and the family settled in California, where Wheeler’s brother Joe was born three years later. (He was later killed in the Second World War in the fighting in Italy.) Not long after Joe was born, the Wheelers moved again, this time to Youngstown, Ohio. “My father had had difficulty in the Los Angeles library,” Wheeler explained. “He was full of ideas of what a library should be. I have a feeling that the librarian there was rather slow-​moving and felt that the whole show was being taken out from under him. One day, without any advance notice, he told my father that his position had been discontinued. The bottom dropped out of the Wheeler family. People who had been in touch with the library—​solid citizens—​wanted to make a big fuss, but my father said, ‘No—​let’s just leave it.’ ” Wheeler’s mother moved back to Washington temporarily with her two sons, and his father found a fill-​in job at the Great San Francisco Exposition of 1914, where he met Theodore Roosevelt, who had been one of his heroes. A couple of months later, he was appointed director of the public library in Youngstown. Wheeler spent most of his childhood in Youngstown. The family was completed by the addition of a brother, Robert, born in 1917 (a geologist until his death a few years ago), and a sister, Mary, born in 1918, who also became a librarian and lived in Vermont. From his account of it, Wheeler’s Ohio boyhood sounded like a very happy one. He had a paper route delivering the Youngstown Vindicator and worked in the library on Saturday mornings. Unlike many theoretical physicists

82  Quantum Profiles I have asked (but like Bell), Wheeler did not have any special early mathematical memories. He did recall that when he was about four years old, being bathed by his mother, he asked her, “What happens when you get to the end of things?” I asked Wheeler if he had numbers in mind. “No,” he said. “Space.” What early scientific memories Wheeler did have had to do with making things—​comptometers, “guns” that operated with a light socket (you put something in the socket, turned on the switch, and the object popped out), and a railway signal. These activities culminated at the age of thirteen, when Wheeler and his friend Verdet Moke founded what they called the Wheeler-​ Moke Safe and Gun Company. It produced wooden combination locks with, Wheeler told me, “little wheels, whittled of wood, with a little notch on each end with a pin connecting each to the next, so you could set the combination. I do remember making a little machine which would solve algebraic equations of the form ax + by = c and dx + ey = f . There were wooden sticks on a board, and where they crossed would give the solution.” By the time Wheeler was a senior in high school, the family had moved again, this time to Baltimore, where Wheeler’s father became the director of that city’s public library. Wheeler attended a high school that was known as the Baltimore City College. His abilities must have been evident, since he recalls that one of his teachers, Lydia Baldwin, “went around to see my father—​to say he ought to do something about me—​to push me ahead. Though my parents thought I was asleep, I overheard them discussing what they were going to do about my education.” As it happened, Wheeler had already skipped a few classes when, at age ten, his father had taken a year off from library work to try (unsuccessfully) to make a go of a family farm in Vermont. Wheeler had attended a one-​room schoolhouse in rural Vermont, and he had been skipped ahead. During that year in Vermont, he had also managed to blow off a small piece of one of his fingers with a dynamite cap. “My father,” he told me, “had gotten together with the neighbors to put up the poles for a power line. That was the only way they could get electricity to the farms in those days—​put in the power lines themselves. To make the holes they used dynamite, and the dynamite was kept in the loft of the pig shed. I fed the pigs there every day, morning and night, so I knew about the dynamite. I was also reading books on explosives—​I loved to read about explosives. So I thought I would take a dynamite cap off and make a little explosion with it clear off across the road. I put a match in the ground and lighted it, and missed, and relighted the match and missed. This got me closer and closer, when it went off in my

John Wheeler  83 fingers. It blew off the end of one finger and part of my thumb. Lucky I have any fingernail left.” Besides leaving Wheeler with a slightly peculiar-​looking finger, this also left him—​oddly—​with a highly developed taste for watching explosions. During the war, when he used to visit Los Alamos, his friends would take him out on the mesa at night when they tested their high explosives. After the war, he attended a going-​away party for the Los Alamos physicist Sterling Colgate. Wheeler recalled, “He was giving away, at the farewell dinner, a case of dynamite. To me this was a lovely thing, but I couldn’t see any legal way to carry it on a plane.” Fireworks have always played a large role in the Wheeler family’s Fourth of July celebrations. In any event, Wheeler managed not to blow himself up before he graduated from high school at age fifteen. By this time, he had taught himself differential and integral calculus and was working his way through a book called Problems of Modern Physics by the great Dutch physicist Hendrik Lorentz. It dealt with both Albert Einstein’s theory of relativity and the old quantum mechanics. “It was over my head in large measure,” Wheeler recalled, “but it was fascinating to me. I can’t remember having the same kind of teachers in mathematics and science that I had had in Youngstown. In the physics class in Baltimore, I used to sit there working on something else. This annoyed the teacher, and he used to try to catch me out. But the class went so slowly that working on something else was the only thing to do.” At sixteen, Wheeler entered Johns Hopkins University with the idea of becoming an engineer. “My three uncles,” Wheeler explained, “were mining engineers. With my interests, how else was I going to earn a living except at engineering? The idea that you could do what you wanted to do, and get paid for it, never occurred to me.” Wheeler’s going to Johns Hopkins was, in Louis Pasteur’s notable phrase, an example of “chance favoring the prepared mind”—​the chance being, in this case, the presence of a first-​rate scientific institution in his “backyard” and the prepared mind being Wheeler’s. As Wheeler put it, “We were a hard-​up family, and the only place I could have afforded to go to college was in Baltimore.” Wheeler’s engineering career lasted one year, during which he took things such as surveying, mechanical drawing, and strength of materials. He then spent the summer rewinding electrical motors at the Pittsburgh Verde Grande silver mine in Zacatecas, Mexico, of which his uncle was the manager. He found this a most unpleasant experience. Also, by this time, he had discovered the physics library, which shared the same facilities with the engineering library at Johns Hopkins.

84  Quantum Profiles While he was doing his homework on the bending of metal beams and the like, he would take a glance or two at the latest issues of the Zeitschrift für Physik. This was 1927, and most of the articles on the then-​new quantum theory were being published in the Zeitschrift. Johns Hopkins had a six-​year program that led directly to a PhD. This meant that there was no clear-​cut distinction between the undergraduates in the program and the graduate students. (Indeed, Wheeler had no undergraduate degree. However, he did have a PhD from Johns Hopkins, along with twelve honorary doctorates.) There were some thirty students in the physics program, and classes were taught mostly in seminar fashion. Students were asked to work for a certain number of weeks with each professor so that they could get a variety of hands-​on laboratory experiences. It was an ideal arrangement for someone with Wheeler’s vivid intellectual curiosity. He recalled sometime after 1929 encountering on campus the physicist Joseph Sweetman Ames, who had become the president of the university. “I don’t think he knew me from Adam,” Wheeler noted, “but he asked me how I was getting along. He said that the whole thing around there was to be very interested in something. I told him I was.” Among the things that Wheeler was interested in was the new quantum mechanics. “It was being used at Johns Hopkins,” he told me, “to make predictions about spectra.” The students had a kind of joint seminar with some of the faculty members in which they tried to educate each other about the new theory. There were few, if any, formal courses on quantum theory in American universities at that time, and people such as Rabi and J. Robert Oppenheimer went to Europe to learn it. Mainly, Wheeler taught it to himself. “At that time,” he recalled, “the family would go to the farm in Vermont for a month in the summer. We’d sold the farm, but we had kept a few acres by a brook where we had a cottage . . . really a sort of camp. Anyway, I would sit out in a pasture with Hermann Weyl’s book Gruppentheorie und Quanten-​mechanik [a classic text which Weyl published in 1928]. That was the way I learned my quantum mechanics. It was wonderful, because at that time I was learning German, and the German and the physics went hand in hand. I retained a great admiration for Weyl and feel so lucky to have known him later in Princeton.” Wheeler’s thesis, which he did with the distinguished spectroscopist K. F. Herzfeld, had to do with the absorption and scattering of light in helium. “Later,” Wheeler reminisced, “when I was in Copenhagen I was told a story about Bohr. [Ernest] Rutherford had been beating on him to publish his

John Wheeler  85 ‘Bohr atom.’ And Bohr said, ‘I can’t. Nobody will believe me until I do all the atoms and all the molecules.’ Rutherford said to him, ‘Bohr, you do hydrogen and you do helium and everybody will believe the rest.’ But with the old quantum theory he couldn’t do helium, and here I was, for my thesis, about to do helium with the best approximations then available—​to explain the refractive index and its dependence on wavelength. Thinking back on it, I cannot think of a happier subject. The thesis was no great thesis, because I was pretty young and green. I didn’t realize all the things that could have been written about the subject, that could have blown up into a really wonderful dissertation. Incidentally, in 1932, Einstein’s friend Paul Ehrenfest came through on his way to Caltech for a visit. I can recall Herzfeld trying to get Ehrenfest to talk at the seminar and Ehrenfest saying it must be Herzfeld who talks. Finally, after a lot of persuasion, Herzfeld agreed to talk. He talked about his ideas for treating problems that do not admit the standard separation of variables in the wave equation. Ehrenfest got up and said, ‘My dear Herzfeld, you are completely crazy.’ It was wonderful to see the spirit of collaboration between the two of them.” Wheeler got his degree in 1933, the depths of the Depression. “A neighbor shot himself,” Wheeler recalled, “because he did not see how he was going to support his wife and children. Well-​dressed people came to the door asking for any kind of job—​painting, mowing the lawn, shoveling coal—​anything. Desperate years. My father had, nonetheless, gotten the city to appropriate money for a new public library. He went again and again to the state legislature to lobby for the money. Baltimore got an unbelievable amount for the money it spent on that library. It was the only library in America to have a storefront window with glass coming down to street level so that everybody could look in and see that a library was an attractive place and not a terrifying place.” Most young physicists had enormous difficulty finding work in their field. Although Wheeler, who was always unassuming about his work, downplayed the quality of his thesis, it was sufficiently impressive that he won one of the very rare National Research Council Fellowships. “I somehow wasn’t aware of all the difficulties there were then. I didn’t know what I was going to do if I didn’t get a job. Recently I wrote a little piece about my friends who were looking for jobs at that time. There was, for example, Larry Hafstead, who was a graduate student along with me. He couldn’t get any decent job so he took a ‘peanut’ job at the Carnegie Institute for Terrestrial Magnetism in Washington. He went on to do wonderful work in nuclear physics and

86  Quantum Profiles became director of research at General Motors, with a research budget of nearly a billion dollars a year. And there was John Mauchly, who couldn’t get a teaching job at any important place. He took a teaching job at a one-​horse college on the outskirts of Philadelphia. He went on to develop the electronic computer, which eventually became UNIVAC and Remington Rand. There was a chap who was interested in the infrared. But nobody was interested in the infrared then; no government laboratory, no industrial laboratory, no university. Then he realized that, good times or bad, people got sick. He took his equipment to the Johns Hopkins hospital, where it was used to measure body temperatures for different parts of the body. He ended up as the director of a big laboratory at Yale devoted to the study of physiological conditions by physical methods.” Wheeler had his choice of working with Oppenheimer in California or Gregory Breit at New York University. He made the somewhat surprising choice of Breit. He had seen Oppenheimer in action at meetings of the American Physical Society and said, “Oppenheimer was much quicker than I was accustomed to. Breit was a slower thinker. I have to ponder and ponder on things, so his style fitted me. I  learned a lot of physics with him that year. He was at the uptown campus of New York University in Washington Heights and I  can recall a lunch one day when one of our experimental colleagues reported on some experiments on electron scattering that didn’t fit the theory. The young theorists were sitting around the table saying the experiments couldn’t possibly be right since they violated the law of the conservation of parity.” The experiments, which were right but were dismissed, anticipated the discovery of parity violation in the weak interactions by some twenty-​five  years. While he was a student at Johns Hopkins, Wheeler found time to lead an active social life. “I was one of the founders and the first president of the Baltimore Federation of Church and Synagogue Youth,” he told me. “I had also been chairman of the graduate student committee that ran the dances for the graduate students. I had taken various girls around. The day I took my PhD oral exam I met my best friend Bob Murray and one of us said—​I think it was me—​‘let’s get Janette Hagner and take her on a walk in the park,’ Druid Hill Park. So we went and got her and we took a walk. I had met her through her sister. Janette had graduated from Radcliffe and was doing some work in history at Johns Hopkins. She had also had a one-​year fellowship to Rome to do Italian history. During the walk, she happened to mention that she was going to be teaching school at the Rye Country Day School, outside

John Wheeler  87 of New York. I took advantage of that while I was at New York University. We went out three times together and we were engaged.” Engaged but not married. That came a year and a half later. “There was the problem of no money. Looking back on it, it was the craziest thing. We should have gotten married anyway and gone to Denmark together.” Every scientist—​Einstein being a notable exception—​can find in his or her career a decisive teacher. For Bohr, it was Rutherford. For Feynman, it was Wheeler. And for Wheeler, it was Bohr. When Wheeler applied for an extension of his National Research Council Fellowship, he wrote on his application that he wanted to work with Bohr because “he sees further than any man alive.” One of the people at NYU told Wheeler that he should wait to go to Copenhagen until he was a “mature physicist” (Wheeler was only twenty-​two), but with Breit’s encouragement, Wheeler applied anyway and was accepted. Wheeler went to Copenhagen via Germany. He remained haunted by the memory of changing trains in Cologne. He found that because of the German inflation, he was the only person in the railway station who could afford the price of breakfast. “There was a storm trooper there,” he told me, “wearing boots and a swastika, striding up and down, glaring at me. On the boat I had met a chap who had had farm jobs in America. He was going back to Germany because he thought that, with Hitler, there was a future there. I always wondered what happened to him.” Bohr was forty-​nine when Wheeler met him. He had, Wheeler explained to me, “two speeds: not interested or completely interested. This applied to everything. E. J. Williams, who was at Copenhagen when I was there, told me that during the Stalin period he accompanied Bohr on a visit to the Soviet Union. Bohr was allowed to visit the Kremlin Museum with Williams. It was a tremendous privilege. It was closed normally. Bohr was just not interested in anything, and Williams felt very apologetic. His guide didn’t seem to get anywhere with Bohr. Then he came to one of those old carriages. You could ride in them. Bohr became fascinated by how the springs were mounted, how you kept the vibration out. He couldn’t be dragged away. It was two speeds: not interested or completely interested.” When Wheeler arrived in Copenhagen, the thing that Bohr was completely interested in was whether quantum electrodynamics was right at high energies. Wheeler told me that before he had come to Copenhagen, he had listened to “an absolutely packed evening lecture by Oppenheimer in which he said that electrodynamics must surely fail when the energies get

88  Quantum Profiles to be about 137 electron masses [a relatively low energy by present accelerator standards]. But Bohr and Williams had developed a point of view from which you could deduce [correctly] that it could not break down at these energies. Hence the new particles that were being discovered that penetrated ten centimeters of lead could not be electrons. This created the climate of opinion that was necessary for the discovery of the meson. Williams was able to take advantage of a cross section I had worked out with Breit for the production of electron-​positron pairs in the field of a nucleus. I remember talking to Bohr and Williams about it. I was so shy that I got up to erase the board with the back of the eraser. Bohr then got up, took the eraser, turned it over, and said, ‘It would be easier if you did it this way.’ “It was a wonderful feeling to see a cross section that seemed to have no prospect of being experimentally determined being put immediately to use. At Eastertime Christian Møller had gone from Copenhagen to Rome to visit [Enrico] Fermi’s lab, and he came back with these reports of unbelievably enormous cross sections for the absorption of slow neutrons by nuclei. They were absolutely at variance with the idea of a particle’s going freely through a nucleus, although that was not, at first, clearly recognized. But Møller presented the results. Before he had gotten fifteen minutes into his talk, Bohr took away the blackboard from him and was explaining how these results could change our whole idea about nuclear structure.” Not long afterward, Bohr developed what has become known as the liquid-​drop model of the atomic nucleus. In this model, the nucleus is treated like a tiny globule of an incompressible fluid. One does not attempt to treat the individual neutrons and protons in the nucleus but only their collective behavior. The model has been enormously successful, especially in the study of reactions involving heavy nuclei. Almost at once, Wheeler began applying it. He was also writing to “any place I had ever heard of ” for a job. A physicist named Arthur Ruark had been brought in to build up the physics department at the University of North Carolina in Chapel Hill. He had heard Wheeler give a lecture, and he hired him as an assistant professor. “The job paid, I think, $2,300 a year,” Wheeler told me. “Janette gave up her job, which paid $2,500 a year, and came with me to Chapel Hill. As I told you, when I look back on it, it was the craziest thing for us not to have gotten married before I went to Denmark and to have gone together.” When I interviewed him, the Wheelers had been married close to sixty years. When he went to Chapel Hill, Wheeler had every intention of remaining there forever. His two elder children, Letitia Wheeler Ufford and James

John Wheeler  89 English Wheeler, were born there in 1936 and 1938, respectively. (His younger daughter, Alison Wheeler Lamston, was born in Baltimore in 1942.) However, in 1938, Wheeler was offered a position at Princeton University. The distinguished theoretical physicist E.  U. Condon had just left the department, and the university had decided to replace him with two nuclear theorists, Eugene Wigner and Wheeler. A program of experimental nuclear physics had also gotten under way at the university. Neither Wheeler nor Wigner was a stranger to Princeton. Wigner had already taught there and, not getting tenure, had gone to the University of Wisconsin before being called back. Wheeler had first visited Princeton in 1933, when he went there from New York to attend the first lecture Einstein gave at the newly created Institute for Advanced Study. (It did not then have its own quarters but shared Fine Hall with the physicists and mathematicians from the university.) Of the lecture, which had to do with Einstein’s ideas on a unified field theory, Wheeler commented to me, “Einstein was not the kind of retail dealer of equations I was accustomed to. He was a wholesale dealer. He was counting them by the dozens.” In 1935, Wheeler had been a three-​month visitor at the Institute himself. But, as he recalled, “My wife wept when we left Chapel Hill; but then in 1976 she practically wept when we left Princeton for Texas.” On January 16, 1939, Bohr arrived in New York aboard the Swedish ship Drottingholm, carrying with him the knowledge that the nucleus had been split; nuclear fission had been discovered the month before by two German scientists, Otto Hahn and Fritz Strassman. It could well have been discovered several years earlier by Fermi in Italy or Irène Joliot-​Curie in France; it could also have been predicted by Bohr and Wheeler, using Bohr’s liquid-​drop model. Wheeler told me that he and Bohr had explored deformations in the drop but not the ones most favorable for fission, and they were not trying to study what would happen if the nucleus was actually unstable. Considering what it might have meant if the Germans had gotten started on the atomic bomb in 1933 rather than in 1939, we can all be grateful that fission was not discovered earlier. In actual fact, Hahn and Strassman did not understand the significance of their experimental results until they were explained to them by their former collaborator Lise Meitner. Being Jewish, she had fled to Sweden along with her nephew, the physicist Otto Frisch, who had earlier fled to Denmark. It was Frisch who gave the name fission to the newly discovered process. Bohr was told about all of this just before leaving Denmark but decided to say nothing until he could be sure that Meitner and Frisch would

90  Quantum Profiles get proper credit for it. Wheeler and Fermi, who had just fled Italy with his Jewish wife, met Bohr and his party at the pier. With Bohr was his son, Eric, and his collaborator, Leon Rosenfeld. Wheeler told me that “Bohr had come, in the first instance, primarily to talk about the quantum theory of measurement and to try to convince Einstein about the quantum theory. But his whole course was perturbed, as was mine, by this fission business.” The first perturbation occurred the very evening of Bohr’s arrival. The Fermis took Bohr and his son to New York for the evening, while Wheeler took Rosenfeld back to Princeton. Wheeler told me what happened next. “At that time I had a major part in running our Monday night journal club. It began, as a rule, at seven thirty. We deliberately had too few chairs so that people would arrive promptly to get a seat. It was necessary to break up just a little before nine thirty, because a lot of people wanted to go to the second show at the movie theater. We usually had three speakers, and as it was a Monday night, I got Rosenfeld to give one of the talks. He didn’t realize that he was not supposed to talk about fission. He spilled the beans, and of course everybody was immensely excited about it. Bohr came to Princeton the next day, and somehow we just naturally began a collaboration on it. The first day or two Bohr dictated several paragraphs based on his idea that fission was just one more nuclear reaction. His whole idea always was to try to bring everything together in a harmonious way. Here the idea was to bring fission under the same set of outlooks that worked for other nuclear reactions. The particle—​a neutron, say—​goes into the nucleus, which takes it up. The nucleus loses all memory of how it was formed. The system vibrates. The excitation changes and moves around the nucleus, and finally the nucleus gets rid of it by giving out radiation, or giving out a particle, or doing this new thing—​undergoing fission. The natural division here, as in so much of the rest of physics, is between energy release on the one hand and the probability of energy release on the other. I can recall digging up a lot of material on the semi-​empirical mass formula [an invention of German physicist C. F. von Weizsäcker which described the masses and binding energies of the nuclei] to see how we could take over some of the empirical masses to estimate the surface tension of the liquid drops representing different nuclei and then calculating the energy release for various breakups. Bohr was disappointed that the calculation did not show two peaks where the two regions for fission fragments are formed with the greatest probability.” While Bohr and Wheeler were developing the theory, experimental discoveries were being made about fission almost daily. As was typical of Bohr,

John Wheeler  91 he fastened on the one that seemed most paradoxical, most difficult to explain: the observation that both slow and fast neutrons would cause natural uranium to undergo fission, while neutrons of intermediate energy would not. Bohr, Wheeler told me, had the inspired idea that it was the rare isotope U235 that was responsible for the slow-​neutron fission. In natural uranium, this isotope makes up only 0.7 percent of any sample, which is nearly all U238, the isotope that is responsible for the fast-​neutron fission. Hence the two observed fission processes in natural uranium represented the fission of distinct isotopes. This extraordinary intuitive guess—​which is what it was—​led to one of the two ways of constructing an atomic bomb: separating the U235 from the U238 to make an explosive mass of pure U235. The other way, proposed a little later by Princeton physicist Louis Turner in an article in Reviews of Modern Physics, was to convert U238 into a new element. It was soon given the name plutonium, and it was also fissionable by slow neutrons. The idea that it was U235 that was responsible for slow-​neutron fission seemed entirely crazy at the time to most of Wheeler’s colleagues. He recalled making a bet of $18.36 against a penny with George Placzek, a well-​known theoretical physicist. (The strange odds mimic the ratio of the masses of the proton and the electron.) In due course, Placzek sent Wheeler a one-​word telegram that read “Congratulations!”—​along with a money order for a penny. Wheeler had several vivid personal memories of this collaboration with Bohr. Near the beginning, one night at about ten, they went to the library to see if they could find some synonym for the word fission. “Fission,” Wheeler said, “was great as a noun, but we didn’t like it as a verb. We tried ‘splitting’ and ‘mitosis,’ but they didn’t seem any better, so finally we used ‘fission.’ ” Wheeler also recalled a Fine Hall janitor for whom fission ran a distant second to keeping the offices neat. Wheeler told me that the janitor “scolded Bohr for spilling chalk on the floor. After that, when he finished working, Bohr would always pick up the rug and kick the chalk under it. “Bohr had a very intense way of speaking. He would say, ‘How can you possibly imagine such and such to be the case?’ His eyes would be almost vertical instead of horizontal . . . almost vertical. At other times, when he was undecided, he would talk about one position with his head turned one way, and the other position with his head turned the other way. He was always ready to reconsider everything.” I asked Wheeler if he had the sense of doing something portentous when he was working on fission with Bohr. “I should have, but I didn’t,” Wheeler answered. “I think it was on March 16—​two months to the day after Bohr

92  Quantum Profiles had arrived in New York—​that we had a meeting in Wigner’s office in Fine Hall, the one that had been Einstein’s before the Institute got its own quarters. There were four or five of us, including Bohr, Wigner, Leo Szilard, and myself. We talked about using fission for submarines, and for making a bomb. Bohr said that using U235 to make a bomb would require the resources of an entire nation. In the end, it took three. “I was not as worked up about it as were Szilard and Wigner. I had the mistaken idea that we would stay out of the war. When I was in Denmark in 1934 and 1935, my Danish friends would listen to Hitler’s Nuremberg rally speeches over the radio and ask me what the United States would do. It was my judgment, based on what had happened in World War I, that we would stay out. I felt that Germany would win any war in Europe, and that as terrible as Hitler was, there was a German culture that one could hope would come back. It is very unfortunate that I felt like that. If I had been more convinced, as Wigner and Szilard were, that we were going to get into the war, I would have pushed harder to begin making the bomb. “I figured out that roughly a half million to a million people were being killed a month in the later stages of the war. Every month by which we could have shortened the war would have made a difference of half a million to a million lives, including the life of my own brother. If somebody could have pushed the project harder in the beginning, what a difference it would have made in the saving of lives! At that time, I thought of my work in nuclear physics as a temporary thing—​an interlude before I got back to more fundamental questions.” Wheeler’s return to what he regarded as fundamental physics was certainly aided by the arrival of Feynman in Princeton in 1939. Feynman, who was only seven years younger than Wheeler, had been an undergraduate at MIT. He was already well known for both his original brilliance and his various and sundry capers. Feynman died in 1988, and in a moving article published in a special memorial issue of Physics Today, Wheeler described his introduction to Feynman: “ ‘This chap from MIT: Look at his aptitude test ratings in mathematics and physics. Fantastic! Nobody else who’s applying here at Princeton comes anywhere near so close to the absolute peak.’ Someone else on the graduate admissions committee broke in, ‘He must be a diamond in the rough. We’ve never let in anyone with scores so low in history and English. But look at the practical experience he’s had in chemistry and in working with friction.’

John Wheeler  93 “These are not the exact words, but they convey the flavor of the committee discussion in the spring of 1939 that brought us twenty-​one-​year-​old Richard Phillips Feynman as a graduate student. How he ever came to be assigned to this twenty-​eight-​year-​old assistant professor as grader in an undergraduate junior course in mechanics I will never know, but I am eternally grateful for the fortune that brought us together on more than one fascinating enterprise. As he brought those student papers back—​with errors noted and helpful comments offered—​there was often occasion to mention the work I was doing and the puzzlements I encountered. Discussions turned into laughter, laughter into jokes, and jokes into more to-​and-​fro and more ideas.” Among the various intellectual capers Wheeler cited, some of which he had described in some detail when I was interviewing him, was the matter of the swastika-​shaped lawn sprinkler. It shot out four jets of water, and the reaction caused the sprinkler to go around and around. What would happen, the two young men wondered, if an identical sprinkler were to be built that sucked in water? Which way would the sprinkler turn? According to Wheeler, the entire physics department lined up on various sides of this pressing question. There was nothing for it except for Feynman to build an apparatus to test the point. It was set up on the floor of the cyclotron laboratory. As it turned out, the apparatus exploded—​spewing water and glass all over the laboratory—​before the matter could be decided. Feynman was banned from the lab. He then proceeded to allow himself to be hypnotized in a demonstration that Wheeler attended at the Graduate College. Wheeler decided that Feynman was acting and that indeed all hypnotism was playacting. At one point, Feynman became interested in a problem involving the neurology of jellyfish. It seems that a jellyfish has a single nerve that goes entirely around it. Feynman wondered why stimulated jellyfish would not continue to vibrate indefinitely, as the nerve impulse went around and around. Jellyfish biologists had suggested that there were in fact two nerve impulses moving in opposite directions, which, upon meeting, would cancel each other and arrest the vibrations. Wheeler told me, “Somehow the boys worked out a way to cancel one of the impulses and the unfortunate jellyfish did vibrate hour after hour. “Feynman used to come over to our house to work or for supper. As my wife was cooking supper, he would explain to our two very young children how you could tell whether the contents of a can were liquid or solid by the way it would go when you tossed it up in the air.

94  Quantum Profiles “And,” Wheeler went on, “the wonderful girl he was engaged to, Arline Greenbaum, would come down to Princeton from time to time for parties at the Graduate College. She would stay with us. But unfortunately she was pushing herself too hard. She was a student in art school, and to get the money she was giving music lessons. It made a terrific program for her, but she came down with this bug. Month after month the doctors failed to diagnose it. It turned out to be tuberculosis. Feynman married her, both of them knowing full well she would not live, and went with her to Los Alamos. I saw Arline the week before she died in the hospital in Albuquerque, with all the tubes feeding oxygen into her. A wonderful girl. It was really a tragedy what happened.” Feynman wrote very movingly about Arline, especially in his second collection of essays, “What Do You Care What Other People Think?” Feynman wrote his PhD thesis under Wheeler’s supervision. It was called “A Principle of Least Action in Quantum Mechanics,” and it is one of the rare PhD theses to have made a lasting impact in the field. In classical physics, given the forces acting and the initial conditions, a particle follows a uniquely determined trajectory between any two points in space-​time. This trajectory can be determined by minimizing a mathematical quantity associated with the system called the action. In the 1930s, Paul Dirac had hinted, but not made very explicit, that a similar principle might hold in quantum theory—​ similar but not identical, because in quantum theory there are no trajectories but rather probabilities that a particle initially located at some point in space-​ time can be found at some other point in space at a later time. The business of the theory is to determine these probability amplitudes. In Feynman’s formulation, the amplitudes are determined by summing the action over all possible histories between the two space-​time points in question. No matter how crazy such a history might appear from the classical point of view, it still must be included in the sum. Classical physics is recovered by letting Planck’s constant go to zero in the formula for the action. This, it turns out, picks out a unique trajectory—​the classical one. It is a very powerful way of looking at quantum-​mechanical formalism and is essential in the generalizations that have been made to the quantum theory of fields. Wheeler was so taken by this work that he decided to try it out on Einstein to see if this formulation would change the old man’s mind about quantum theory. The result was predictable. Wheeler told me, “Einstein listened patiently to me for twenty minutes, and when I ended up by saying, ‘Doesn’t this look perfectly beautiful? Doesn’t this make you willing to accept the quantum theory?’ he said, ‘I still cannot believe that God plays dice. But maybe I have

John Wheeler  95 earned the right to make my mistakes.” No beautiful formalism could alter the dictum of Wheeler’s quantum-​mechanical baseball umpire: “They ain’t nothin’ till I calls ’em.” For Einstein, “they” were something whether anyone called them or not. Feynman and Wheeler were working on several other problems, which they never got to finish because of Pearl Harbor. Once the United States had been attacked, there was no question about Wheeler getting involved full-​ time in the war. Up to that time, Wheeler’s involvement with the nascent atomic-​bomb project had been peripheral. His paper with Bohr on the liquid-​ drop model of fission had been published in the open literature. (Ironically, the September 1, 1939, issue of the Physical Review in which it appeared also carried the paper by Oppenheimer and Hartland Snyder in which the notion of what Wheeler later named a black hole first appeared.) It took some time before the physicists, who were accustomed to the free exchange of scientific ideas, began to voluntarily restrain their communications on fission and related matters. But until Pearl Harbor, Wheeler had ambivalent feelings about whether there would be a war and whether this country would get dragged into it. Soon after Pearl Harbor, Wheeler went to the chairman of the Princeton physics department and said that if he were not granted a leave of absence to go to Chicago to work with Fermi on the first nuclear reactor, he would have to resign. He was granted a leave. His next problem was to find lodging in Chicago for himself and his family. All the real estate agents there told him that nothing was available. “Finally,” he explained to me, “I adopted the practice of walking along a street, any street, and spotting a house I thought would be a nice place to rent, ringing the doorbell, and saying, ‘I am a stranger here and I’m looking for a place to rent. You don’t know, by any chance, of a place in the neighborhood that’s for rent? Or, by any chance, is your own place for rent?’ I got nowhere—​many tries. Finally, I tried one house. The lady said, ‘No, I don’t know any place for rent. No, this is not for rent But, now that you mention it, I think we’d be willing to rent it.’ That’s where we lived—​across from the International House.” Because of Wheeler’s engineering background—​ and, very likely, his temperament—​he was able from the beginning to function as a kind of bridge between the physicists working with Fermi to make the first self-​sustaining, chain-​reacting nuclear pile and the professional engineers who had been brought in as consultants. For these reasons, Wheeler thinks, Arthur Compton, who ran what was cryptically called the Metallurgical Laboratory

96  Quantum Profiles at the University of Chicago (in reality, the reactor group) appointed him the liaison between the Chicago project and the Du Pont Company, which had the responsibility of constructing the first plutonium-​production reactors. On Thanksgiving Day, 1942, the Fermi reactor in Chicago went critical. I asked Wheeler if he had been a witness. “No,” he told me. “I was in Wilmington with the Du Pont people. I really wasn’t interested in a reactor demonstration. To me, it was obvious that it would work.” Wheeler had been going back and forth twice a week on the train between Chicago and Wilmington for several months, and finally, in February 1943, he decided to move his family to Wilmington. One of the problems he was called upon to deal with in Wilmington was where to locate the first plutonium-​producing reactor. Various sites were considered and ruled out—​for example, Florida was ruled out since it had more thunderstorm days per year than any other place in the country. Finally, the plant was sited on the Columbia River in the state of Washington, because of the isolation of the place and the quality of the water. (Pure water was absolutely essential as a cooling agent for the reactor.) Wheeler recalled a Du Pont engineer, Roger Williams, who was responsible for many of the site decisions and also for plant safety. Wheeler told me, “Roger Williams realized how important health and safety would be. Du Pont had a long tradition of safety. I learned from the Du Pont people, many of whom had been plant managers, how in the very early days of the company they had had lots of explosions. You recall how du Pont [Éleuthère Iréné du Pont de Nemours], being a friend of [Thomas] Jefferson, tried, on a visit to America, to buy land in Virginia near Jefferson’s. He was not allowed to. There was a law against it. Pennsylvania? No, a law against it. So the poor devil had to end up in Delaware. That’s how come Du Pont, and the gunpowder works, were in Delaware. They had a lot of explosions until they learned to do things in the safest possible way.” “Du Pont,” Wheeler went on, “is still famous for its safety record. The key idea was not to have safety experts that went around lecturing people on safety. That had about the effectiveness of pouring water on a duck’s back. Instead, they trained various foremen on how to hold conferences—​not to always talk oneself. ‘Well, boys, the higher-​ups tell us that we’ve got to do this safely. What are we going to do to make this safe?’ Then he’s instructed to shut up, and then someone would say, ‘The last time we did something like this, I almost broke my ankle. I stumbled with a load of cement on that hose.’ Then they get the idea of putting the hose under a board so he won’t stumble

John Wheeler  97 on it. This paid off in safety, since people thought ahead about what they were going to be doing. It also paid off in efficiency. Roger Williams realized that there was going to be radioactivity, with all the hazards that were involved, so he put an enormous amount of effort into consulting experts and people in general. He also did a psychological thing. He called it health physics—​not radiation physics—​and that terminology is used not only in this country but all over the world.” As it turned out, the plant, which was known as the Hanford Engineering Works, was located in Richland, Washington. It employed some fifty thousand workers, mostly, Wheeler told me, “Okies” and “Arkies.” Wheeler said that when the prospective workers got off the train in Richland, they would be met by the “wolves”—​who tried, in one way or another, to separate them from their money—​and the “sheepherders,” whose function was to get the workers to the plant intact. With a certain amount of affection, it seemed to me, Wheeler described a beer hall that featured about one murder per night. The windows on it were made sufficiently low that tear gas could be tossed in to calm any excessive exuberance. In July 1944, Wheeler moved his family to Richland. “I was being paid by Du Pont,” he told me, “as a kind of mascot to the enterprise. I was brought into this or that discussion group to answer this or that question. I had to do estimates on the greatest variety of things on the face of the earth. How much radioactivity would go downstream in the water? What kind of excursions in temperature could be expected? What was the danger of getting too much plutonium together? The heating and cooling of the plant—​is it turned on or off? How much shifting of the graphite blocks will that cause? The channel for the cooling water—​what can we do to widen or narrow that? How much will that affect the radioactivity? “Of course, we were all the time keeping in touch with the people in Chicago who were doing experiments, by that time largely on the chemical processing of the water. Would the water have to be demineralized? If you look at the photographs of the Hanford plant as it was in the beginning, you’ll see these gigantic towers going up and you will wonder, what in the world has that got to do with a nuclear plant? Well, they were the towers for demineralizing the water. They never had to be used. But if they did, it would have meant months of delay if they weren’t ready on time.” In the meantime, Feynman had gone to Los Alamos. Among other things, he had figured out the size of an explosive mass of liquid, rather than solid, plutonium. This turned out to be smaller than the solid mass, further

98  Quantum Profiles complicating the safety problem at Hanford. Wheeler told me that Du Pont had to make a $200 million decision: whether or not to build additional plant facilities to deal with this new safety problem. Wheeler computed that the probability of anything going wrong was so remote that this extra expense could not be justified. It was not done, and nothing went wrong. At 12:01 a.m. on September 27, 1944, the Hanford pile was allowed to start producing power at something like full strength. Many dignitaries were on hand, including Fermi. Wheeler was in the central laboratory, computing various things, when he began getting very disturbing reports. When the safety rods that moderated the reactor were pulled out, at first, the level of reactivity climbed. This was expected. But then, mysteriously, it began to fall. Even with the rods completely pulled out, the pile, in Wheeler’s words, “died the death.” He added, “Everybody was scurrying around. There were various theories. One was that nitrogen from the air had gotten fixed in the pile and was absorbing neutrons. Another was that there was something in the water. But it had been one of my jobs to consider every possible way that things might go wrong. I was therefore very aware that a fission product, when it decays, could give rise to an isotope that could absorb neutrons. When, a few hours later, the reactivity began rising, I was sure that this was what had happened. The second nucleus had decayed into a third one which did not absorb neutrons. Outside my office there was a big chart of the nuclei. By looking at it I could see that the culprit had to be xenon-​135, decaying into iodine-​135. So I did some figuring on that. By then Fermi had come into my office and he accepted this explanation. “But the real hero of the story was a Du Pont engineer named George Graves. He kept asking questions like ‘Radioactivity? Who told the nucleus to be radioactive? Fission product? What in the hell are fission products?’ Little by little, he began asking these pregnant questions. We had a couple of hour sessions most every day. Once he got into it, he insisted that, instead of the 1,500 fuel tubes that we had planned to put in, we had a margin for error of another 500. Actually we had 2,004. That took a lot of gumption, since it cost a lot of money. But thanks to his foresight it was possible to reload those extra tubes with uranium and give the pile the reactivity it needed to override the fission-​product poison. “It was quite a place,” Wheeler recalled. “The mess hall in one of those plants was a huge place—​big as a basketball court—​table after table. Nobody was served until the table was filled up. Then the plates were brought with food and passed around. The people ate in absolute silence. It was not the

John Wheeler  99 fashion to talk. There was an entertainment program that was run on money from slot machines. It brought in really big names. They would get off the train in the middle of the night in this godforsaken town of Pasco and be brought to a place they had never heard of. In Hanford there had been these wonderful farms that had been run by irrigation—​asparagus, fruit. But they had been taken over by the government and the trees were dying. Nobody had time during the war to look after things like that. The houses were put up in a big rush, and the tar pavement sidewalk squirted out the way toothpaste is squirted from a toothpaste tube. But in the hot sun the tar would crack and asparagus would come up through the cracks. “I recall Walt Simon,” Wheeler went on, “the plant manager in the beginning, telling me about the day that General [Leslie] Groves visited. I saw him at the end of that day. He told me that General Groves kept saying things like ‘Simon, why isn’t this town further along? Simon, why isn’t this done and that done?’ Simon would always be very polite and tell him the story. Finally, this being so polite got under Groves’s skin, and at the end of the day he said to Simon, ‘Simon, what’s the matter with you? Are you a man or a worm?’ And Simon said, ‘Well, General Groves, we have people back in Wilmington to answer questions like yours.’ “I also remember meeting Bohr in Washington—​one of us from Los Alamos, Bohr, being a consumer of plutonium, and one of us from Hanford, me, being a producer. Bohr had just finished a discussion with [Franklin D.] Roosevelt about the idea of an open world. Bohr said, ‘How could such a man as I talk to the president of so great a country in the midst of the greatest war in the history of the world? I simply put it to him man to man. What other way is there?’ You probably read the last speech of Roosevelt, the one he didn’t live to give, where he quotes Jefferson about science being a link between different countries of the world. Surely that was a fallout from Bohr’s discussion with him.” Wheeler told me a remarkable fact about the Hanford plant that I  had never heard before. It was the only plant in the United States that was shut down because of enemy action during the war. “How? Well,” Wheeler said, “the Japanese had an idea, which was a great idea—​we kept it quiet in the newspapers so they wouldn’t know how great an idea it was.” They sent paper balloons with incendiary bombs, in the air across the Pacific. Some of them set forest fires in the Pacific Northwest. One of them draped itself around the power line that fed the water pumps to the pile and shut it down. That incident, as one might imagine, caused a great deal of anxiety around the

100  Quantum Profiles project. Wheeler recalled that “there was a radar that kept up a surveillance against any possible overflights of planes. They picked up something and they checked all the airfields within a hundred miles. That particular thing turned out to be a flight of birds. “But the news of the balloon somehow percolated around among the children at school. My small boy, and a friend, told my wife that the Japanese were landing from a balloon and that we had to do something about it. She thought it was preposterous. But they insisted that the Japanese would land from a balloon. So she called up security and, instead of laughing it off, they took it immensely seriously. Well, it was not many days after that that I was coming out from lunch with my colleagues. Someone pointed up to the sky and said, ‘I think I see a balloon up there.’ I looked and couldn’t see it. Then someone else saw it, and then finally I saw it. It turned out to be the planet Venus in broad daylight.” Wheeler had enough contact with Los Alamos to know about the successful Trinity test of the atomic bomb on July 16, 1945. He was quite sure the war would now end. “I could see that the war would end,” he told me. “I wanted to get my family back east, even though nobody else had an indication that the war would end. A few weeks before school began I took them up to Vancouver and put them on the trans-​Canada train to Maine where they could spend some time with my wife’s parents. On the train, my wife was in the observation car with the newspaper. She had known what was going on, since she had been in on it before we had any secrecy. There were the headlines about the atomic bomb being dropped in Japan. She was so excited. All these Canadians were sitting around the observation car showing no signs of any interest, any excitement. Finally, she couldn’t contain herself, so she said, ‘Do you see this news?’ They said, ‘Well, yes.’ She said, ‘You see the war will be over in a few days.’ They thought she was crazy.” In the fall of 1945, Wheeler returned to Princeton and to fundamental physics. He decided that cosmic radiation represented a relatively inexpensive way for the university to get into elementary-​particle experimental physics, so he helped set up a cosmic-​ray laboratory. An expert on the safety aspects of reactors, he did a fair amount of advising and consulting. He was one of the people responsible for having safety domes built over reactors to hold in fission products in case of an accident. Wheeler told me of a meeting that he had with his British counterparts on reactor safety in October 1949. “In our work, we had come up with the formula that a plant, for safety reasons, should be situated no closer to a city than 0.01 mile times the square

John Wheeler  101 root of the reactor’s power level in kilowatts. It turned out, when we compared notes, the British had come up with an essentially identical formula, which shows that meteorology is the same in different countries. We went into earthquakes and fires, and the possibility of big oil tanks that would be ignited in case of trouble. After all that, we got to the question of what the chance would be of realizing the worst-​case scenario. I argued that there was no way to figure it. You ought to figure, as well, the chance that somebody could come along who could turn off safety system A or B or C, someone who is so well trusted that he gets through the security systems. I said that this was something that nobody could predict, because it depended on the climate of opinion at the time. I had collected figures on sabotage in World Wars I and II. I raised the question of what kind of person would do this. I said that such a person had to be completely trusted, technically very good, a loner, animated by some strange ideology. As I was speaking, Klaus Fuchs was listening to me across the table. A month later he was in jail for spying at Los Alamos. “A few years ago, Sir Rudolf Peierls, who had been responsible for bringing Fuchs into the bomb project, told me that when he read that Fuchs was in prison he went immediately to see him. He said to Fuchs, ‘There has been some terrible mistake. We’ve got to get proper legal counsel for you.’ Fuchs said, ‘No, there’s no mistake. I was a spy.’ Peierls said, ‘How could you?’ Fuchs answered, ‘Well, I meant to give control of the world to the Russians.’ Peierls said, ‘But how could you?’ ‘But then I meant to tell them what was wrong with them.’ ” Wheeler told me a little epilogue to this. In 1979, the year of the Einstein centennial, Wheeler gave eighteen Einstein lectures in eight countries, involving eight crossings of the Atlantic. One of the lectures was in East Germany. “It was very strange compared to the others. The audience was restricted only to important political figures—​the prime minister and the like. Among the list of notables, I noticed the name Klaus Fuchs. I asked an East German colleague if, during the coffee break, he would be willing to bring Fuchs over. When he came over I was careful to have my notebook in one hand and a coffee cup in the other. I didn’t want to shake hands with him. We talked for about five minutes about the East German nuclear power program that he was busy with.” In 1949, Wheeler was awarded a Guggenheim Fellowship. He decided to use it to go to Paris so his children could learn French. But he commuted to Copenhagen every couple of weeks to talk to Bohr. As it happened, this

102  Quantum Profiles was also the time when there was great agitation in this country—​much of it being carried out in secret—​about whether the United States should enter into a full-​scale crash program to build a hydrogen bomb. Wheeler took no part in this discussion. He was, as he told me, “minding my p’s and q’s in Paris.” But being in Europe so soon after the war gave him an acute sense of its fragility. “It seemed to me,” he recalled, “like a house of cards which a wind from the east could blow down. At any rate, the phone started ringing in the pension where we were living in Paris. It was my friends from the Atomic Energy Commission in Washington, putting the heat on me to go to Los Alamos and take part in the H-​bomb enterprise. I certainly didn’t want to do it. I held off the decision until I could go to Copenhagen and talk to Bohr. I was staying at his house for two weeks. One day at breakfast I told him of the struggle I was having with my conscience about going back to Los Alamos. It was not his way to advise a person directly, but I can never forget a phrase he used. He asked, ‘Do you image for one moment that Europe would now be free of Soviet control if it were not for the bomb?’ That was enough to tip the scales.” Wheeler then went on, “I arrived in Los Alamos in February of 1950 and got up to speed on a lot of things because I had not worked on bomb design. I reviewed the classified literature and looked at ways to make things go. Of course, in retrospect, one can see that we, the whole community from the working days of Los Alamos to that time, had, as far as the H-​bomb was concerned, been trying to get the right answer to the wrong question. We were then at Los Alamos still struggling to get the right answer to the wrong question. I said to myself, ‘Look, we ought to have more people in this enterprise, and we’re not going to get more people to Los Alamos in the present state of people’s minds.’ People were tired of war. The only way to get them would be to get them to come to Princeton for a year or two. So, with the approval of Los Alamos, and checking it out with the Princeton administration and with Oppenheimer at the Institute, we set up in Princeton.” Wheeler was able to get the use of some buildings that had been abandoned by the Rockefeller Institute for Medical Research, at what is now the Forrestal Center. Princeton astrophysicist Lyman Spitzer had agreed to help with the project, and because of his mountaineering interests had named it Project Matterhorn. As it turned out, he never did work on the hydrogen bomb because, while skiing in Aspen, he got an idea for using nuclear fusion in a controlled manner for making power. It was this device that Wheeler named the stellarator. It was the forerunner of what is now the most

John Wheeler  103 promising method for making fusion power, the so-​called tokamak. This meant that the Matterhorn project became two Matterhorn projects, A and B, with B, under Wheeler’s direction, engaging in bomb design. Wheeler told me that at the time, he wrote, phoned, or visited about 120 scientists in an attempt to recruit them for the work. Very few senior people were interested, but he did manage to recruit a few of the younger ones. In December 1950, Stanislaw Ulam and Edward Teller, as Wheeler put it, “suddenly realized that we had all been asking the wrong questions. By asking the right questions they immediately put us on the right track. On the other hand, Teller was at absolute loggerheads with the group at Los Alamos. He felt that they did not have the people that were needed, or the push that was needed. It was clear to me that we at Princeton could provide a very useful function with what we had. So instead of being a project to search over a long term for a solution, it became a short-​term project to calculate out specific designs. We ran through burning calculations with this fuel or that fuel or the other fuel, or this dimension, that dimension, the other dimension. It was a mixture of hydrodynamics and nuclear physics—​of design. Through the month of May and beyond, we were calculating night and day. We were using the IBM facilities in New York, the UNIVAC in Philadelphia, and the facilities at the Bureau of Standards in Washington—​all of them to meet the computing needs we had at that time. From today’s perspective, it was ridiculous. But we were working with what we had. Sometimes those poor devils, like John Toll, who was a graduate student then, worked for thirty-​six-​hour stretches.” In June 1951, the General Advisory Committee to the Atomic Energy Commission met at the Institute for Advanced Study to discuss the current technical status of the project. As Wheeler was talking, Toll rushed in with a chart he and his group had spent all night preparing. Wheeler said, “I interrupted my speaking while they raised the window from the outside so as to slide the chart through. The secretary pasted it up on the blackboard, and you could see from the chart how the burning progressed.” It was this computation that convinced Oppenheimer that the hydrogen bomb was, in his indelible phrase, “technically sweet,” and the bomb was built. I asked Wheeler if it had, in his view, really been necessary. If the United States had not built it, what would the Russians have done? He pointed out that the Soviets exploded their hydrogen bomb nine months after the Americans, which must have meant, he was persuaded, that they were working on it while the US debate was still in progress. Wheeler witnessed

104  Quantum Profiles the first test of a hydrogen bomb on November 1, 1952, in the Pacific. It was the largest test the United States ever made (apparently larger than had been anticipated), although some of the above-​ground Soviet tests were even bigger. Part of the fallout from these tests was, very likely, Wheeler’s attitude toward fallout shelters. While most of his colleagues looked on skeptically, Wheeler had one constructed in the basement of his home in Princeton. He told me that his architect had been through the bombardment of Budapest and told him that while it was not necessary to have a “fancy” shelter, some shelter was really important. Wheeler’s view, not shared by most people, was that shelters were “a part of life in the last quarter of the twentieth century. My conscience bothers me all the time that I have not done something to get shelters for my children. The trouble is that they’re scattered around so much—​they’re so mobile—​it would take some doing. Our shelter in Princeton was not solely for us. It was for the neighborhood. The neighborhood knew that, and we had supplies enough.” Even before he finished with the Matterhorn project, Wheeler was anxious to get back to teaching and fundamental physics. Since 1952, Wheeler had written some half dozen books and innumerable articles on Einstein’s relativity theory and its implications for gravitation and cosmology. It was in this context that at a conference in 1967, he coined the term black hole. Prior to that, he had been using locutions such as “completely collapsed gravitational object” to describe the collapsing stars first discussed by Oppenheimer and Snyder in 1939. In fact, Wheeler’s first serious encounter with relativity, a subject he is so often identified with, did not begin until 1952. He was given permission to teach a course in the theory at Princeton that year. Einstein was still alive, and at the end of the course, he invited Wheeler to bring his students over to his house for tea. One of them asked Einstein what would happen to his house after his death. Einstein replied that it would never become a place of pilgrimage where the pilgrims would “come to look at the bones of the saint.” Wheeler’s students from his relativity period, and their students and their students’ students, populate the physics faculties of universities all over the country. It had been Wheeler’s intention to live out his professional life in Princeton. Throughout the years, he had had several offers to leave Princeton but always turned them down. However, in 1976, he received an offer from the University of Texas at Austin that was too good to turn down. It was not a matter of financial inducement—​Wheeler went to Texas on half salary—​but

John Wheeler  105 the fact that the Ashbel Smith and Roland Blumberg Professorship, which he was offered, had no formal retirement age. At Princeton, as at most universities, the retirement age was seventy, and after that, the professors were allowed to lecture only on special occasions. For Wheeler, the notion of life in a university without students and regular teaching was intolerable. He once said to me, “As far as I am concerned, graduate students are the number one way of advancing. How can you fight any battle except alongside your graduate students?” Part of his arrangement with Texas included money for students. During the first four years he was in Austin, Wheeler organized conferences for undergraduates from the United States, Canada, and Mexico—​something that he called “recruiting through resonance”—​and persuaded some outstanding students to come to Austin. When I  visited Wheeler in Texas in 1985, he told me that he had picked a definite date to retire. Indeed, a few years later, the Wheelers moved back to Princeton. For a physicist of his eminence, Wheeler had relatively little involvement in government affairs. His abiding interest was always how nature works—​how the laws of nature are put together on the deepest level. This, of course, has philosophical and metaphysical overtones, and therefore many of Wheeler’s articles for the general public often sound philosophical and metaphysical. (Freeman Dyson once commented, after reading something of Wheeler’s, that it sounded like Beowulf) Despite Wheeler’s intentions, this has given some aid and comfort to the New Age quantum-​Buddhists. For example, in The Dancing Wu Li Masters, Gary Zukav quotes the following from Wheeler:  “May the universe in some strange sense be ‘brought into being’ by the participation of those who participate? . . . The vital act is the act of participation. ‘Participator’ is the incontrovertible new concept given by quantum mechanics. It strikes down the term ‘observer’ of classical theory, the man who stands safely behind the thick glass wall and watches what goes on without taking part. It can’t be done, quantum mechanics says.” Of this somewhat Beowulfian passage, Zukav comments, “The languages of eastern mystics and western physicists are becoming very similar.” (See the story of Bell and the Dalai Lama in c­ hapter 1.) Wheeler told me that he had avoided reading certain books on the interpretation of quantum mechanics—​he did not specify which—​because “then I  can avoid having to comment on them—​anything I  said would be used against me. If I damned them it would be prejudicial. If I praised them . . . trouble.” Nonetheless, he became extremely annoyed when, at a meeting of the American Association for the Advancement of Science, he

106  Quantum Profiles was put on the same program with three parapsychologists. He prepared an uncharacteristically acidic written statement, which he handed out at the meeting. It contained, in reference to parapsychology, the phrase “Where there’s smoke, there’s smoke.” Both from his course at Columbia and from conversations with him, I concluded that Wheeler’s views on quantum mechanics were pretty much orthodox Bohr. When I asked Wheeler if that was true, he replied, somewhat elliptically, “Yes, if you are willing to say that following Bohr is to wake up every morning ready to change your views completely.” From Wheeler’s point of view, at least on the morning he described it to me, Bell’s inequality is simply a part of ordinary quantum mechanics with no mystical overtones whatsoever. Wheeler had no interest in theories with hidden variables. He said to me, “We had Bohm here. I invited him to Austin for a week so he could talk about it. I don’t think anyone was following the Pied Piper. In my course at Columbia I was just trying to state what quantum mechanics is as clearly as possible. That phrase ‘No elementary quantum phenomenon is a phenomenon until it is a registered phenomenon, that is to say, brought to a close by an irreversible act of amplification’—​that is the essence of it. However, I am still puzzled by elementary quantum phenomena that are not put to use: the flash on a zinc-​sulfide screen on some faraway planet where there is no life. It’s just part of the grand mass of collisions between electrons and atoms that go on all the time—​all over the place. It doesn’t rate any special claim. There’s no heavenly choir that’s clapping its hands at having that happen. I am just driven crazy by that question. I confess that sometimes I do take 100 percent seriously the idea that the world is a figment of the imagination and, other times, that the world does exist out there independent of us. However, I subscribe wholeheartedly to those words of [Gottfried Wilhelm] Leibniz, ‘This world may be a phantasm and existence may be merely a dream, but,’ he went on to say, ‘this dream or phantasm to me is real enough if using reason well we are never deceived by it.’ ” For a while, Wheeler turned away from elementary-​particle physics. He once told me, “I must have got the feeling that the only thing that could be worse than a tunnel that comes to a dead end is a tunnel that goes on forever.” As a thought experiment, he invented an object that he originally called a kugelblitz—​a ball of radiation—​held together by it own gravitational attraction. Later he changed its name to geon, the name that has stuck. As he described it to me, “It’s something in which light goes around in a circle. The light energy generates an equivalent mass, and that mass holds the thing

John Wheeler  107 together gravitationally as it goes around in that circle. It’s stable against losing any individual photon, but it’s unstable in the sense that a pencil is unstable. A pencil standing on its tip can fall over one way or the other, although every individual atom in the pencil is stably held there, just as the individual photons are held together in this geon. But the geon is unstable, because if you rotate it more rapidly, it will fly apart into free photons, and if you rotate it more slowly, it will contract inward and collapse.” The geon was meant to serve as a kind of “toy model” of a black hole. “Then,” Wheeler went on, “I realized that although I thought I was getting away from the problems of particle physics and the constitution of matter, I wasn’t at all. Because as this thing collapses, the radiation gets denser and denser and its wavelength gets shorter and shorter. You begin to produce pairs of positive and negative electrons, and then pairs of all the other particles. So you might as well have started with the grand mess to begin with. So that didn’t offer any true way through. “After that,” Wheeler continued, “I got deeply concerned with what the quantum theory has to say about this whole subject. I read all the papers on quantizing general relativity, written by wonderful people. But they certainly were not transparent to me, not in a way that one could see at a glance what was going on. At any rate, I ended up with this picture of what quantizing gen­ eral relativity means—​the idea of superspace. This is a space in which each point represents a three-​dimensional geometry; it’s a space in which a history of a geometry is not a line running through it but a leaf cutting through it. But this leaf has only one-​third the dimensionality of the superspace as a whole. The three-​dimensional geometries that lie on a leaf can be fitted together like the boxes in a Chinese puzzle. They can be fitted together to make the four-​ dimensional space-​time geometry, fitted together in a unique way.” When I told Wheeler I was not sure that I could see all the leaves fitting together, he laughed and went on, “That is only the classical story. But the quantum story is that there is no longer a sharp distinction between the three geometries that constitute most of superspace and the particular three geometries that constitute some particular space-​time. Three geometries that occur with appreciable probability are far more numerous than can be fitted together in any one space-​time. The very idea of space-​time is then a wrong idea, and with that idea failing, the idea of ‘before’ and ‘after’ also fails. That can be said so simply, and yet it is so hard for the lesson to grab hold in the world. It’s a straight analogy with what you have in the case of a particle moving in ordinary space-​time. In classical physics it moves in a world

108  Quantum Profiles line, a one-​dimensional world line. But in quantum mechanics this becomes a wave packet localized near where the classical world line would have been. We know that the idea of a classical world line is, strictly speaking, absolutely wrong. Yet for many purposes it is just the right thing to use, even though the true story would be to use a wave packet. In the same way, the idea of space-​ time is absolutely wrong, but in most cases it is just the right thing to use. I wrote down the wave equation that describes the propagation of a wave in this superspace in a schematic form that was later spelled out in more detail by Bryce DeWitt. This is the equation that people like Jim Hartle and Stephen Hawking use to discuss cosmology. “But,” said Wheeler, “we’re not content merely to utter words about the universe. We want to see the machinery taken apart. And, by George, we’re so far from taking the machinery apart—​just unbelievably far. For example, we feed in dimensions—​four dimensions, six dimensions, ten dimensions, eleven dimensions—​as if at the bottom of things there is any dimensionality at all. There can’t be. It must be derived from some point of view, some way of doing physics, some overall picture in which dimensionality, at least in the beginning, does not even start to enter. Time. Why is there any such thing as time? Why should it be one-​dimensional? Time cannot be fundamental. The ideas of before and after fail at very small distances. They fail at the Big Bang. Why is the quantum there? If you were the Lord, building the universe, what would convince you we couldn’t make a go of it without the quantum? In our work in physics, we take the quantum theory as a given. It’s a sausage grinder. We drop our problems in, and turn the crank, and get out the answers. Where did the sausage grinder come from?” Wheeler smiled and concluded, “It’s such an exciting thing to be in physics. I must say that every day, when I wake up, it’s a miracle. Why should there be any world here? It’s incredible. What’s the explanation for it? It must be absolutely beautiful—​absolutely simple. And how stupid we are not to see it. I feel in desperation trying to find a clue all the time.”

Epilogue The principal conversations with Wheeler on which this account is based took place in the spring of 1985 in Austin, Texas. At the time, Wheeler, who was then seventy-​four, told me that he had given the university administration a firm date for his retirement from the University of Texas but that he

John Wheeler  109 had not yet made it public. He had in fact decided to retire the following year. As it happened, that year Wheeler had a triple-​bypass operation and then moved back to Princeton. Not knowing how his life had been affected by all of this, I was a little hesitant about troubling him with yet another interview. However, mutual friends encouraged me to call him at his office in the physics department at Princeton University. When I did so, he invited me to come down and see him that very week So on a lovely, sunny winter’s day at the end of February 1986, I took the train from New York to Princeton and found Wheeler in his third-​floor office in Jadwin Hall. Wheeler looked totally unchanged, as did the state of his office: a warren of books, preprints, notebooks, and schedules. He said that the day before, a TV crew from Nova had been there to talk to him about quantum mechanics, and the next day, a Japanese TV crew would be by to ask him about the Bohr-​ Einstein debate. He showed me an early copy of his new book A Journey into Gravity and Spacetime, which, judging from the delightful illustrations I  saw, would be one of those festive, Wheelerian intellectual banquets. Just before my visit, Wheeler had sent me a copy of his latest paper, titled “Information, Physics, Quantum: The Search for Links.” It is pure Wheeler at his most Beowulfian. It features “three questions,” “four no’s,” and “five clues.” (The italics are Wheeler’s.) Among the questions, one finds “How come the quantum?” and among the clues, one finds “No question? No answer!”—​an allusion to the quantum-​mechanical umpire (“They ain’t nothin’ till I calls ’em”). Along with the paper came a postcard with Wheeler’s return address. It had several entries on the back, with blank spaces for responses. Among the entries were “The idea in it (if any!) which in your estimation has the best chance to move us ahead? Page no. or phrase,” and “The idea most likely to be mistaken?” It reminded me of Wheeler’s Columbia University course. It was clear that we were not going to get any peace in Wheeler’s office, so we repaired to a temporarily unoccupied lounge on the floor below. When I told Wheeler how well I thought he looked, he said that because of his heart surgery, he was “good for another hundred thousand miles.” Of his move to Princeton, Wheeler commented, “Janette and I finally realized that we had been very poor parents. We had not brought up a single one of our children right; not one of them had settled in Texas. They all live up and down the Metroliner route, so we decided to move back to these parts. I had already retired from Texas. I thought that at the age of seventy-​five, it was not respectable to keep a chair away from some younger person. We moved into a retirement community some ten miles from Princeton, so I don’t have to

110  Quantum Profiles mow the lawn and I don’t have to repair the roof. My friends here at the university were kind enough to give me an office, so we are now back in business.” For Wheeler, business inevitably included students. He had three PhD students in Texas, which he still visited for several weeks a year, and he also supervised some undergraduate honors theses at Princeton. “Undergraduate theses,” Wheeler commented, “are often more adventurous than PhD theses. Students don’t have to go through the whole rigmarole. I have the feeling that it is so important to learn—​to teach. We both know of the little old lady who said, ‘How can I know what I think, until I hear what I say?’ I leave, in order to catch my bus, at three fifteen in the afternoon, before the departmental tea. The tea is where you meet graduate students, so I don’t know many here. I love that phrase of Oppenheimer’s, ‘Tea is where we explain to each other what we don’t understand.’ ” I told Wheeler that I had had a number of conversations with Bell about quantum theory. “He’s a wonderful fellow,” Wheeler noted. “Did he say to you,” Wheeler asked, laughing, “ ‘I’d rather be clear and wrong, than foggy and right’?” I  told Wheeler that Bell had not used exactly those words but that it certainly sounded like him. I  also told Wheeler that from the time that Bell began to study quantum theory, he had conceptual problems with it and that I had asked Bell if, at that time, he thought that the theory might simply be wrong, to which Bell had answered, “I hesitated to think it might be wrong, but I knew that it was rotten.” At this, Wheeler burst into a marvelous peal of laughter. The idea of the young Bell rebelling against the “rottenness” of quantum theory struck Wheeler as incredibly funny. I explained to Wheeler that Bell’s problems were not in the mathematics but in the meaning of concepts such as “irreversible,” “apparatus,” “measurement,” and the like, and I asked Wheeler if he had had similar misgivings when, as a teenager, he began studying Weyl’s book in that field in Vermont, surrounded by cows. “No,” Wheeler answered, “I had the feeling that the stuff was beautiful. I learned it from Weyl, and Weyl had the art of putting things in a lovely perspective. More so than anybody else I have ever read. That book was just a treat. So the feeling of ‘rotten’ would be the absolutely last feeling I would ever have about it. ‘Beautiful’ is what I would call it. To me, it’s the magic way to do it. I think that having started early and having used it in lots of different contexts, all the way from my doctor’s thesis on the dispersion and absorption of light in a helium atom, to nuclear physics, to the decay of elementary particles, I feel absolutely at home with it. But John Bell’s question

John Wheeler  111 I certainly sympathize with. An ‘irreversible act of amplification’? As Eugene Wigner always says, ‘What means it “irreversible” ’?” Did Wheeler have an answer to Wigner’s question? “No, I  don’t,” he replied. “I think it is just wonderful to have puzzles like that staring us in the face. You’d be amused,” he went on. “Every day I try to write down something in my notebook, although I don’t always succeed, pushing things ahead just a little bit. I only got in two or three sentences this morning. ‘Nada. The photon doesn’t exist in the atom. It doesn’t exist in the photodetector after the act of emission, and you have no right to talk of what it’s doing in between. Nada—​ it’s nothing.’ Then there’s the irreversible act of amplification where you’ve got a whole lot of things. It’s nada to nada.” I asked him if this was not just the point of Einstein’s unease. How can it be, he’d asked, that the photon is not there even “in between”? Wheeler agreed, and then I asked him if he had ever been troubled by that. “No,” he said. “Quantum theory does not trouble me at all. It is just the way the world works. What eats me, gets me, drives me, pushes me, is to understand how it got that way. What is the deeper foundation underneath it? Where does it come from? So that we won’t see it as something that is unwelcome by friends that we admire—​John Bell and many others—​it will be something that will make you say, ‘It couldn’t have been otherwise.’ We haven’t gotten to that stage yet, and until we do, we have not met the challenge that is right there. I continue to say that the quantum is the crack in the armor that covers the secret of existence. To me, it’s a marvelous stimulus, hope, and driving force. And yet I am afraid that just the word—​‘hope’—​is what does not eat, or possess, or drive so many of our colleagues in the field. They’re content to take the theory for granted, rather than to find out where it comes from. But you would hardly feel the drive to find out where it comes from if you don’t feel that the theory is utterly right. I have been brought up from ‘childhood’ to feel that it is utterly right. Here I was, reading that book of Weyl’s at the age of eighteen and just crazy about it.” I then commented to Wheeler that from his perspective, the EPR experiment and all the fuss surrounding it must be something of a “nonstarter.” “Yes, yes,” Wheeler agreed. “Aage Bohr [Niels Bohr’s Nobel Prize-​winning physicist son] expressed the same point to me the last time I talked to him. He just couldn’t understand why there were all these conferences—​conference after conference—​on EPR, when it is just the way it works. It is just exactly the wrong thing to be asking about. There is a conference coming up in Finland in August with some people I’d love to talk to, but I’ve written them to say that

112  Quantum Profiles I’m not going. If you keep trying to pull apples off the apple tree, after a while it doesn’t do. I hope that I am not being too propagandistic in speaking of the idea that when we see it all, it will be so simple we’ll all say, ‘How stupid we’ve been all this time!’ We’ve got to look for the right word, the right image. So you try one word for a day, for a week, for a month, or for a year, and then you give it up and try another one.” I asked Wheeler if he had ever been tempted by the hidden variables. “It’s so interesting,” Wheeler responded. “You’ve probably seen this picture of the potential that you have to use in the Bohm–​de Broglie approach to describe, by hidden variables, the double-​slit experiment. You see the electron coming in and doing this crazy thing. You may think that the Himalayas are wonderful, but this potential beats them by far. Yet they never tell you where the ‘screwdriver’ is—​where in that morass of valleys and peaks the electron is going to start off. It just transforms the problem that eats them, back to square one. But in the course of it, it encumbers the landscape with a lot of decoration.” I was curious about whether Wheeler had been surprised by Einstein’s reaction when, in the 1940s, he went to see him with Feynman’s new formulation of quantum theory. “Yes, yes, I was,” Wheeler answered. “I thought it would ring a bell. Maybe I just didn’t pound it hard enough. Maybe I was just too much in awe of him to beat on a table and shout.” Since I had by then read a good deal of Einstein on quantum theory, I suggested to Wheeler that his objections went far beyond formalism. The way I put it was that he could have presented Einstein with a formalism that was written with a gold fountain pen and gold ink, and it wouldn’t have changed his view. The thing that Einstein couldn’t abide was Wheeler’s quantum-​mechanical umpire: “They ain’t nothin’ till I calls ’em.” Wheeler added, “ ‘I can’t believe God plays dice’ was Einstein’s response.” I told him that I didn’t think it was the matter of dice that bothered Einstein. After all, he had been one of the creators of modern statistical mechanics, which is built in a fundamental way on probabilities. I suggested to Wheeler that what bothered Einstein was “reality.” He couldn’t stand the idea that “they ain’t nothin’ till I calls ’em.” He insisted that one calls them the way they are. He felt that there was an objective reality that would include a description of the photon between the detectors. It was not an improvement of the quantum-​mechanical formalism that Einstein was after; his concern was with reality. Speaking of the influence of Einstein, Wheeler told me a story involving the logician Kurt Gödel. Gödel was perhaps Einstein’s closest intellectual

John Wheeler  113 companion at Princeton. The two of them made innumerable walks together between the town of Princeton and the Institute, talking mainly about quantum theory. In any event, in the 1970s, Wheeler, Charles Misner, and Kip Thorne wrote their book on gravitation. They were working in different cities, but for the completion of the book, they were able to find an office at the Institute for a few weeks so that they could finish it. “We’d been slaving away,” Wheeler recalled, “and I said, ‘Why don’t we take twenty minutes off and have a little break? What shall we do? How about going around and seeing Gödel?’ So we went around, and knocked at his office. It was a nice spring day, sunny, but he was in there with his overcoat buttoned around him and an electric heater on the floor [constant fear of the cold was one of Gödel’s many eccentricities]. I introduced my young collaborators and said that I wondered if we could ask him what he thought of the relation between his principle of the undecidability of mathematical propositions and the indeterminism principle of Bohr and Heisenberg. But Gödel changed the subject. He wanted to know whether in the course of our work on this book on gravity we had found any evidence for, or against, a preferred sense of rotation of the galaxies. We had to confess that we just hadn’t even looked into that. We hadn’t said anything about his theory, his exact solution of Einstein’s equations of general relativity, which, incidentally, I had heard him present at the Einstein celebration here some years earlier. He was disappointed with us. “It turned out that he himself, as a preliminary step to get some evidence, had taken down the great Hubble atlas of the galaxies. Gödel, whom you think of as the mathematician among mathematicians, had taken a ruler and got the angle and made a statistics of these numbers and concluded that within the statistical error, there was no preferred sense of rotation. Incidentally, I ran into a man at the Institute a couple of years ago who was working on a biography of Gödel. He had gone through the papers of Gödel, and here were these pages after pages after pages of those numbers. It took a long time for him to figure out what they were. Of course, they were just this statistical work. “About a year after our visit to Gödel, I was down the hall here in the office of Jim Peebles [a prominent Princeton astrophysicist], talking to him about cosmology. Suddenly, the door burst open, and a student came in and threw down on the table a big thing. ‘Here it is, Professor Peebles!’ So I said to him, ‘What is it?’ He said, ‘It’s my thesis.’ ‘What’s it about?’ ‘It’s about whether there is any preferred sense of rotation in the galaxies.’ ‘How marvelous,’ I said. ‘Gödel will be so pleased.’ ‘Who is Gödel?’ ‘Well,’ I said, ‘if you

114  Quantum Profiles called him the greatest logician since Aristotle, you’d be downgrading him.’ ‘Are you kidding?’ ‘No, no.’ ‘What country does he live in?’ ‘Right here in Princeton,’ I answered. So I picked up the phone and dialed Gödel, reached him at home, and told him about this. Pretty soon his questions got to the point that I couldn’t answer them. I turned it over to the student, and pretty soon it got to the point that the student couldn’t answer them. He gave the phone to Peebles, and when Peebles finally hung up, he said, ‘My, I wish we had talked to Gödel before we did the work.’ “But it was at a cocktail party about a year after this at the house of Oskar Morgenstern—​only about eight or ten people including Gödel—​that finally Gödel broke down and said why he had been unwilling to talk about the relation between indeterminism and undecidability. He had walked and talked with Einstein enough, so he didn’t believe in quantum theory; he didn’t believe in indeterminism.” John Wheeler died on April 6, 2008, at the age of ninety-​six. The next part of this book deals with the correspondence of Einstein and his friend Michele Besso. Some of this correspondence has to do with quantum theory, and in it one finds Einstein at his most persuasive—​the sort of language that must have convinced Gödel.

3 Albert Einstein Collected here are three short pieces on Albert Einstein’s evolving views toward quantum theory, Einstein and J.  Robert Oppenheimer’s contrasting conclusions about the creation of black holes, and Einstein’s long-​standing friendship with Michele Angelo Besso.

Quantum Misgivings In 1923, Louis de Broglie suggested as part of a proposed PhD thesis that particles like electrons might also have the character of a wave. His thesis adviser, Paul Langevin, sent a copy of the thesis to Einstein, who replied that he found de Broglie’s ideas interesting and that he had some similar ideas. But exactly what those ideas were we never learned. Two years later, Erwin Schrödinger found the equation that describes these waves.1 Einstein was delighted. That is, until Max Born, among others, showed that the waves were not what Einstein was expecting. Rather than acting like light waves that oscillated in space, as both Einstein and Schrödinger had imagined, these were, in fact, waves of probability. Where they had large amplitudes, a particle was most likely to be found. At this point, Einstein and quantum theory parted company. In 1926, he wrote to Born: “Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but it does not really bring us any closer to the secret of the “old one” [Einstein’s affectionate way of referring to God]. I, at any rate, am convinced that He is not playing dice.”2 This marked the beginning of a period in which Einstein sought to demonstrate that the theory itself was wrong. This, in turn, led to monumental debates with Niels Bohr. In truth, Einstein did not emerge from these exchanges as the winner. He eventually settled on the view that the theory was not a complete description of reality; he spent the rest of his life trying to

116  Quantum Profiles find a suitable replacement. But working without any guidance from experiment gave little chance for success. Many people tried to induce Einstein back into the mainstream. John Wheeler told me that when his student Richard Feynman produced a new formalism for quantum theory, Wheeler thought it was so beautiful that his colleague would surely be converted. Einstein, of course, was having none of it. Einstein was a classical physicist at heart. As Jean Cocteau once said, poets tend to sing from their family trees. Einstein’s family tree was classical physics, the physics he learned as a student. While quantum theory was, in a sense, his child, it was not a child that he was prepared to accept. During his lifetime, Einstein wrote a vast number of letters. One cannot help but wonder how he had time for anything else. On April 16, 1926, he penned a note to Schrödinger. Although relatively brief, it is one of the most remarkable letters he ever sent. Einstein wrote that he had just heard about Schrödinger’s wave equation from Max Planck, and it seemed to him that there was something wrong with it. He wrote out the equation as

divgradϕ +

E2 ϕ = 0. b2 ( E − ϕ )

This equation, he noted, was defective. For two independent systems, the energies must be additive, which was clearly not the case for this equation. Einstein then proposed another equation to resolve the dilemma. The equation he offered was, in fact, Schrödinger’s original equation. Einstein had misremembered it. The Fifth Solvay International Conference took place in Brussels in October 1927.3 Einstein arrived at the conference determined to show that quantum theory was wrong. To help make his point, he offered a Gedankenexperiment intended to demonstrate that the Heisenberg uncertainty relation between position and momentum, ∆x ∆p >  / 2 , was not generally true. Einstein described an apparatus as follows.4 A diaphragm is suspended from a pair of springs that allow it to move up and down freely. Any displacements can be measured using a pointer and a scale. When a particle passes through a narrow slit in the diaphragm, its momentum is transferred to the diaphragm. The particle’s momentum is measured by the displacement of the springs, while the slit measures its position. It might then appear that both the position and the momentum of the particle could be measured simultaneously

Albert Einstein  117 to arbitrary accuracy. Bohr pointed out that Einstein had assumed that the position of the pointer could be measured to arbitrary accuracy without disturbing the momentum of the diaphragm, and hence the measurement of the particle’s momentum. When the uncertainty in this measurement is taken into account, the uncertainty between the particle’s position and its momentum is restored. Bohr had won. Undeterred, Einstein arrived at the Sixth Solvay Congress in 1930 having formulated another, far more diabolical Gedanken-​machine. This new device was designed to show that the energy-​time relation ∆E ∆t ≥  / 2 was not valid. This uncertainty relation is on a different footing from the others, which involve noncommuting operators; time cannot be represented by an operator, while energy can. Einstein described another box, this time suspended by a single spring. The box contained radiation and could be weighed, it was assumed, with arbitrary accuracy. At a predetermined time, according to an accurate clock, a shutter would open and a single photon would escape. Since photons carry energy, the mass of the box would change. This box would then be reweighed, from which the change in energy could be determined. The result would be a simultaneous measurement of time and energy, defeating the uncertainty principle. This demonstration gave Bohr a sleepless night, but the next day he was triumphant. Einstein had forgotten his own relativity theory! In arriving at his solution, Bohr analyzed how this measurement would actually be made. In the equation

∆q ∆T = g 2 , T c

the accuracy with which a determination could be made in terms of the displacement of the box is represented by ∆q.5 T is the time interval for this to take place in the absence of gravitation, and ∆T is the time interval in the presence of gravitation. Next, the notion of impulse is needed. This is the force applied over a time interval dt and is equal to the change in momentum during this same time. In this case, it is Tmg, where m is the mass of the box. The mass is only known with an accuracy of ∆m. The impulse then becomes T∆mg. For the measurement of the momentum to be meaningful, this impulse has to be greater than the uncertainty in the momentum ∆, hence

118  Quantum Profiles

T ∆ mg > ∆ p.

Substituting the formula for T yields

T ∆mc 2 > ∆p∆q >  / 2.

Since ∆mc2 is ∆E, the uncertainty principle is saved. At this point, Einstein stopped claiming that the theory was wrong. But for him, the theory still did not adequately describe reality. In this, he found an unexpected ally in Schrödinger. In December 1935, Schrödinger published a long article in Naturwissenchaften titled “Die gegenwärtige Situation in der Quantenmechanik [The Present Status of Quantum Mechanics].”6 This is the paper in which he described what has come to be known as the cat paradox:7 One can even set up some ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical 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 one 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 which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The ψ-​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.8

Putting aside the issue of producing a wave function for a macroscopic cat, what Schrödinger is really discussing in this excerpt is the phenomenon he termed entanglement. In this situation, the cat is described by a wave function,

ψ cat = ψ dead + ψ alive .

Albert Einstein  119 If the cat is replaced with spin in two directions, up and down, the real quantum-​mechanical issue becomes clear. Writing the spin wave function as

ψ spin = ψ up + ψ down

describes a situation in which the spin is neither up nor down. This is the true novelty of quantum mechanics. When observed, the cat will be either dead or alive. The observation projects out one piece of the wave function, while the other is simply detached; the same goes for the spins. There is much in Schrödinger’s 1935 paper about measurement. Though Einstein hinted at it, he never really came to grips with what is now known as the measurement problem. Put simply, quantum mechanics, as characterized by the Schrödinger equation, cannot describe the kind of projections that Schrödinger is describing. The solutions to the Schrödinger equations are reversible in time, while projections are not. Projections have no inverses. Various attempts have been made to solve the measurement problem, but in my view, none of them is completely satisfactory. Schrödinger was inspired by a paper published in May 1935 by Einstein, Boris Podolsky, and Nathan Rosen.9 “The appearance of [their] work,” Schrödinger wrote, “was the impetus to the present—​shall I  say paper or general confession?”10 At the time, Podolsky, who seems to have actually written the paper, was a fellow at the Institute for Advanced Study. Rosen was a much younger assistant to Einstein. Podolsky and Rosen, and subsequently Schrödinger, made their argument in terms of position and momentum; this approach lends their papers a classical air. It is much simpler to frame the argument in terms of spin. Particles like electrons have a spin of ½ in the usual units. With respect to some axis, the spin can only point in one of two directions, up and down. Suppose there are a pair of electrons in a state described by the wave function as

u (1)up u (2)down .

Suppose also that there are two observers equipped with magnets. The magnets can interact with the spin of the electrons, causing the electrons with spin up to follow one trajectory and the electrons with spin down to follow

120  Quantum Profiles another. This will constitute a measurement of the electron’s spin orientations. There is nothing here, it should be noted, that involves entanglement. Consider another state in which the spins of paired electrons amount to an overall spin of 0. This is known as a singlet state, and, normalization aside, it can be described as

u (1)up u (2)down − u (1)down u (2)up .

In this scenario, there is a fifty-​fifty chance whether, say, electron 1 is spin up or spin down. This is an entangled state. If nothing is done to destroy the entanglement, there will be a perfect anti-​correlation between the two spin directions, no matter how far apart the magnets are. If one observer sees spin up, the other will sees pin down, and vice versa. In a letter to Born, Einstein described this sort of thing as spukhafte Fernwirkung (“spooky action at a distance”). In this instance, “action at a distance” is an apparition from classical physics. There is no action here, spooky or otherwise. In common with position and momentum, the values of the spins in different directions are connected by an uncertainty principle. For any measurement of the value of the spin in direction z, the value in direction x, as far as that experiment is concerned, is completely indeterminate. A subsequent measurement in direction x will reveal the same anti-​correlation. Confronted with this situation, Einstein, Podolsky, and Rosen concluded that the wave-​ function description cannot be the whole story. There must be some underlying theory that makes sense of it all. In 1944, Einstein wrote to Born: We have become Antipodean in our scientific expectations. You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture. I firmly believe, but I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of the quantum theory does not make me believe in the fundamental dice-​game, although I am well aware that our younger colleagues interpret this as a consequence of senility. No doubt the day will come when we will see whose instinctive attitude was the correct one.11

Schrödinger died on January 4, 1961. Along with a small group of colleagues, I had visited him in his apartment in Vienna the previous spring.

Albert Einstein  121 There was no cat. Schrödinger did not like cats. As we were leaving, he remarked, “There is one thing we have lost since the Greeks.” We paused. “Modesty,” he added, in his lightly accented English. I have no idea what he meant, and I regret not asking him.12

Black Holes On May 10, 1939, a paper by Einstein titled “On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses” was received by Annals of Mathematics.13 On July 10, 1939, a paper by Oppenheimer and Hartland Snyder, “On Continued Gravitational Contraction,” was received by Physical Review.14 Oppenheimer and Snyder’s paper was the first to be published, appearing at the beginning of September; Einstein’s paper followed a month later. The two papers, which are both correct within the limits of their assumptions, offered opposing views on the creation of black holes. Einstein showed why black holes could not be created. Oppenheimer and Snyder, on the other hand, demonstrated how to create them. This discussion explains how they could both be right. The story begins in 1915. Karl Schwarzschild was stationed on the Russian front. He had volunteered for the German army at the outbreak of war. At the time of enlisting, Schwarzschild was a professor of physics and director of the Astrophysical Observatory in Potsdam. While serving in the army, he still found time to continue his scientific research. Schwarzschild was familiar with the general theory of relativity, the first version of which had been published in early December 1915. Prior to its publication, Einstein had presented the new theory to the Prussian Academy of Sciences during a lecture in Potsdam on November 25.15 In his spare time at the front, Schwarzschild solved a problem in relativity that Einstein did not think had an exact solution. His letter to Einstein describing the solution was sent on December 22, less than a month after the lecture in Potsdam.16 Under Newtonian gravitation, using the force law between two masses M and m, where a is acceleration and G is the gravitational constant, 6.674 08(31) × 10-​11 m3 kg-​1 s-​2, the equation for Newton’s law is

GmM = ma. r2

122  Quantum Profiles Finding the trajectories of gravitating objects involves solving the vector form of this differential equation. In general relativity, however, there is no gravitational force—​gravity alters the geometry of space-​time. An exact solution is a closed expression for this alteration, such that

ds 2 = g ijdx i dx j ,

where ds2 represents the square of the infinitesimal distance between two space-​time events, gij is the metric tensor, and repeated indices are summed one to four. Einstein had not sought exact expressions for this metric in contrived situations. Instead, he focused on approximate expressions in more physically realistic situations, such as planetary orbits or the bending of starlight as it passed the sun. He replied to Schwarzschild the following month: “I read your paper with utmost interest. I had not expected that one could formulate the exact solution of the problem in such a simple way. I liked very much your mathematical treatment of the subject. Next Thursday I  shall present the work to the Academy with a few words of explanation.”17 In devising his solution, Schwarzschild had analyzed the gravitation produced by a spherical mass of constant density. This scenario had long been studied under Newtonian gravitation and is sometimes referred to as the Kepler problem. From the observations of Tycho Brahe, Johannes Kepler determined that the planetary orbits were elliptical rather than circular. Isaac Newton, and others, showed that the orbits produced by such a spherical mass acting on a test mass would be conic sections: an ellipse (the circle was a special case), parabola, or hyperbola. Schwarzschild’s contribution was centered on the four-​dimensional geometry. He showed that test particles move along paths that minimize the four-​dimensional distance between two points in space-​time. The Newtonian solution would then emerge as an approximation when the gravitational interaction was taken to be weak. The Schwarzschild metric is

dr 2  r ds 2 = − c 2 dτ 2 = −  1 − s  c 2 dt 2 + + r 2 dθ2 + sin2 θ dϕ2 , rs  r 1− r

(

)

Albert Einstein  123 where τ denotes the time measured by a clock in the rest frame of the moving object.18 The polar coordinates speak for themselves. Consider the quantity rs, known as the Schwarzschild radius. For a spherical mass M,

rs =

2GM . c2

It has the dimensions of length, as is evident if the numerator and denominator are multiplied by m. GMm is the potential energy multiplied by a distance. If G is set to zero, the metric becomes the flat space-​time metric in polar coordinates. The 2 in the equation is inexplicable except by calculation. Despite having a radius of more than 696,000 kilometers, the sun’s Schwarzschild radius, the corresponding value for rs, is approximately 2.95 kilometers. This is just as well, because, as we shall see, if these two values were the other way around, the sun would, in fact, be a black hole. Supermassive black holes have been found at the center of galaxies, including our own, that have masses a billion or more times that of the sun and correspondingly large Schwarzschild radii. At the Schwarzschild radius, the metric is singular—​there is no concept of time, and space is infinite. There is also a singularity at the origin. It has been known for many years that it is possible to redefine the coordinates so that the singularity at the Schwarzschild radius disappears. When written in this form, which both Einstein and Oppenheimer used, the physics is more transparent. When Einstein was writing his 1939 paper, possible orbits for a test mass in the vicinity of a spherical mass that was producing the Schwarzschild metric were well understood. Circular orbits would be possible, provided they were not too close. The limit was 1.5 times the Schwarzschild radius. At this radius, the object would be moving at the speed of light. For any smaller radius, it would have to move at speeds greater than that of light. This is such a curious result that a derivation merits consideration.19 For a circular orbit, the Schwarzschild metric reduces to

 r ds 2 = − 1 − s  c 2 dt 2 + r 2 dθ 2 . r 

This leads to a simple relationship for the angular velocity

dθ = ω , namely, dt

124  Quantum Profiles



ω2 =

 GM   2  c r3

.



This is the Schwarzschild version of Kepler’s third law. Putting this relationship into the metric yields

 3 GM  2 ds 2 =  1 −  dt , r c 2  

which says that for circular orbits, the radius must always be larger than 1.5 times the Schwarzschild radius. Einstein made use of a version of this in his argument. He imagined trying to construct a shell around the central mass by putting successive particles in circular orbits around the sphere at the Schwarzschild radius: The essential result of this investigation is a clear understanding as to why the “Schwarzschild’s singularities” do not exist in physical reality. Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The “Schwarzschild singularity” does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light.20

A Schwarzschild black hole is a self-​gravitating mass described by a metric with a Schwarzschild singularity.21 Oppenheimer and Snyder showed that such an object can be formed by collapsing matter. Their conclusion was correct. What does this mean for Einstein’s paper? A clue can be found in the sentence “Although the theory given here treats only clusters whose particles move along circular paths it does not seem to be subject to reasonable doubt that more general cases will have analogous results.” He did not consider paths that were only, or even partially, radial. This makes all the difference.

Albert Einstein  125 When Oppenheimer and Snyder wrote their paper, the final fate of stars had already been studied extensively. A star with five times the mass of the sun could undergo a supernova explosion, leaving behind a core consisting almost entirely of neutrons. There would be no counterpressure from nuclear reactions to counterbalance gravitation. In their paper, Oppenheimer and Snyder present the Schwarzschild metric followed by this excerpt, where r0 denotes the Schwarzschild radius: We should now expect that since the pressure of the stellar matter is insufficient to support it against its own gravitational attraction, the star will contract, and its boundary rb will necessarily approach the gravitational radius r0. Near the surface of the star, where the pressure must in any case be low, we should expect to have a local observer see matter falling inward with a velocity very close to that of light; to a distant observer this motion will be slowed up by a factor of (1 –​r0/​rb). All energy emitted outward from the surface of the star will be reduced very much in escaping, by the Doppler effect from the receding source, by the large gravitational redshift, (1 –​r0/​rb)1/​2, and by the gravitational deflection of light which will prevent the escape of radiation except through a cone about the outward normal of progressively shrinking aperture as the star contracts. The star thus tends to close itself off from any communication with a distant observer; only its gravitational field persists. . . . Although it takes, from the point of view of a distant observer, an infinite time for this asymptotic isolation to be established, for an observer comoving with this stellar matter this time is finite and may be quite short.22

In short, Oppenheimer and Snyder’s remarkable paper predicted the existence of black holes. Yet neither of the pair did any further work on the topic, and there is no evidence that they ever discussed it, despite both working at the Institute for Advanced Study starting in 1947. It seems that Oppenheimer dismissed the whole thing as an exercise for students. Einstein died in 1955 and Oppenheimer in 1967, long before the study of black holes became fashionable. As for Schwarzschild, while serving at the front, he contracted pemphigus, a rare autoimmune skin disease for which there was no known cure. He died in Potsdam on May 11, 1916.23

126  Quantum Profiles

The Best of Friends In the autumn of 1946, a young physicist became an instructor at the University of Geneva. As part of his duties, Pierre Speziali was charged with maintaining the mathematics library. It was not a position without perks; Speziali recalled often spending more time reading the books than cataloging them. Each Thursday morning, an elderly man with a gray beard came to read some of the books. On one such occasion, he and Speziali began talking, apparently in Italian, although the old man was also fluent in French and German. His name was Michele Angelo Besso. It is unclear whether Speziali recognized the name at first. If he had read the closing remarks in Einstein’s 1905 masterpiece on the special theory of relativity, it may have sounded familiar: “In conclusion I wish to say that in working at the problem here dealt with, I have had the loyal assistance of my friend and colleague M. Besso, and I am indebted to him for several valuable suggestions.”24 According to Speziali, they spoke for an hour or more about the history of science before the old man borrowed a couple of books and went off to audit a lecture. Besso, as it turned out, was auditing several courses. In July 1953, at the age of eighty, he gave a lecture titled “An Attempt at a Visualization of the Structure of Space-​Time.” During the following summer, Speziali visited Besso many times at his house in Geneva. Beneath a giant tree in the garden, the pair discussed some of the great moments in the history of physics. At the end of one visit, Besso walked Speziali to the road and stood still as if he had something else to say. It was the last time they saw each other. Besso died on March 15, 1955. Some years later, it occurred to Speziali that if there was any correspondence between Einstein and Besso, it would likely be of interest and could be published as a tribute to Besso. By this time, Speziali had become acquainted with Besso’s only child, Vero. He provided Speziali with seventeen letters from Einstein to his father. Six were sent prior to 1918, while the remainder were from the period 1950–​1954. Vero thought that there might be some others stored in the basement of his father’s country house. In all, 110 letters from Einstein to Besso were found. Einstein’s secretary, Helen Dukas, had kept the letters from Besso to Einstein, of which there were 119. In 1972, Speziali published the letters after translating them into French from the original German.25 He also included copious footnotes and a biography that offered a glimpse of the deep friendship between Einstein and Besso.

Albert Einstein  127 Besso was born on May 25, 1873, in Riesbach, a district of Zurich. For some generations beforehand, Besso’s family had been living in Trieste. His father, an insurance executive, had moved to Zurich at the behest of his employer.26 The family returned to Trieste in 1879, but Besso was sent to Rome for his secondary education. Speziali’s biography includes a high school report card that shows Besso doing well in mathematics. An uncle suggested that he continue his studies at the Swiss Federal Polytechnic School (Eidgenössische Polytechnische Schule) in Zurich. This was the institution that Einstein referred to as the Poly. It later became the Eidgenössische Technische Hochschule. When they first met in 1896, Besso was twenty-​three and Einstein was seventeen. Besso had enrolled at the Poly in 1891, and when Einstein arrived five years later, he had essentially graduated and was writing a thesis in order to become an instructor. Exactly how they met is not clear, but they liked each other immediately, and Einstein helped Besso with his thesis.27 In 1902, Einstein began work as a technical expert, class III, at the Federal Office for Intellectual Property in Bern. The following year, he married his longtime girlfriend, Mileva Marić, who had been the only female student at the Poly. At the time of their marriage, the couple were already parents, although the fate of their first child is an enduring mystery. In 1901, Mileva had become pregnant and returned to her native Serbia to have the baby. The child, a girl, affectionately referred to as “Lieserl” by Einstein, disappeared, and no trace of her has ever been found. Mileva returned to Switzerland alone, and Einstein never met his daughter. There is no mention of Lieserl in any of Einstein’s letters to Besso; it is unlikely that Besso ever heard of her. Indeed, the first news that Besso received about Einstein’s marriage was in a letter from January 1903. “I am now a married man,” Einstein wrote, “and my wife and I lead a very agreeable life. She occupies herself perfectly with everything, is a good cook, and is always happy.”28 This would change, and Besso would be in the middle of it. There are a couple of other letters from 1903 and then none until 1909. The reason for the lapse in correspondence is that Besso had begun working at the patent office in Bern, a position he likely attained with the help of Einstein. The two men walked to and from work together each day.29 Aside from Besso, it seems that Einstein did not have any other real friends. Philipp Frank, who succeeded him at the German Charles-​ Ferdinand University in Prague, wrote that Einstein “always managed to maintain a certain ‘free space’ around him which protected him from all disturbances.”30

128  Quantum Profiles Besso was the only person who managed to penetrate that space. He was present through some of Einstein’s most intimate ordeals, including his marital troubles. On October 31, 1916, Einstein wrote to Besso from Berlin: “As for divorce, I have definitively renounced it. We will now go on to scientific things!”31 His attempt to preoccupy himself with work proved unsuccessful. In 1918, Einstein wrote to Mileva: The endeavor finally to put my private affairs in some state of order prompts me to suggest the divorce to you for the second time. I am firmly resolved to do everything to make this step possible. In the case of a divorce, I would grant you significant pecuniary advantages through particularly generous concessions. . . . Now I request being informed whether you agree and are prepared to file a divorce claim against me. I would take care of everything here, so you would have neither trouble nor any inconveniences whatsoever.32

Throughout the upheaval, Besso remained close to Mileva and the couple’s two sons, Hans Albert and Eduard. He did what he could to mediate. Some of the most joyous of Einstein’s letters are his accounts of the time he spent with his sons. These occasions also yielded some of his most somber correspondence, such as when he realized that Eduard had mental problems so severe that he would need to be institutionalized. On March 9, 1917, Einstein wrote to Besso: “The state of my youngest son causes me a great deal of concern. It is out of the question that one day he might become a man like the rest. Who knows, perhaps it would have been better if he had left this world before having known life. For the first time in my life, I feel responsible and I blame myself.” 33 Eduard had musical talents, and for a while he studied psychiatry. But his mental problems became so severe that he was institutionalized in the Burghölzli Hospital in Zurich, where he eventually died in 1965. After migrating to the United States in 1933, Einstein never saw Eduard again, but he paid for his treatments and tried to maintain communication. Hans Albert became a professor of hydraulic engineering in California. I have the impression that he and his father were not close. In 1926, when Besso was on the edge of losing his job because of a “lack of zeal,” Einstein wrote to the patent office defending Besso’s abilities. The

Albert Einstein  129 intervention of Einstein probably saved his job. At the end of 1938, Besso retired at the age of sixty-​five. Einstein wrote to offer his congratulations. Their correspondence gradually became more one-​sided in the years that followed. Besso often wrote several letters before Einstein would reply and apologize for his tardiness. Besso’s final letter to Einstein was written from Geneva and dated January 29, 1955, less than two months before Besso’s death. He wrote in part: What is important to me personally is my father’s absolute refusal to accept any representation or even any denomination of God (which he thought was in complete conformity to the Torah.  .  .  . “You should not make any image or representation . . .”); so there only remains natural law, which for me amounts to giving meaning to research itself, to recognizing in immediate experience a value of the representation which is free of all contradictions and which represents a spiritual being in which we participate . . . with an open door to beauty, recognizing joy and goodness and the other genres of truth, goodness, and beauty. 34

The letter is signed, “Your old, old, old Michele.” In a footnote, Speziali indicated that he found this letter difficult to translate and was helped by Besso’s son, Vero. Before this, there had been a lifetime of letters that are not difficult to interpret or translate, although some require knowledge of physics to be fully comprehensible. On March 21, 1955, less than a week after Besso’s death, Einstein wrote to Vero and to Besso’s sister, Bice Rusconi. It is one of the most beautiful and poignant letters he ever wrote. It is really very kind of you to give me so many details of Michele’s death during these so painful days. His end was in harmony with his entire life, with the image of his being surrounded by a circle of his own family. The gift of leading a harmonious life is rarely conjoined with such a sharp intelligence, above all to the degree in which one found in him. But what I admired the most about Michele the man is the fact that he was capable of living for so many years with one woman, not only in peace, but also in constant agreement, an enterprise at which I  have lamentably failed twice. . . .

130  Quantum Profiles Now he has gone just before me again, leaving this strange world. It doesn’t mean anything. For us, believing physicists, this separation between past, present, and future retains only the value of an illusion, however tenacious it may be. Your A. Einstein35

Einstein died just a few weeks later, on April 18, 1955.

4 Wendell Furry

  

I had three memorable interactions with the physicist Wendell Furry over a period of some seven years. The first was in the fall of 1948, when I took a semester of freshman physics as a Harvard sophomore, which Furry taught. The second was on January 15, 1954, when I went to a courthouse in downtown Boston to listen to Furry’s testimony before Senator Joseph McCarthy’s Permanent Subcommittee on Investigations, which was investigating “Subversion and Espionage in Defense Installations.” The third was a little more than a year later, when I had to defend my PhD thesis and Furry was one of the examiners. He asked a question that I could not answer, and it came close to causing me to fail the examination. Wendell Hinkle Furry was born in Prairieton, Indiana, on February 18, 1907. As the name of the town might indicate, it was a farm area, and

132  Quantum Profiles

his father was a local pastor. After high school, Furry went to DePauw University, also in Indiana. At first, he thought he might become a chemist, but he soon switched to physics and mathematics. He was advised to do his graduate work at the University of Illinois. He got an assistantship that paid seven hundred dollars a year, which covered all his basic expenses. Furry was very fortunate that at the time he was a graduate student, a very distinguished physicist named F.  Wheeler Loomis became the chairman of the department, which he built up to become among the best in the United States. He was able to use his influence to get Furry one of the rare National Resource Council’s postdoctoral fellowships. He later became the second-​in-​command of the wartime radar project in Cambridge, which must have played a role in Furry’s joining the project. Furry also had an offer to become an instructor at Harvard, which he turned down to go to Berkeley to work with J. Robert Oppenheimer. It was during his time with Oppenheimer that Furry did some of the work for which he is most remembered. I will give two examples. The first is Furry’s theorem in quantum electrodynamics. I will use a Feynman diagram, which is, of course, anachronistic (see t­ he figure above). The wiggly lines are photons, and the arrows are electrons or positrons, depending on which way they are pointed. The significant thing is the odd number of photons. Furry’s theorem says that all diagrams like this with odd numbers of external photons must vanish. I do not know how Furry proved his theorem, since I have not read his original paper, but we would now use charge conjugation invariance and argue that diagrams like this violate it.

Wendell Furry  133

  

The second thing that Furry was involved with I will also illustrate with a Feynman diagram (see the figure above). An electron at rest has no kinetic energy, but it does have a mass energy. The “bare mass” is a parameter that one puts into the quantum electrodynamic formalism. But it is not the mass one would actually measure. This has to be corrected by the fact that, as the diagram shows, the electron is constantly interacting with its electric field. This produces an inertial effect that is reflected in a change in the mass. A calculation of this was first published in 1934 by Victor Weisskopf. He found that it was quadratically divergent. If you cut the integrals off, they would tend to infinity as the square of the cutoff as you increased the cutoff. Furry redid the calculation and found that Weisskopf had made a mistake. In fact, the divergence was only logarithmic—​a mild divergence. Furry went to Oppenheimer to ask what he should do. Oppenheimer said that he had two choices: he could publish without informing Weisskopf, or he could inform Weisskopf, which would be the decent thing to do. Furry chose the latter and allowed Weisskopf to publish his own correction. Weisskopf also showed that the self-​energy was logarithmically divergent to all orders in the coupling constant. By 1947, thanks to the work of the Dutch physicist Hendrik Kramers, it was realized that this infinity could be shoved under the rug. If one used the observed electron charge in the formalism, this would include the self-​energy, and to use this charge to then calculate the self-​energy, one would be double counting. This is an example of “renormalization.” Furry got an offer from Harvard in 1934 to be an assistant professor and spent the rest of his academic life there. In 1939, he published a paper on neutrinoless double beta decay, which is still referred to. The following figure is another anachronistic diagram. At the time, one did not describe beta decay in terms of intermediate weak boson transmitters. The interactions were supposed to be direct contacts. The diagram shows a process first discussed by Maria Mayer in 1935. The reader will note that two electrons emerge with no

134  Quantum Profiles n

P W− e– V e– W−

n

P

accompanying neutrinos. What Furry did was to indicate what the observation of this process would say about neutrinos. First, a remark about antiparticles. If a particle is electrically neutral, it can or cannot be identical to its antiparticle. The neutron is not, while the neutral pi meson is. What about the neutrino? Here we must briefly introduce the mysterious figure of Ettore Majorana. He joined Enrico Fermi’s group in Rome as a theorist, and Fermi proclaimed that he was the most brilliant physicist he had ever encountered. Majorana got to spend a year in Germany, and something must have happened there that transformed him. He became a recluse and stopped publishing anything in physics, although he kept working on his own. But in 1937, he decided that he wanted to join the physics community again and competed for a professorship. He had to submit a published work, and Fermi put together something that Majorana had done on the neutrino. He showed that there were two possibilities:  a Dirac neutrino that differed from its antineutrino and what is now called a Majorana neutrino that did not. Furry observed that neutrino-​less double beta decay is only possible for Majorana neutrinos, and active experiments are now in process. As for Majorana, he got a position in Naples. On March 25, 1938, while on the ferry from Palermo to Naples, he disappeared, leaving no trace. As for Furry, I do not know what other research he did at Harvard, but he was not promoted to full professor until 1962. Contrast this to the case of Julian Schwinger, who was eleven years younger than Furry. He came to Harvard in 1947 at the age of twenty-​nine as a full professor. For Furry, this must have hurt. I have an ineluctable memory of Furry coming to audit a

Wendell Furry  135 Schwinger classroom lecture with a copy of Time magazine, which he read ostentatiously during the lecture. If Schwinger noticed, he did not let on. If anyone had asked me to conjecture what Furry’s politics were, I would have said he was a Midwestern Republican. He looked and acted like someone who would have been right at home at a county fair. When I learned that since 1938, he had been for several years a member of the Communist Party, I could hardly believe it. What I find more remarkable is that he was allowed to work on radar. It was widely believed at the time that radar was much more essential to the United States winning the war than the atomic bomb. What kind of search did the FBI do so that not only Furry but a half dozen other members of the Party worked on radar? I am not aware of any espionage emanating from the Cambridge group, while the espionage at Los Alamos is well known. This was what McCarthy was investigating that day in Boston. I went to witness the hearing because I thought Furry might welcome a friendly face if he remembered who I was. I have the stenographic transcript of the hearings (see ­the figure below). It was printed by what was called the Harvard University printing office. I cannot explain how it came to be autographed by the three principals. There was a Leon Kamin, a teaching fellow at Harvard; McCarthy; and Furry, who signed with “Best Regards.” What is missing is an autograph of Roy Cohn, who was the chief counsel for the committee and later the tutor of Donald Trump.

136  Quantum Profiles The university had taken the position that to keep his job, Furry had to answer all questions that dealt with himself but was not obliged to “name names” or identify others. What McCarthy wanted was a list of these names and others. There was a cat-​and-​mouse game of which the following exchange is typical: the chairman: Do you know anyone connected with Harvard who is or was a member of the Communist Party? mr. furry: Sir, I am not sorting people for the committee. the chairman: Answer the question. mr. furry: Well, I would like to make this statement, and that is that I have never at any time known anyone who held a permanent position on the Harvard faculty with the exception of myself or who has since come to hold or who now holds a permanent position on the Harvard faculty, to be a member of the Communist Party; apart from that, I will refuse to answer the question. In the end, McCarthy summed up: This in the opinion of the chair is one of the most aggravated cases of contempt that we have had before us, as I see it. Here you have a man teaching at one of our large universities. He knows that there were six Communists handling secret government work, radar work, atomic work. He refuses to give either this committee or the FBI, or anyone else the information which he has. To me it is inconceivable that a university which has had the reputation of being a great university would keep this type of creature teaching our children. Because of men like this who have refused to give the Government the information which they have in their own minds about Communists who are working on our secret work many young men have died in the past, and if we lose a war in the future it will be the result of the lack of loyalty, complete (immorality) [unmorality] of these individuals who continue to protect the conspirators.

Furry was cited for contempt in a case he eventually won. The Harvard Corporation wanted to fire him, but many in the physics department said they would quit, so he was not fired. Norman Ramsey, later to win a Nobel Prize, went to Washington to confront McCarthy. He made such a favorable

Wendell Furry  137 impression that McCarthy actually offered him a job. Furry became department chairman in 1965 and died in 1984. The last direct encounter I had with Furry was in the spring of 1955, when he was on the committee that examined me on my thesis. Indeed, apart from my thesis adviser, I think he was the only examiner. A bit of personal history here: I graduated from Harvard in 1951 as a mathematics major. After freshman physics with Furry, I never took another physics course until my first year in graduate school, when I took Schwinger’s introductory quantum mechanics course. I got my master’s degree in mathematics in 1953, and the chairman of the math department told me that I was taking too many physics courses and that I would have to choose between physics and mathematics. I chose physics. But I had a schedule in mind. I wanted to get my degree in no more than two years. I had been working my way through school as a teaching fellow, and there was a limit to the number of years you could do that. There appeared to be some exceptions, such as Tom Lehrer, who became a friend and was nearly a perpetual graduate student. I  knew that I wanted to work in the general area of field theory and elementary particles. I also knew that I didn’t want to work with Schwinger. He had a platoon of students whom he saw rather briefly every week or so. I needed much more attention than this. There was a young instructor named Abraham Klein who was taking on students. I am now puzzled by his actual authority to do this, since in the annals of the department, I am listed as a Schwinger student. Let me say how the field appeared to me at the time. Quantum electrodynamics seemed to me to be a settled subject. The weak interactions—​beta decay and the like—​seemed almost an irrelevance. This changed dramatically a few years later, when it was discovered that they did not conserve parity. There were a few strange particles, but no one quite knew what to make of them. However, the action was in the interactions of pions and nucleons, where there were new experimental results. But here the theorists were stuck. It was more or less trivial to write down Feynman diagrams. But these were expansions in a coupling constant that was greater than one, as opposed to quantum electrodynamics, where the expansion constant was about 1/​137. Nonetheless, such calculations were carried out and even published. But at this time, a new expansion had been proposed by the Russian physicist Igor Tamm and the American physicist Sidney Dancoff: the Tamm-​Dancoff expansion. The idea was basically to ignore all the diagrams with loops and to expand the number of particles in the intermediate states. Some fairly sensible results had been achieved, and Klein was

138  Quantum Profiles an expert. Indeed, he proposed a problem on which I could begin work at once. It involved the nucleus of heavy hydrogen: the deuteron. One might imagine that the charge distribution of the deuteron in the ground state would be a nice sphere representing the fact that the ground state is an S state with no orbital angular momentum. Hence there would be no quadrupole moment. But there is one, which means that some other angular momentum state must mix with the S state. The next possibility is an angular momentum 1 state, a P state, but this has the wrong parity, so the S state must mix with an angular momentum 2 state, a D state. One could raise the following question: if one considered the exchange of mesons, how would this affect the situation? Intuitively, one would say the exchange occurs when the neutron and proton are close to each other, and this would change the shape of the charge distribution. That is what I was set to calculate using the Tamm-​Dancoff method. Eventually, this came down to spending weeks doing numerical integrals on a mechanical calculator—​a mindless waste of time but supplying some sort of answer, which I am ashamed to say became my first physics publication. Then came the defense. Furry asked the question whose answer would be obvious to any real physicist: how big is the next term in the expansion? I had no idea, and neither did Klein. He said something that seemed to satisfy Furry enough so that he left the room. I got my degree and learned a real lesson from a very good physicist.

5 Philipp Frank Nur zwischen uns Töchter von Pfarrern (“Just between us daughters of parsons”)—​Erwin Schrödinger to Philipp Frank Wien, Wien, nur du allein

Eventually, this will be a review of the book Exact Thinking in Demented Times by the Austrian mathematician Karl Sigmund.1 Sigmund is a professor of mathematics at the University of Vienna, noted for his work on game theory. He is aware of the tradition in Vienna that existed until the 1930s of small discussion groups that met often in the coffeehouses for which Vienna was famous. He states that these coffeehouses are now mostly gone. I don’t know if there are still such groups and where they meet. But before I turn to the book, I want to explain how I got involved with the subject of the book: the Vienna Circle. The Vienna Circle was an informal group of philosophers, mathematicians, physicists, and the like who met in the 1920s and early ’30s to discuss matters of mutual interest. This was not just any group. Among the philosophers there was Ludwig Wittgenstein, and among the mathematicians there was Kurt Gödel. Among the physicists was my first great teacher of physics, Philipp Frank. I entered Harvard as a freshman in the fall of 1947. I had received what I would call a classical education at a private school in New York—​Latin, French, English literature, and the like. We also had a smattering of mathematics and physics. The math I  took was some elementary algebra like solving quadratic equations, some trigonometry, and Euclidean geometry. The physics course I took was well-​meaning but totally uninspired. A few years earlier, Murray Gell-​Mann had taken the same course and had the same reaction, but when he went to Yale at the age of fifteen, he began the study of physics, and when I went to Harvard two years later, my goal was not to study physics or any other science. But Harvard had a science requirement. Before the war, it meant taking the introductory course in some science, but

140  Quantum Profiles

Philipp Frank

the president of Harvard, chemist James Bryant Conant, had a new idea. He had spent the war directing scientific research, including the creation of the atomic bomb. Indeed, he had been at the Trinity test on July 16, 1945, when the first bomb was successfully tested. He now decided that the Harvard science courses for nonscientists should be completely revamped so there would be a strong emphasis on the history and indeed the social responsibility of science. So he had asked for the creation of a curriculum of courses that went under the name of natural sciences. Every Harvard freshman not majoring in a science was required to take one of them. Conant himself taught one. I knew nothing of this when I came to Cambridge, but I must have been told of it by my freshman adviser. I also learned that there was a wonderful helper, the Confidential Guide of College Courses, known colloquially as the Confi Guide. It assembled the reactions of students to courses and their instructors, and it could be brutally frank. From it I learned that the easiest of the natural sciences courses was Natural Sciences 3, which was taught by historian of science I. Bernard Cohen. His lectures were said to be clear and

Philipp Frank  141 his exams reasonable, so I enrolled. Cohen had a deep baritone voice and excellent handwriting. We began with the Greeks—​such as Aristotle and Pythagoras, then a leap to Nicolaus Copernicus, Johannes Kepler and Isaac Newton, on whom Cohen was a particular expert. None of it was very difficult, and I followed along with an amiable indifference until nearly the end of the first term. Then came relativity. I found its claims about thing like the shrinking of length and the slowing of time for moving objects almost unbelievable and absolutely fascinating. In the course of his discussion of relativity, Cohen said something about there being only five or maybe ten people in the world who understood the theory. Years later, I learned that this was taken from the astronomer Arthur Eddington, who, when asked in the 1920s if it was true that only three people in the world understood the theory, replied, “Who is the third?” In any event, I took Cohen’s claim as a personal challenge. I would become the next person who understood the theory—​whatever that meant. I decided that the way to proceed was to go to Widener Library and take out a book by Albert Einstein on the subject. I felt that if I read it very slowly—​ maybe a page a day—​I would soon have an understanding of the theory. I found in the catalog a book by Einstein titled The Meaning of Relativity, just what I needed. The first sentences read: “The theory of relativity is intimately connected with the theory of space and time. I shall therefore begin with a brief investigation of our ideas of space and time, although in doing so I know that I introduce a controversial subject.” I could not imagine why space and time should be “controversial,” but I read on. The discussion seemed a little dense, but I thought I got the general points. On the fourth page, however, the whole project collapsed. There was the equation

s 2 = ∆x12 + ∆x22 + ∆x32

This was a quadratic equation, but what were the variables? What was one supposed to solve for? Einstein was not helpful. He said that it described a Euclidean space in Cartesian coordinates. I had absolutely no idea what this meant, and as I  looked further into the book, there were equations with symbols such as aμ√ which might as well have been written in Egyptian hieroglyphics. I decided to ask Cohen for help. He might well have dismissed me as a foolish freshman, but instead, he made a suggestion that changed my life.

142  Quantum Profiles He said that in the spring, a Professor Philipp Frank was teaching a course at about the same level as his on modern physics. It would certainly deal with relativity, a subject on which Professor Frank was an acknowledged expert. Indeed, I was told, he was a friend of Einstein and had succeeded him at the German University in Prague. Moreover, Professor Frank had just published a biography of Einstein, Einstein: His Life and Times. Cohen said that I could take his course and Professor Frank’s simultaneously, and that is what I signed up to do. The course met, as I remember, on Wednesdays at around three in the afternoon in the large lecture hall in the Jefferson Laboratories. It was pretty full when I arrived for the first lecture. In addition to those of us who were taking the course, there were a great many auditors from all over the Boston area. I had never seen Professor Frank and had no idea what he would look like. I could not have invented the real Philipp Frank. He was a short man with something of a limp. I later learned that this was the result of an encounter with a streetcar in Vienna, where he had been born in 1884. He usually had a very amused expression and liked telling what he called “cracks.” On one occasion, he came to class to tell us that a small boy had thrown a snowball in his general direction, announcing that he came from the fourth dimension. His accent was not easy to place. I came to think that his languages were built on top of each other like the cities of Troy—​German, Czech, Russian, English, and God knows what else—​and that different remnants would appear from time to time. He, too, began with the Greeks and told us how they had introduced epicycles to “save the appearances”—​to account for planetary motions (see ­the figure below).

Epicycles on Epicycles Earth

Planet

  

Philipp Frank  143 Later, when he came to the Keplerian ellipses which did away with the epicycles, he made a point that I did not understand until I had taken some math courses. He said that epicycles were a Fourier expansion of the elliptical motion and that from the point of view of pure science, both descriptions were equally good. It was a matter of aesthetics which you chose. When it came to Newton, he told us what the famous story about the falling apple and gravitation must have meant. Newton must have imagined a tree that stretched to the moon and which hung from it like an apple and was subject to the same forces. Then came relativity. Frank began by explaining coordinate systems. I then understood the equation that had baffled me. He could not resist a story. He had gone to Berlin to visit Einstein sometime after Einstein had published his popular book on relativity. Frank was very pleased with it and said that even his young stepdaughter Margot understood it. Einstein left the room, and Frank asked the girl if that was true. “Oh, yes,” she said, “I understood everything except what is a coordinate system.” Frank told us that the speed of light was the universal speed limit, and it was the same in all coordinate systems. This raised a question for me. How did Einstein know? In his day, about the fastest things going were streetcars, so how did he know that the speed would be the same in all coordinate systems? After the lecture, I went up to Frank and asked him. He gave me an answer I did not understand for several years. Einstein knew that the ratio of an electric field to a magnetic field for an electromagnetic wave in empty space was the speed of light, and that clearly did not depend on the coordinate system. Of course, what is assumed here is that the Maxwell equations retain their form. He told us about non-​Euclidean geometry, a revelation to me. He noted that one can make a triangle out of segments of great circles on a sphere and that the interior angles add up to greater than 180 degrees. He told us about the fourth dimension and how Einstein had replaced the forces of gravity with geometry. He also told us about the “traveling twins,” one of whom stayed home while his sibling did a round trip and returned with fewer heartbeats. “Travel and stay young,” Frank said. We did a bit of quantum theory, including the uncertainty principle. The lectures lasted for about an hour and were followed by what Frank referred to as a “certain interval.” That was followed by a question period in which Frank adumbrated some of what he had said for those who knew “a little of mathematics.” I remember that he solved the differential equation

144  Quantum Profiles

dN / dt = − λ N

to exhibit exponential decays. I had no idea what he was doing, but I wrote it down in my notebook. I  also made a decision. I  was going to study physics and mathematics, and if possible, I was going to study further with Professor Frank. In my sophomore year, I took freshman physics, which I did not like very much—​too many pulleys and inclined planes. I also took calculus, which I liked a lot, and I eventually majored in mathematics. I also took a reading course with Frank. We studied Wittgenstein’s Tractatus Logico-​Philosophicus, which I did not get much out of, and Ernst Mach’s The Science of Mechanics, which I thought was wonderful. One could see what it meant to Einstein. Of time, Mach said, Newton wrote: “ ‘Absolute, true and mathematical time of itself and by its own nature flows uniformly on, without regard to anything external.’ This is opposed to relative or common time which is the kind of thing measured by clocks.” To this, Mach replied, “It would appear as though Newton in the remarks here cited still stood under the influence of medieval philosophy, as though he had grown unfaithful to investigate actual facts.”2 Mach was really an experimental physicist, so he certainly would not have been able to produce anything like the theory of relativity. He did not believe in the existence of real atoms, even after Einstein’s work on Brownian motion. In a public exchange with Ludwig Boltzmann, who was Frank’s teacher, he asked, “Have you seen one?” I have often thought of this when I think about the confined quark. Frank took his degree from the University of Vienna in 1907. The year before, Boltzmann had committed suicide. He once told me that Boltzmann was the most brilliant scientific lecturer he had ever heard. In many of the European universities, there was a curious position called a privatdozent, a private lecturer. To qualify, the candidate had to write a special thesis and, once qualified, could give lectures paid directly by the students. Frank became a privatdozent. He also began publishing papers in both physics and the philosophy of science. A paper that he wrote in 1907 caught Einstein’s attention. Frank claimed that the law of the conservation of energy was not really a law, since it could never be refuted. One simply invented a new form of energy so that the law was maintained. This had just happened when Einstein invented mass energy, which explained the energy produced in radioactivity. Einstein wrote to Frank that while he agreed, the essential point was that only

Philipp Frank  145 very few new forms of energy had to be invented, which was why the “law” was useful. This began a friendship that lasted for the rest of Einstein’s lifetime. He died in 1955, and Frank lived until 1966. I spoke at his memorial service at Harvard. When Frank was still in Vienna, Mach had returned from Prague and was a professor. Frank got the idea that a meeting between Mach and Einstein might be arranged, and he set about it. At their meeting, which occurred in September 1910 when Einstein had come to Vienna to obtain the credentials he needed to work in a state university, they discussed the existence of atoms, and Mach insisted that while they might be useful theoretical constructs, they did not have a real existence. He never changed his mind. I should also mention two of Frank’s classmates at the University of Vienna. One of them was Erwin Schrödinger. They remained friends for life, and when it came time to leave Europe, Frank considered an offer from an Irish college, knowing that Schrödinger had gone to Dublin. Ultimately, Frank chose Harvard. Once he showed me a letter he had recently gotten from Schrödinger in which he was complaining about some criticism he had received from Einstein. The letter began, “nur zwischen uns Töchter von Pfarrern” (just between us daughters of parsons). The other friend was Richard von Mises, with whom Frank wrote a well-​known text on differential equations. Von Mises eventually came to Harvard, and I was once hired to assist him with an English translation of his book Positivism. In 1912, Einstein had recommended that Frank succeed him at the German University in Prague, where he remained until 1938, when he emigrated. Frank once told me that in the 1930s, there were three factions at the university. There were the Nazis, who were afraid the Russians would invade. There were the Communists, who were afraid the Germans would invade. And there were the Jews, who knew that whoever invaded, it would be bad for them. There was only one thing the three groups could agree to. They hired a tutor to teach them English so they could emigrate to America. This us to Sigmund’s book. The book begins with profiles of the dueling figures of Boltzmann and Mach. Sigmund writes: “Mach and Boltzmann were alike not only in their looks but also in their careers. They had similar heavy physiques, bushy beards and thin-​rimmed glasses; in their youths they learned from the same teachers, and as university students they both enjoyed great success. More importantly, Mach and Boltzmann were both headstrong and opinionated and they relished it.”3

146  Quantum Profiles Mach was born in 1838 in Moravia, making him some six years older than Boltzmann. His father had been a schoolteacher but had taken to farming. Mach was at first sent to a boarding school but lacked the physical fitness to accommodate to the regime, so he was home-​schooled. If accounts are to be believed, at the age of fifteen, he stumbled on a book by Immanuel Kant and devoured it. (At a much more advanced age, I tried to read Kant and gave up.) Duly reinforced, Mach attended a gymnasium and then the University of Vienna, where he studied mathematics and physics, The stunning thing about Mach was his apparent mastery of all fields of science. He seemed to have known everything and to have contributed to nearly everything. In physics, he is known for his photographs of high-​speed projectiles. “Mach n” is n times the speed of sound. He was interested in the workings of the human mind and the ego and gave popular lectures with Sigmund Freud in the audience. He spent twenty-​eight years as a professor in the German University in Prague, beginning in 1867, before becoming a professor at the University of Vienna. Three years later, he suffered a stroke while on a train trip and spent the rest of his life as a homebound invalid, which is how Frank and Einstein found him. Boltzmann’s father was a tax official who died when Boltzmann was fifteen. His mother spent her entire inheritance on education for her son, who from an early age was extremely gifted in music and mathematics. At first, he was interested in philosophy, but Sigmund quotes him as saying, “I first encountered philosophers a long time ago, and at that time I had no idea what they meant by their utterances and tried to become better informed.” He goes on, as Sigmund says, with a club rather than a foil: “To head straight into the deepest depths I first turned to Hegel; but oh! what obscure, vacuous balderdash.”4 At only twenty-​five, he was appointed a full professor of mathematical physics in Graz. There then began a pattern that continued for the rest of his life. He took an appointment at the University of Vienna but after three years returned to Graz. There he remained for fifteen years but then started to accept and then instantaneously reject professorships from various universities. In 1902, he became his own successor in Vienna and was required to pledge to Emperor Franz Josef himself that he would stay put. Mach was still in residence, and the two of them clashed on the existence of atoms. At one meeting of academicians, Mach cheerfully announced, “I don’t believe that atoms exist.” Boltzmann could not believe what he had just heard. His mercurial changes of mood became apparent to his colleagues. He suffered more and more from ill health, and in 1906, he canceled his lectures.

Philipp Frank  147 On September 5, he hung himself while on vacation in Italy. Of the two, Boltzmann was the much greater physicist. He has a constant named after him, while Mach has just a number. It was common at that time in Vienna for small groups of academics to meet informally to discuss matters of common interest. In this way, the prototype of the Vienna Circle, the Urkreis, was formed. Much later, Frank recalled, “I belonged to a group of students who met every Thursday evening in one of the old coffeehouses of Vienna. We would stay there until midnight and beyond discussing questions of science and philosophy.” When I knew him in Cambridge, there were no coffeehouses, but sometimes we would meet in the Hayes Bickford cafeteria in Harvard Square. I don’t think we resolved any great philosophical issues. By the end of the World War I, the original circle had pretty much dispersed. Frank was in Prague, and von Mises, who had served as a test pilot for the Austro-​Hungarian army, was in Dresden. But the spirit was there, and what is usually referred to as the Vienna Circle was reanimated with fresh recruits. Two of the most interesting were Wittgenstein and Gödel, who was the only person to have been nominated while still a student. Wittgenstein is a curious case, especially for a group as critical as the Circle. Gödel thought that much of what he said about mathematics was nonsense,5 but by and large, the other members of the Circle seemed to think that the Tractatus should be taken with great seriousness. It was written during the time Wittgenstein was serving as a soldier in the war. He might have been able to buy his way out, as his father was a steel magnate and was one of the richest men in Europe, but he did not. After his father died, he started to give away the money he had inherited and began teaching in a provincial elementary school, where he was not much liked by his students. I never asked Frank what he actually thought of the Tractatus, but when I read it as a sophomore, I took it seriously. I thought long and hard about statements such as “The world is the totality of facts, not of things.” Only years later did it occur to me that you could replace this statement with its negative and get one that was equally true or not true. Bertrand Russell was much taken by the Tractatus and arranged for Wittgenstein to come to Cambridge, where he spent the rest of his life. He gave lectures that no women were allowed to attend, and if one happened to show up, he would simply stop talking until she left. Some of the other members of the reconstituted Vienna Circle were the philosophers of science Rudolf Carnap and Moritz Schlick and the mathematician Kurt Reidermeister, a founder of the theory of knots.

148  Quantum Profiles In 1929, the group published a sort of pamphlet titled The Scientific World View. As Sigmund states, this is the first place where the identification “The Vienna Circle” actually appeared in print. Sigmund notes that some people still called it the Schlick Circle after the science-​oriented philosopher who was one of the founding members. He had actually succeeded Mach and Boltzmann and in 1936 was assassinated by a student who objected to his liberal political beliefs. By 1933, it was clear that Nazism was on the rise in Austria. Nonetheless, the Circle kept on with its meetings. But some of its members who had taken positions in Germany lost them. Von Mises, who was then in Berlin and was Jewish, emigrated to Turkey, where he became a professor at the University of Istanbul before he eventually came to Harvard. By that time, he had published his Kleines Lehrbuch Des Positivmus (The Little Primer of Positivism), of which I had a small role in the English translation. Von Mises did not, and for good reason, trust my German, nor did he trust the English of the native German-​speaking collaborator I brought on board, But he seemed to feel that the two of us together could do the job. He was a rather a formal man, the mirror image of Frank. In February 1934, the government closed down the Ernst Mach Society, a discussion group like the Circle, on the grounds that it was political. By 1938, the time of the Anschluss, there was no more Vienna Circle. Its members had largely departed from Austria and would become distinguished academics at a variety of foreign universities. Sigmund gives a complete list. In the early 1940s, a new version of the Circle was created in Boston, called the Institute for the Unity of Science. Sigmund does not describe this, since it is a little off his subject. The Institute met under the auspices of the American Academy of Arts and Sciences. Among the members are a few remnants of the old Circle such as Carnap, Hans Reichenbach, Herbert Feigl, and Frank. There are also people such as Ernst Nagel and Willard Quine, who spent time in Vienna visiting the old Circle. One of the things the new Circle did was to create elements of an International Encyclopedia of Unified Sciences, for which Frank wrote an entry titled “Foundations of Physics.” As one might imagine, it contained an extremely lucid account of relativity and quantum theory. But Frank decided to bring it more up to date by discussing things like nuclear physics. Here it is clear he was on slippery ground. For example, he thought that the neutron might be a bound state of a proton and an electron which, of course, has the wrong spin. It is not for nothing that the neutron is a bound state of three spin-​½ quarks. The little booklet was first published in

Philipp Frank  149 1946, and I must have read it around that time. I simply did not know enough to bring matters like this up with Frank Sigmund seems to have been born to write this book. As a student at the University of Vienna, he attended lectures by Bela Juhos, who was one of the last members of old Circle still standing. Every day, Sigmund walked into places the Circle frequented and went to the coffeehouses where they met. He writes, “I had my office on the same corridor as the lecture room where the Schlick Circle had held its meetings, and I was a regular in the coffeehouses where they had held their lively discussions. (Today the lecture room is a quantum physics laboratory, and most of the coffeehouses have closed their doors.)” The book is delightful and a true nostalgic labor of love.6 I would like to thank Gerald Holton, another disciple of Frank, for many helpful suggestions.

6 J. Robert Oppenheimer Some years ago, I  received a somewhat curious request from a publisher, which had in its possession a partially completed biography of J.  Robert Oppenheimer written by the physicist Abraham Pais. The biographer had died on July 28, 2000, at the age of eighty-​two, before completing it. The publisher wanted my opinion about whether it should publish the unfinished manuscript as it stood. At this time, Pais had a substantial reputation as a historian of science, and he had also been a professor at the Institute for Advanced Study beginning with Oppenheimer’s tenure as director there. He was therefore in an excellent position to write a very substantial biography. I agreed to read the manuscript and to write a report on it. That forms the first part of this chapter. The second part deals with what actually happened to the book. What follows is what I wrote to the publisher verbatim, acknowledging that there could have been stylistic improvements. Let me begin by saying that the fact that this biography is unfinished would not, in and of itself, preclude its publication in my view. (It is a pity that it stops before the Oppenheimer trial begins, but much has been written about the trial.) I  could easily imagine a biography called Oppenheimer; An Unfinished Life, with epilogues by people like [Freeman] Dyson. What should not be done is to have someone ‘finish’ the book. Pais had, whether one liked it or not, a very distinct voice, which cannot and should not be duplicated. So the real question is, is what is there worth publishing? This is, as I will explain, a close call with a probable weighting, I think, in the negative. Let us turn to the book. Pais begins with a preface in which he states his intention and sources. His intention is clearly to write the definitive biography of Oppenheimer, having expressed his dissatisfaction with all the others. He thinks he can do this because he knew Oppenheimer, obtained 7,400 pages of FBI documentation, spoke to friends and family, etc., etc. It is against this expressed intention that the book must be judged. Let us begin at the beginning which is Pais’s description—​taken verbatim from his autobiography—​of how he

J. Robert Oppenheimer  151 met Oppenheimer. In fact, much in this book is taken from somewhere. For someone like myself, who is steeped in this literature, I recognize many of the old friends that all of us who have written about this quote. What is curious is that nowhere in the references do I find conversations with people cited. My suspicion is that Pais talked to these people informally before he planned to write this book and that he didn’t use a tape recorder. By the time he wrote it many of them, like [I. I.] Rabi, were dead. This, you will see, is a pity. Pais then discusses Oppenheimer’s childhood. There is a problem right at the beginning. Pais tells us that Oppenheimer’s father added, for no particular reason, the “J” in front of “Robert.” How does he know? Did he take the trouble of looking at birth records? A biographer, whose name I cannot recall, did this and found on the date of Oppenheimer’s birth there was a Julius Robert Oppenheimer registered in New York. Moreover, Pais quotes both General [Leslie] Groves and J. Edgar Hoover, in their official reports. referring to “Julius Robert Oppenheimer.” Pais never comments on this. Didn’t he notice? The man’s name was Julius Robert Oppenheimer and the fact that he said it is “J for nothing,” as I will explain, is significant. I think at the heart of Oppenheimer’s personality was the fact that he was born a Jew in an anti-​Semitic America—​details shortly—​and never resolved this. More important than what I  think is what Rabi thought. Rabi probably had a deeper insight into Oppenheimer’s psyche than anyone. Pais tells us that he spoke to Rabi and that Rabi said he thought that Oppenheimer was uncomfortable about his Judaism. Period. This is a perfect example of what I was saying above about interviews, as opposed to casual conversation. I interviewed Rabi for hours with a tape recorder. When the subject of Oppenheimer came up, he told me all about Oppenheimer’s pretensions and game playing, and then said he didn’t mind because he understood his “problem.” I asked what was his problem, and Rabi said “identity.” He added that if Oppenheimer had studied Yiddish rather than Sanskrit, he would have been one of the best physicists who ever lived. There is more wisdom in this observation than I can find in all of Pais’s book. But what was the anti-​Semitism like? Oppenheimer went to Harvard when there were Jewish quotas for students and faculty, and when no recognizable Jew could get into any of the Final Clubs which dominated the social scene. But it went deeper than that. When Percy Bridgman, one of Oppenheimer’s favorite teachers, wrote a letter to Ernest Rutherford in 1925 recommending Oppenheimer, he felt constrained to add, “As appears from his name, Oppenheimer is a Jew, but entirely without the usual qualifications of his race. He is a tall, well

152  Quantum Profiles set-​up young man, with a rather engaging diffidence of manner, and I think you need have no hesitation whatever for any reason of this sort in considering his application.” In other words, he was not like those Julius, herring eating, big nosed yids that you usually find. Bridgman was, by the way, not at all an anti-​Semite. This was simply something he found relevant in a letter of recommendation. In his “definitive” biography Pais does not bother to quote this letter. Oppenheimer was, in [Aldous] Huxley’s phrase, like a chameleon on tartan—​a lot of wasted emotional energy. Incidentally, from what I know, Oppenheimer never slept with a Jewess. There is a term in psychoanalysis for that. It is called “Portnoy’s Complaint.” Pais does, as one would expect, a scholarly job of examining Oppenheimer’s scientific output. The part of the book will certainly stop any nonscientific reader. I do not agree with his final evaluation, but there is room for discussion. The sentence he quotes as anticipation of the positron seems absolutely far out to me. I also think he totally underestimates the importance of the papers on “black holes.” But Pais did not know that much about astrophysics and cosmology, which is one of the few weaknesses in his [Albert] Einstein biography. He also repeats what I used to believe about [John] Wheeler and the name “black hole.” Recently I  saw a rebroadcast of an interview with Wheeler in which he was asked about this. He said he gave a lecture years ago and someone in the audience said why don’t you call it a black hole—​which he did. It reminded me of the old story of the Wise Men building the crèche. One of them hit his finger with a hammer and said, “Jesus Christ!” The other said, “That’s what we’ll name the kid!” Oppenheimer was not happy about his scientific accomplishments, but he was in the very Big Leagues. I once wrote an essay called “The Merely Very Good,” which explored the ratio Oppenheimer is to [Paul] Dirac as Stephen Spender is to W. H. Auden. Now we come to the Institute. The very long preamble on its founding etc. is certainly very interesting, but does it belong in this book? When Pais begins discussing the Oppenheimer era and his own role and views, I have to say my personal temperature begins to rise. Much of this has all of the name-​dropping, nauseating self-​aggrandizement that ruined the second half of Pais’s autobiography. “I had the privilege of playing squash with Gandhi” etc. I will give a couple of examples. Pais recycles from his autobiography his first sight of Dyson, whom he refers to, with no apparent irony, as a “smart kid.” Leaving aside the fact that Pais was only five years older, there is also the fact that Dyson was then discussing his work in quantum electrodynamics, a subject that Pais had worked on and had gotten nowhere with. In

J. Robert Oppenheimer  153 his autobiography, at one point he admits this. The work was useless. When writing about Dyson, there is in Pais always a somewhat nasty edge. Dyson doesn’t feel this, so perhaps it is none of my business. But then Pais gets down to appointments and visitors at the Institute. Of course he must tell us how brilliant he was when he took one of Jerry Bruner’s tests, as if this had some relevance to Oppenheimer. But the best is [Sin-​Itiro] Tomonaga. He says that Tomonaga was the deepest of the Japanese physicists and that he won the Nobel Prize and that moreover in his acceptance speech he cited Pais’s work on electrodynamics—​probably as another failed attempt. What has this to do with Oppenheimer? I was also not satisfied with his treatment of Kitty Oppenheimer, whom he calls the most despicable women he ever met. The feelings, I can tell you, were mutual. But the example he gives of her behav­ ior at a party seems a little slim. There is no doubt that she was an alcoholic, something that must have given Oppenheimer a great deal of pain. But they stuck it out, which is more than Pais did with his first two wives. Incidentally, Pais informs us that in his view, Oppenheimer was a latent homosexual—​ whatever that means. I  always thought he had a certain feline cruelty—​ whatever that means. I thought Pais’s Los Alamos treatment was OK with a little too much of Oppenheimer’s speeches. It seems as if he never saw the film The Day after Trinity, which is the best I know. If he had, he would have heard Dyson’s explanation of the famous “sin” quotation, that the people who built the bomb had a great deal of fun while doing it. The time of their lives. He would also have heard Frank Oppenheimer saying that after the test went off at Trinity, his brother said, “The thing worked,” which is not in the Gita. Pais did his homework with respect to the hydrogen bomb, for which I give him credit. This is one of the better parts of the book. What made Oppie so endlessly fascinating to people who knew him? Let me give three examples from my own experience. When I went to the Institute, I  was warned that there would be periodic “confessionals” with Oppenheimer at which you were supposed to say what you had been doing recently. When it came my turn, I  said that I  had been reading [Marcel] Proust. Oppenheimer gave me a kindly look and said that when he was my age, he had gone on a bike trip to Corsica—​Pais mentions this in passing—​ and that he had brought Proust along which he read at night by flashlight. He was not bragging. He was sharing something. I had worked with an Austrian physicist named Walter Thirring, whom Oppenheimer admired. He came to visit Princeton, and I gave a little party for him. I asked Oppie more as a joke

154  Quantum Profiles than anything but warned the other invitees that I had done so. Much to our astonishment, Oppie showed up, but instead of wearing one of his Langrock suits, he wore a jacket that looked as if it had been eaten by gerbils. We were in our best clothes. Finally, after I left the Institute and was living in New York, Oppie came to town. He went to Columbia, and Mal Ruderman called me to tell me that Oppie was asking everyone if they knew from where the title of a speech which he was calling “The Added Cubit” came from. I had no idea, but I called Robert Merton and asked, on the off chance I would meet Oppie. Merton identified the passage in the New Testament. Well, I did meet Oppie. He said, “Your father is a rabbi, so you should know where ‘The Added Cubit’ comes from.” He had the wrong testament for my father, but I immediately gave the answer. Oppie looked at me very strangely. I never explained. Pais says that Oppie had a “wretched life.” I think this is total nonsense. He could have had a much happier life, but so could we all. He created a generation of physicists. He did very fine work. He had a good deal of fun, and many people loved him. Not so shabby. After Pais died, his widow, Ida Nicolaisen, decided that the book should be finished and published. To this end, the physicist and historian of science Robert Crease was engaged. The joint book, J. Robert Oppenheimer: A Life, was published in 2006 by Oxford University Press. I now turn my attention to it. The first thing I want to say is that the finished book seems to me to be better than the manuscript I was sent to review, although it still has many of the flaws I pointed out. One of the improvements is a section of photographs. One of them shows Oppenheimer’s birth certificate (see the following figure). This is a document that I am now very familiar with. At one point, I decided that I would settle the matter of his first name once and for all. I located the bureau that maintains all the birth certificates for people born in Manhattan and went there for a visit. I found that if I could produce the name and birthdate of the individual in question and pay a nominal fee, I would be furnished with a copy of the birth certificate, which I was. It records the birth of “Julius Robert Oppenheimer.” I am looking at it as I write this. It gives his father’s name as Julius and says that he was born in Germany and was thirty-​ four years old. I wonder if anyone ever called Oppenheimer Julius, even his parents. He was always Robert. I would be amazed if anyone ever called him Bob. I have tried to explain why he always said the J was for nothing. His physics papers were always signed “J. R. Oppenheimer.” The other thing that struck me about the photos was that all or nearly all of the physicists are smoking. Einstein’s addiction to smoking a pipe is well

J. Robert Oppenheimer  155

known. I remember a story about Julian Schwinger. He was one of the best theorists of his era and won the Nobel Prize for his work on quantum electrodynamics. He was noted for his nocturnal work habits. Before he was married, he would work all night in his office at Harvard. One night, the cleaning lady came in to find that Schwinger’s wastebasket was on fire. He had thrown a lit cigarette butt into it without noticing. Oppenheimer was a chain cigarette smoker. He died of cancer of the larynx at age sixty-​two. In the pictures, most of them are smoking. It is clear from the book that Pais did not like Oppenheimer. The feeling, as I can testify to, was mutual. As I mentioned in my review of the manuscript,

156  Quantum Profiles he found Oppenheimer’s wife, Kitty, “despicable.” In the book, he gives as an illustration what she did at a party. Kitty told an Institute secretary that she should no longer wear pink but rather blue. Pais said that this made him “tremble with rage” but that he said nothing. What was he supposed to say? Early in my tenure at the Institute, I attended a very large party at the Oppenheimers’ house, where among the guests were John O’Hara the novelist and the governor of New Jersey and where I felt that I was the last person entitled to be there. She was very warm and hospitable. Pais’s real problem was that he was incredibly competitive about everything. I played squash with him a few times, and it was like going to war. As a physicist, he was competent but not really in the first rank. He is remembered for a couple of things he did in the theory of elementary particles. When cosmic-​ray particles began to appear that no one had anticipated, Pais formulated a rule for how they should be produced in association. But he was never able to produce a theory for them. This was done by Murray Gell-​ Mann, who was awarded a Nobel Prize for his work. It was also clear that Pais was the least gifted of the physics professors at the Institute. They included T. D. Lee and C. N. Yang, who also won the Nobel Prize for their work, and Dyson, whose genius was universally recognized. Pais did not have a chance, and all the self-​aggrandizing in his book is, I imagine, a reaction. Like the fox, Oppenheimer did many things in physics, but like the hedgehog, he also did one big thing. That was his paper with his student Hartland Snyder in 1939 which created the notion of the black hole. Here is the abstract: When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star’s mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized

J. Robert Oppenheimer  157 case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

What I would like the reader to take away from this rather terse scientific abstract is the image of the collapse, which they say will take place in the “order of a day.” The star will collapse to what they call its “gravitational radius.” To an external observer, the light from the collapsing star is shifted more and more to the red, until at the gravitational radius it is no longer visible—​a black hole. But to an observer on the surface of the star, things will appear unchanged until after the star collapses beyond this radius, when the observer will be torn apart by gravitational tidal forces. The reasoning in the paper is so clear that you could use it in a course. But Oppenheimer got no satisfaction from this work. He seemed to see it as a student exercise that anyone could have done. He had the misfortune to arrive on the scene in physics just after quantum theory had been created by people not much older than he was. He never seemed to have gotten over this. My own view is that if he had lived to see the present era of black-​hole physics, he might well have won a Nobel Prize. Pais devotes a significant amount of space to the Oppenheimer hearings before the Atomic Energy Commission, which began on April 12, 1954, and ended on May 6. The issue was whether Oppenheimer should be deprived of his clearance to have access to information about nuclear weapons. This struck many people as absurd, since Oppenheimer had been instrumental in creating them. But there was a phobia about the Russians on the one hand, and on the other, he had made a very powerful enemy, Lewis Strauss, who was chairman of the commission; he also happened to have been chairman of the board of trustees of the Institute. Oppenheimer had made him look foolish in another hearing, which made Strauss extremely angry. Oppenheimer could have avoided the hearings if he had been willing to give up his clearance voluntarily. This he was unwilling to do. The full transcript of the hearing has been available for many years, and I did not think that Pais had much to add. They read like a Shakespearean play with the villains (Edward Teller) and the heroes (I. I. Rabi). Oppenheimer thought he could outsmart everyone, but he was overtaken. He did not make an entirely credible witness. I got an unexpected insight into this a few years later, when I was at the Institute. I was going to New York by train and had seated myself in the “dinky,” which went from Princeton to Princeton Junction, when Oppenheimer got on. He saw me and sat down and for some reason began talking about “his case.”

158  Quantum Profiles I certainly did not bring it up. He said that while it was going on, he felt that it was happening to someone else, which was a little the way he testified. He lost, and people who had known him before said that he was never the same. Some people at the Institute, such as Dyson, found that Oppenheimer now devoted more time to its affairs than he had before. There was some concern that Strauss would see to it that Oppenheimer would be terminated as director, and the physicists like Dyson were prepared to leave. But this did not happen. Before I leave this somewhat unpleasant subject, I want to bring up one more point. Strauss was a religious Jew, and I  doubt that Oppenheimer ever set foot in a synagogue to pray. Strauss decided that Oppenheimer was “immoral.” He had been told by the physicist Ernest Lawrence—​a Berkeley colleague of Oppenheimer and the inventor of the cyclotron—​that Oppenheimer had had an affair with the wife of a colleague of his at Caltech named Richard Tolman. In the book, Pais simply states that there was such an affair as a matter of fact. How this is consistent with his claim that Oppenheimer was a “latent homosexual” is not clear. I decided to investigate. There were still people around who were at Caltech at this time. They were sure that this never happened. When Oppenheimer came to Caltech, even when he was married, he stayed at the Tolmans’. I was able to read some of the correspondence between Oppenheimer and Ruth Tolman, and it seemed to me like the correspondence between old friends. In one of the letters, she writes, “Come to us when you can, Robert. The guest house is always and completely yours.” Pais is at his best describing Oppenheimer’s losing battle with cancer. A day or so before he died, Oppenheimer came to the Institute to join the discussion on the next group of physicists who had asked to come as visitors the following year—​people Oppenheimer knew he would never live to see. He died on February 15, 1967. Three days later, there was a memorial that took place in Alexander Hall on the Princeton campus. A few very distinguished speakers gave elegies. Even General Groves, who had chosen Oppenheimer as the man to head Los Alamos, was there. There was also music by the Juilliard String Quartet and a recording of Stravinsky’s Requiem Canticles. I was surprised to see on the program that the music had been selected by George Balanchine. Why Balanchine? What an odd connection. As it happened, I saw Balanchine at the Pilates gym in Manhattan the Monday after the service. I told him that I had not realized he was a friend of Oppenheimer’s. He said he wasn’t and had been very surprised

J. Robert Oppenheimer  159 when he was asked, apparently by Oppenheimer whom he had never met, to select the music. This was such an odd recollection that I decided to try to find out what really happened. After some considerable detective work, I  determined what had occurred. In the 1950s, something called the Congress of Cultural Freedom was formed. Its purpose was to provide a liberal, somewhat left-​ wing answer to Communist ideology. Oppenheimer joined, as did Nicolas Nabokov, Vladimir’s cousin. He eventually became its secretary general. In 1959, the Congress held a meeting near Basel at which Oppenheimer spoke. Among other things, he told the delegates: I find myself profoundly in anguish over the fact that no ethical discourse of any nobility or weight has been addressed to the problem of the new weapons, of the atomic weapons. . . . What are we to make of a civilization which has always regarded ethics as an essential part of human life, and which has always had in it an articulate, deep, fervent conviction, never perhaps held by the majority, but never absent: a dedication to ‘ahimsa,’ the Sanskrit word that means ‘doing no harm or hurt,’ which you find in the teachings of Jesus and Socrates—​what are we to think of such a civilization, which has not been able to talk about the prospect of killing almost everybody except in prudential and game-​theoretic terms?”

Oppenheimer and Nicolas Nabokov became friends, and in 1967, when Oppenheimer was dying of cancer, Nabokov was living in Princeton. He was working with Balanchine on a ballet, and he must have discussed with Oppenheimer the possibility of having Balanchine select the music for the memorial service, which is what happened. In thinking about this, two things struck me. The first was that even in death, Oppenheimer had assumed another persona, that of Balanchine. The second was something that neither Nabokov nor Balanchine knew: the Congress of Cultural Freedom had been funded by the CIA.

7 Victor Weisskopf Eine Halbjude

When I was beginning my career in physics in the 1950s’, most of my teachers in theoretical physics were Jewish, as were most of the students. Of course, there were the exceptions—​but they were exceptions. This was also true, by the way, in Russia and inspired the riddle:  Who does antitheoretical physics in the antiword? Answer: Anti-​Semites My great teacher was Julian Schwinger, who shared the Nobel Prize with Richard Feynman in 1965. The third person on that prize was the Japanese physicist Sin-​Itiro Tomonaga, again an exception. A physicist who was not technically my teacher but from whom I  learned a great deal was Victor Weisskopf. He was at MIT while I  was at Harvard. I  got to know him pretty well during my two postdoctoral years, when Weisskopf joined our Harvard group at what was a weekly lunch with Schwinger. Many years later, I wrote a sort of profile of him for the New Yorker. I say “sort of profile” because he was the then director general of the CERN physics lab in Geneva, and much of what I wrote dealt with CERN. Weisskopf was born on September 19, 1908, to a comfortable and cultivated Jewish family in Vienna. He became an excellent pianist. He got his degree in physics from Göttingen in 1931. His teacher was Max Born, who was also J.  Robert Oppenheimer’s teacher. He then took up postdoctoral positions first with Werner Heisenberg and then with Erwin Schrödinger. In 1933, he became Wolfgang Pauli’s assistant in Zurich. Pauli was noted for his brilliance in physics and his scathing wit. Pauli had to chose between Weisskopf and Hans Bethe, and he chose Weisskopf, who was given a calculation to do and made a mistake. “I should have taken Bethe,” Pauli said, a story that Weisskopf often told. Weisskopf was not especially good at calculations, but he made up for it by his very deep understanding of the physics. After Pauli, Weisskopf went to Niels Bohr’s institute in Copenhagen, where he met and married his first wife, who predeceased him.

Victor Weisskopf  161 By this time, the anti-​Semitism in Germany was only too apparent, and Weisskopf—​and also Bethe—​found academic jobs in the United States, Bethe at Cornell and Weisskopf at the University of Rochester. I grew up in Rochester at that time, where my father was a prominent rabbi. He had a lot to do with helping the newly arrived refugees adapt, and Weisskopf remembered him with affection. Pauli was fairly safe in Switzerland, although he spent the war in Princeton. He had a colleague in Zurich, to which he returned after the war, named Markus Fierz. I remember sitting with Fierz outside the restaurant at CERN having a coffee. Fierz told me about an exchange he had just had with Pauli. In great confidence, Pauli confessed to him that he was a Halbjude. This was a strange choice of language to have used, since it was one of the Nazi racial categories for people who had a Jewish parent, although in Pauli’s case, it fit. His father was a Jew who had converted to Catholicism. Indeed, Pauli was raised as a Catholic. He was certainly a Halbjude. Fierz told me that he responded to Pauli’s odd confession by telling him that he had always thought he was a Doppel Jude, a double Jew. Early in the war, Bethe and Weisskopf found themselves at Los Alamos, where they were joined by many other Jewish refugee physicists. They might have liked to work on radar, but they could not get the clearance. I. I. Rabi, who played an important part in radar and was also a consultant at Los Alamos, told me that he had difficulty getting clearance to work on radar. He had been born in Galicia and had come to the United States as a baby. Nonetheless, it was difficult for him to get clearance to work on radar. He once said to me, “With the atomic bomb, we might win the war, but without radar, we would certainly lose it.” Bethe became head of the theoretical physics division, and Weisskopf became head of one of its groups. He transformed himself into a nuclear physicist. This was a very good fit. It required less calculation and more physical insight. After the war, he coauthored a basic text on nuclear physics. It remains one of the best, and I consult it whenever I am stuck on something. Weisskopf also played a role in trying to educate people on the danger of nuclear weapons. One thing always struck me. During the time I knew him, he never said a single word about Los Alamos, and neither did anyone else I knew who had been there. It was still too close to the war. Weisskopf was a wonderful teacher. When I was a student, I once went down to MIT to hear him lecture on quantum mechanics. He walked into a very crowded classroom and began by saying, “Boys”—​there were only men—​“last night I had wonderful night.” There were raucous cheers. “No.

162  Quantum Profiles No,” he said. “I finally understood the Born approximation.” One of his most noted students was Murray Gell-​Mann. Gell-​Mann had had a somewhat checkered undergraduate career at Yale, which would not admit him to its physics department for graduate work, nor could he get fellowships in any of the other departments he applied to. But Weisskopf took him on as his assistant, which meant that Gell-​Mann could work on anything he wanted to. He used Weisskopf as a sounding board for his new ideas. After he had invented quarks, with their strange fractional charges, he called Weisskopf to tell him. “What have you been smoking?” Weisskopf asked. Weisskopf (called Viki) and I had one thing in common. We both loved Jewish jokes. Here are two I heard him tell. A young man leaves the shtetl to come to Vienna to study. His father, who has never seen Vienna, comes for a visit. He says, “Look what the Jews have done. They invented the electric light bulb, the street car, and the automobile.” “No, Papa, they were all invented by goyim.” “If the goyim invented all that, just think what the Jews must have done.” A couple is having marital problems and go to see the rabbi, who first listens to the husband. He says to him, “You are right.” Then he listens to the wife and says, “You are right.” The husband asks how they both can be right. The rabbi says, “You are also right.” Weisskopf died on April 22, 2002, at the age of ninety-​three. He had known a full life, with both esik (vinegar) and honik (honey)—​with much more of the latter than the former.

8 Tom Lehrer In my junior year at Harvard, which was in 1949, I moved into Eliot House, one of the undergraduate living quarters. One of my roommates was taking an introductory course in calculus, and he showed me his graded homework. In addition to the usual question marks, there were very funny squiggles and comments from the grader. I asked who he was and was told it was Tom Lehrer. The name meant nothing to me at the time, but I later learned that Lehrer was then in graduate school. He had entered Harvard at the age of fifteen and had graduated in 1946 at the age of eighteen. He was only two years older than I was but was already in his third year of graduate school. By this time, he was beginning to be known around the campus. In 1945, he had written his football rally song, “Fight Fiercely Harvard”: Fight fiercely, Harvard, Fight, fight, fight! Demonstrate to them our skill Albeit they possess the might Nonetheless we have the will.

I had no idea who wrote this and assumed that it must be an old Harvard tradition like the Hasty Pudding. In the following year, this situation changed. First, I met Lehrer at various math department functions. I was a math major. Second, I heard him give a performance at Sanders Theater on the Harvard campus. It was an overflow audience. I heard two songs, and I realized I was in the presence of some kind of genius. The combination of satire, music, and performance was something I had never seen before. But the third event was the decisive one. The master of Eliot House was the classics professor John Finley. I barely knew him. He was not interested in the sciences, and as far as I could remember, the only time I actually spoke to him was at an obligatory tea. So I was completely dumbfounded when he asked me—​indeed, commanded me—​to organize the entertainment for the lunch for the seniors like myself graduating

164  Quantum Profiles in 1951. I had had no association with any of the Harvard undergraduate entities such as the aforementioned Hasty Pudding, which did what might be called entertainment. I had no association with any of the literary journals where creative undergraduates might publish. I was a simple math major. Why me? What was I going to do? But with my back to the wall, I had two brainstorms. One was Lehrer, and the other was Al Capp, the creator of the comic strip Li’l Abner. If Finley knew of my connection with these people, he had the power of clairvoyance. Capp, who then lived in Boston, was an acquaintance of my father. I had met him a couple of times. Many decades later, I learned that he was related to Oliver Sacks, who was also related to Aubrey Eban. What a family! Capp agreed, and so did Lehrer. Finley insisted that I include someone who played the recorder. He performed first and fortunately very briefly. Then it was Lehrer’s turn. Below is typical of the genre: I love my friends and they love me We’re just as close as we can be And just because we really care Whatever we get, we share! I got it from Agnes She got it from Jim We all agree it must have been Louise who gave it to him Now she got it from Harry Who got it from Marie And ev’rybody knows that Marie Got it from me Giles got it from Daphne She got it from Joan Who picked it up in County Cork A-​kissin’ the Blarney Stone Pierre gave it to Shiela Who must have brought it there He got it from Francois and Jacques Aha, lucky Pierre!

Tom Lehrer  165 Max got it from Edith Who gets it ev’ry spring She got it from her daddy Who just gives her ev’rything She then gave it to Daniel Whose spaniel has it now Our dentist even got it And we’re still wondering how But I got it from Agnes Or maybe it was Sue Or Millie or Billie or Gillie or Willie It doesn’t matter who It might have been at the pub Or at the club, or in the loo And if you will be my friend, then I might . . . (Mind you, I said “might” . . .) Give it to you!

I thank Tom Lehrer for permission to quote this. I had the satisfaction with watching Finley’s face while this was going on. He looked as if he had just eaten a persimmon. But it got worse. Capp got up and began by saying that he had enjoyed the songs about murder, rape, venereal disease, and John Finley. At this very moment, some photographer took a picture of the three of us. Capp, looking very pleased with himself, is standing and in full cry. Finley’s face is a frozen mask of disapproval, and I am grinning like the Cheshire Cat. Alas, I cannot find this picture to share it with you. This performance had remarkable consequences for Lehrer. Capp had a weekly radio program, and Lehrer became a fixture. I think that this was the first time he had been let loose on the general public, although the program only lasted four weeks.” In the fall of 1951, Lehrer and a small group of co-​conspirators gave the first of two performances of The Physical Revue, named after the standard American physics journal the Physical Review. I was then a first-​year graduate student in mathematics, but I went to the physics lecture hall to listen. It was wire-​recorded on a spool of fine steel wire by Norman Ramsey, who later went on to win the Nobel Prize. (One can listen to it on YouTube.) By

166  Quantum Profiles this time, I had moved into the new Walter Gropius–​designed dormitories for male graduate students. There was the World Tree, a stainless-​steel sculpture by Richard Lippold. At the time of the vernal equinox, Lehrer and his co-​conspirators planted ball bearings, “world seeds,” under it, and a metal “world bird” on a branch as a spring offering. Here is what appeared in the Harvard Crimson: Spring yesterday came to Harvard Square. While some people like Ellen Krohn ’53 and Menso Boissevain ’52 welcomed the new season in esthetic reverie, others turned to the more symbolic rituals to observe the vernal equinox. At the Fertility Rites held at 8:26 a. m. yesterday, the sacred ceremony of consecrating the soil with bull’s blood was performed to the solemn notes of “Ten Thousand Men of Harvard,” played by the Harvard Band. High Medicine Man Thomas A. Lehrer 4G was chanting “Hail Gropius, unorthodox, we hail thee at the vernal equinox,” in front of the World Tree. Others were absorbed in contemplation.

Lehrer and I sometimes had lunch together in the graduate dining room. On one occasion, a student waiter dropped a tray filled with silverware and dishes, with a resounding crash. “They are playing our song,” Lehrer commented. In early 1953, Lehrer released his first record. He had rented the Transradio Studio in Boston for fifteen dollars. The recordings were made into four hundred LPs at Lehrer’s expense. They sold for $3.50 each. I still have my copy. He was surprised when a large number of orders came in from the San Francisco area. It turned out that the San Francisco Chronicle columnist Herb Caen had heard it and had given it a rave review. Eventually, the record (Songs by Tom Lehrer) sold 350,000 copies and was distributed by RCA. In the meantime, Lehrer was still a graduate student and had published at least one technical mathematics paper. But in 1955, he was drafted into the army for two years, part of which he spent at Los Alamos and most of which he spent at the National Security Agency in Washington. I never found out what he did at these places. He once told me that NSA stood for No Such Agency. My guess is that it was probably codebreaking. One of our Harvard math professors, Andrew Gleason, had spent the war cracking Japanese codes. It was after his military service that Lehrer’s career as a touring performer took off. During the time I knew him, Lehrer spoke to me very little about his family. I had the feeling he was an only child, since he never spoke about any siblings.

Tom Lehrer  167 It is easy to learn online that he was born in New York City on April 9, 1928. One can also learn that he attended the Horace Mann private high school. I am very familiar with the New York private high schools of that era, having attended one, so I know that anyone who went to Horace Mann must have been from a family that was comfortably well-​off. I believe that his father manufactured ties. He did tell me that his mother encouraged him to study the piano and that a teacher of classical piano was provided. But Lehrer wanted to learn popular music, and a suitable teacher for that was also found. In the summers, he attended Camp Androscoggin in Maine. It is still in operation, and the charge for what they call “tuition” is $12,900. He was both a camper and a counselor, and he told me that one camper he counseled was Stephen Sondheim. Because of the difference in rank and age, they never talked much. Very much later, Lehrer got the idea of making the story of Sweeney Todd into a musical. He never did anything about it. It was one of Sondheim’s greatest successes. Even as a high school student, Lehrer’s gift for satirical verse was evident. On being asked on his application to Harvard to supply an example of his writing, he sent a verse that contained the lines, “I will leave movie thrillers /​And watch caterpillars /​Get born and pupated and larve’d /​And I’ll work like a slave /​And always behave /​And maybe I’ll get into Hava’d.” I can imagine that an admissions officer felt that a fourteen-​year-​old high school student who had used “pupated” in a verse was probably worth taking a chance on. It was when he was fourteen that his parents got divorced. After leaving the army, Lehrer became a very successful full-​time performer. He never did get his PhD, but he did teach mathematics at places like MIT, where he spent nine years. His last academic job was at the University of California at Santa Cruz, where he taught musical comedy as well as mathematics. I met a physicist from Santa Cruz and asked him if he had ever met Lehrer. He said that although he did not know much about him, they shared an office. When I explained who Lehrer was, he was genuinely surprised. The last time I saw Lehrer was in New York in the early 1980s, when he had accepted the job in California. He said that he was tired of the severe Cambridge winters and felt that he deserved to have fun and never shovel snow again. He had stopped writing satirical songs because the ideas no longer came easily to him. Lehrer’s last public performance was in 1972, when he appeared at a campaign rally for the Democratic presidential candidate George McGovern. It happened that a friend of mine, the actress Estelle Parsons, was also appearing, so I went. It was like the closing of a cycle. I had seen Lehrer at the beginning of his public career and now at the end. He still wrote songs,

168  Quantum Profiles including a wonderful song for kids for TV’s Electric Company about the “new” math, but they were always performed by other people. From time to time, we email each other. We once reminisced about a math graduate student who was known for his obnoxiousness. He was so obnoxious that to find a practical unit of obnoxiousness, you had to use a millionth of his actual name. Lehrer was in his day unique, and his songs still show up. We could certainly use someone with his gifts now.

9 Max Jammer

Likewise if there were a hole in the empyrean sphere and if the littlest man had a lance the lower end of which he drove with a rectilinear motion towards the outermost surface of the empyrean heaven he would come to a certain part of the lance in the course of its motion; to pass through the last sphere, although outside this sphere no space exists. (Richard of Middleton, fourteenth century, quoted in Max Jammer, Concepts of Space [New York: Dover Publications, 1954]) This arbitrariness is constrained to the theory of supergravity, an extension of general relativity which associates with every boson a fermion and which restricts on algebraic grounds the number of dimensions to eleven. As shown by Edward Witten any higher dimensionality would imply the existence of massless particles with spin greater than 2. (Jammer, Concepts of Space, 246)

I first met Max Jammer sometime around 1952 in the Harvard office of Harry Austryn Wolfson. I had been instructed by both my father and an uncle that I had to meet Wolfson. He was not entirely easy to find. He had an office in the bowels of Widener Library, and as I recall, there was no name on the

170  Quantum Profiles door. When you opened it, you found a smallish man who studied you in a friendly way through thick glasses. You could hardly see him over the mound of books and papers. As he later explained to me, he was working on a study of the “choich fodders,” the founders of the Christian church. The accent was understandable once you realized that he had been born in a shtetl in Belarus and that his mother tongue was Yiddish. He was born in what is now Vilna Governorate in 1887 and emigrated with his parents to the United States in 1903. Five years later, he entered Harvard, and he never left. He created the first Judaic studies center in the United States. He had written a monumental study of Baruch Spinoza, and that was why Jammer had come to see him. He wanted to discuss Spinoza’s views of space. If there were ever two people who were polar opposites in personality, they were Max Jammer and Harry Wolfson. What they had in common was scrupulous scholarship. They must have relished their conversations. Indeed, in his foreword to Jammer’s book on space, Wolfson said that coming to Harvard gave him the resources he needed to do his work, and Wolfson, whom he frequently acknowledged, was certainly one of the resources. Wolfson was a lifelong bachelor who had a special fondness for westerns. Jammer was married and had children. He had been born in Berlin on April 13, 1915, but in 1935, he migrated to what was then Palestine. He had studied physics at the University of Vienna and then at the Hebrew University in Jerusalem, from which he got his PhD in experimental physics in 1942. He then served in the British army. After the war, his interests switched to the history and philosophy of science, and that was what he had come to Harvard as a lecturer in 1952 to pursue. His first book was Concepts of Space:  The History of Space in Physics, which I have been quoting from. It was published first in 1954. It has a thoughtful foreword by Albert Einstein. Jammer had many talks with Einstein in Princeton. This was followed in 1961 by Concepts of Mass in Classical and Modern Physics and in 1962 by Concepts of Force: A Study in the Foundations of Dynamics. Concepts of Mass in Contemporary Physics and Philosophy was published in 2000. There were two books on quantum theory: The Conceptual Development of Quantum Mechanics in 1966 and what I  consider his masterpiece, The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspectives, in 1974. These were followed by Einstein and Religion: Physics and Theology in 1999 and Concepts of Simultaneity: From Antiquity to Einstein and Beyond in 2006.

Max Jammer  171 Jammer died on December 18, 2010, at age ninety-​five. I am going to discuss only three of the books: Concepts of Space, Einstein and Religion, and The Philosophy of Quantum Mechanics. To discuss all the books fully would require a book in itself. There is a problem, at least for me, in reading Jammer’s early books such as Concepts of Space. When he was discussing many of the earlier commentators on space who wrote in Latin, he did not regularly present translations. In the later books, he did. My own command of Latin stopped in high school, but in reading the commentary I can usually get the point. Isaac Newton’s Principia was, of course, written in Latin, but some of his comments about space and time have been so often repeated that the relevant passages almost translate themselves. The famous Scholium that dominated physics until the time of Ernst Mach, whose Science of Mechanics played a very important part in Einstein’s conception of relativity, reads: I do not define time, space, place and motion, as being well known to all. Only I  must observe that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

Then Newton goes on: Absolute space in its own nature without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, or aerial, or celestial space determined by its position in respect to magnitude. Absolute and relative space always remain numerically the same. For if the earth, for instance moves, a space of our air which relatively and in respect to the earth remains always the same, will at one time be one part of the absolute space into which air passes; at another time it will be another part of the same, and so absolutely understood, it will be continually changed. (quoted in Jammer, Concepts of Space, 99–​100)

172  Quantum Profiles John Maynard Keynes, the economist, managed to purchase a considerable portion of Newton’s Nachlass—​letters, speculations of all sorts—​and was astonished at what he read. He had always assumed that Newton was the first of the men of reason but decided that this Newton “was not the first of the age of reason. He was the last of the magicians.” Keynes was not prepared to deal with Newton’s alchemy. In reading what he had written here about absolute space and time as being beyond measurement and, as he also wrote, the “sensorium of God,” one is not unreasonably tempted to see Newton the magician. But Keynes missed the point. Newton understood what we call Galilean relativity. He even employed Galileo Galilei’s metaphor of a sailing ship. Galileo noted that if a ship is moving in uniform motion, someone on board cannot tell whether the ship is in motion or stationary in moving water. Without being able to specify the absolute state of motion, Newton’s laws become meaningless. Force is defined by its capacity to produce acceleration, and to Newton these motions were absolute in the sensorium of God, and that was enough. The question of absolute motion also comes in the famous rotating-​bucket experiment, in which a bucket of water is rotated in empty space, and the surface of the water, he argued, assumes parabolic form. He explained this by assuming that there is a rotation in absolute space which produces the requisite force. Jammer devotes a large part of his book to describing how this puzzle played out in subsequent centuries. Before I turn to this, I cannot resist noting that Jammer quotes letters in French that passed between the Dutch physicist Christaan Huygens and the German polymath Gottfried Leibniz. The letters are full of spelling errors, and Jammer, being the scholar that he was, did not correct them so we could read the originals. I turn next to Mach. I almost think that I know him personally. My teacher Philipp Frank did know him and did arrange for one meeting that Mach and Einstein had. Mach did not believe that atoms existed, and Frank and Einstein were trying to persuade him to change his mind, which he didn’t. He once asked the noted physicist Ludwig Boltzmann if he had ever seen one—​a question I muse over when I consider the confined quark. Mach was born in Chirlitz, which was then part of the Austrian empire, on February 18, 1838. He was home-​schooled until the age of fourteen, and after three years in a gymnasium, he entered the University of Vienna, where he studied physics. One of the things he did was to measure the Doppler effect, which was at the time a matter of contention. He took some members of the faculty who doubted to a vantage point where they could hear the change in frequency of a moving train whistle. He did some important work on ballistic

Max Jammer  173 shock waves that moved in the medium in which they were produced supersonically. The Mach numbers, which give the ratio of the speed of an object in a medium to the speed of sound in that medium, are certainly what he is best known for. If Mach had done only scientific research, he would not have the importance that he has. But he is best known for his work in the history and philosophy of science and above all for his book The Science of Mechanics. This book had an explosive effect on the young Einstein and was certainly one of the influences that led to relativity. Jammer quoted the most famous passage in The Science of Mechanics. The book was, of course, written in German, but fortunately Jammer gave the English version: Newton’s experiment with the rotating vessel of water 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. No one is competent to say how the experiment would turn out if the sides of the vessel increased in thickness of mass till they were ultimately several leagues thick.” (quoted in Jammer, Concepts of Space, 142)

This proposition in various forms is what is known as Mach’s principle. Einstein used it as a guide to his formulation of general relativity. Mach was not really a theoretical physicist, and it is not clear that he ever really understood relativity. When Frank and Einstein went to see him, they discussed the use of atoms in statistical mechanics. They thought that they had convinced him, but he later wrote that he still did not believe in them. Jammer devoted a good deal of space to the invention of non-​Euclidean geometry. This depended on that Euclid’s proposition that there was through an external point one and only one line parallel to a given line. For centuries, this was thought to be a theorem that could be proven from the other axioms, but then consistent geometries, such as the one on the surface of a sphere, were formulated, and it became clear that it was an axiom that described the geometry of a plane. It was the great German nineteenth-​century mathematician Carl Friedrich Gauss who first thought that space itself might be non-​Euclidean. He decided to test this by measuring the interior angle sum of a triangle formed by three distant mountains to see if the sum departed from 180 degrees. There was no measurable deviation. But the first mathematician to really bring us to the modern era was the German Bernhard

174  Quantum Profiles Riemann. I need to issue a word of warning to readers who enter into this part of Jammer’s book. Jammer took no prisoners. He rejoiced in the mathematics and even offered proofs that I do not recall having seen before. For a reader who has the technical background, this part of the book is a rich treat. Riemann created what is known as differential geometry in an arbitrary number of dimensions. The key element is the “distance” between two points in this space that are separated by an infinitesimal distance. These infinitesimals are denoted by dxi. The geometry is defined by an array of quantities gij, and the “distance” is given by a sum over i and j of gijdxidxj. The quantity gij is known as the metric tensor. Riemann had an intuition that this geometry would somehow be determined by gravity, but it was Einstein, in his general theory of relativity, who made this a reality. There is something that Jammer did not include that I think is quite amusing. A few years after Einstein created the special theory of relativity in 1905, the mathematician Hermann Minkowski made it four-​dimensional by introducing a metric that depended on space and time. Einstein at first did not like this at all and said that once the mathematicians had gotten hold of his theory, he no longer understood it himself. But when it came to gravity, he realized that Minkowski’s formulation was the way to go. I have mentioned Mach’s principle that that there cannot be an inertial effect in the absence of a material cause. As Jammer pointed out, experts are until the present day undecided about whether general relativity satisfies this criterion. Jammer discussed Einstein’s foray into cosmology. Einstein had an idée fixe that the universe should be neither expanding nor contracting. But solutions were discovered to his equations that allowed both. We use them to this day. For some philosophical reason, Einstein firmly decided that the universe had to be stationary and that while these solutions were correct, that did not apply to our universe. So against the collapse due to gravity, Einstein introduced a new term into his equations, with a new constant that is now referred to as the cosmological constant, which he fixed just so that the universe would be stationary. Then the astronomer Edwin Hubble found by measuring the redshift of light from distant galaxies—​Mach’s old Doppler effect—​that the universe was, in fact, expanding. We now know that this expansion is accelerating due to some “dark energy.” One explanation is the cosmological constant, but the magnitude involved does not seem to fit with anything we know. This effect is a deep mystery. Toward the end of the book, Jammer entered into the world of elementary particles. In particular, he discussed the matter of parity—​the distinction

Max Jammer  175 between left-​handed and right-​handed coordinate systems. It was shown experimentally about a half-​century ago that interactions involving neutrinos do make a distinction. Here I think Jammer was a little outside of his patch. He had the properties of the neutrinos backward. I wish I had seen the manuscript before he published it. But this does not diminish my admiration for his book. In the last chapter of the revised edition, which I have, Jammer summarized all the reading he had done in the prior forty years. It is a little like watching a landscape from a speeding train. In truth, I did not get much out of it, but the rest of the book made up for it. Jammer’s most accessible book is Einstein and Religion, which was first published in 1999. He had had many discussions with Einstein before the latter’s death in 1955. Jammer returned to Israel in 1956 and became a professor and later president of Bar-​Ilan University in the Ramat Gan district of Tel Aviv. This meant he had convenient access to the Einstein archives at the Hebrew University in Jerusalem. This is a fantastic repository of information about Einstein. I have made use of it myself by means of the Internet. In one instance, I wanted to find a photograph of a fireplace in Fine Hall in Princeton, where there is displayed Einstein’s aphorism Raffiniert ist der Herr Gott, aber boshaft ist Er nicht, which I translate as “God is sophisticated but not malicious.” This is something that Einstein said when he was told in 1921, on his first visit to Princeton, of some experiments that alleged to refute the special theory of relativity. The experiments were, of course, wrong, but the aphorism endures. The archives found the picture for me. A second example is of a very different nature. In the 1920s, a German physicist named Emil Rupp described some experiments he had been doing to study the quantum nature of radiation. This caught Einstein’s attention, and he began communicating with Rupp suggesting modifications, which Rupp then replied to explaining his alterations. This exchange went on for several years, until a notice appeared in the Zeitschrift für Physik that Dr. Rupp had been “ill” since 1932 and that during this period, he had published papers that were “fictions.” In short, Rupp was a fraud. He entered a sanatorium and died in 1939. I had not seen anything written about this odd episode, so I decided to write a short article. I explained to the staff of the archives what I was trying to do, and they sent me all the correspondence they had between Einstein and Rupp. The archives were a wonderful resource, and Jammer acknowledges them frequently in his book. In an essay published in 1941, Einstein presented his famous aphorism, “Science without religion is lame, religion without science is blind.” If I had

176  Quantum Profiles to summarize Jammer’s book in a few words, I would say it is an attempt to explain this aphorism. As for myself, the more I think about it, the less I understand it. Einstein never wrote anything like an autobiography. The closest he came was in a response to a collection of essays that were written by a number of scientists and philosophers and collected in a volume. This is what he said about his early encounters with religion: When I was a fairly precocious young man I became thoroughly impressed with the futility of hopes and strivings that chase most men restlessly through life. Moreover, I soon discovered the cruelty of that chase, which in those years was much more carefully covered up by hypocrisy and glittering words than is the case today. . . . As the first way out there was religion, which is implanted into every child by way of the traditional education-​ machine. Thus I  came—​though the child of entirely irreligious (Jewish) parents—​to a deep religiousness, which, however, reached an abrupt end at the age of twelve. Through the reading of popular scientific books I soon reached the conviction that much in the stories of the Bible could not be true. The consequence was a positively fanatic orgy of freethinking coupled with the impression that youth is intentionally being deceived by the state through lies; it was a crushing impression. (Albert Einstein: Philosopher-​ Scientist, Vol. 7 in the Library of Living Philosophers, Evanston, Ill., Library of Living Philosophers, 1949; trans. Paul Arthur Schilpp)

Einstein never practiced a formal religion once he passed age twelve. I doubt if he ever entered a synagogue for a service. But he did maintain a strong interest in religions as a phenomenon with a fascinating history. This I can testify to from a personal experience. A number of years ago, I got the idea of trying to write a profile of him for the New Yorker. I had no clue how to start, but I had the inspired idea of contacting Helen Dukas, whom I had gotten to know when I was at the Institute for Advanced Study in Princeton. In 1928, Einstein’s then-​wife Elsa was looking for a secretary for him. She had heard of Dukas, who was then in Berlin working as a secretary for a publishing house. It was decided that Dukas would fill the bill. In 1933, she emigrated to the United States with the Einsteins and went to Princeton with him. When his wife died in 1936, Dukas also became his housekeeper. When I knew her, she was living in the Einstein house on Mercer Street in Princeton, and when I contacted her about the profile, she suggested that I come to the

Max Jammer  177 house and perhaps get some ideas. It was a modest two-​story house with no garage and no driveway. (Einstein did not own a car, and I am not sure if he ever learned to drive. He would walk to the Institute and, at least in his later years, was driven back in one of the Institute’s station wagons. The only time I ever saw him, he was getting into a station wagon.) On the second floor of the house, he had his own apartment. When I saw it that day, it was just as he had left it. I noticed a small bookcase and was naturally curious to know what he had been reading. Among the books was James Frazer’s The Golden Bough, which is a comparative history of religions. As Jammer noted, Einstein took a great deal of flak from various religious representatives for the part of his aphorism where he says that religion without science is blind. I was surprised at the personal level of some of these criticisms. The problem was that Einstein’s God was not a personal God to whom one could pray. He had, as he himself said, a Spinozian view of God, as expressed in statements like the following by Spinoza, who was ostracized for making them. To his community, he was a heretic, and that name and worse were applied to him. Here is what Spinoza wrote: “The universal laws of nature, according to which all things exist and are determined, are only another name for the eternal decrees of God, which always involve eternal truth and necessity. So that to say that everything happens according to natural laws, and to say that everything is ordained by the decree and ordinance of God, is the same thing.” For Einstein, God, whom he sometimes referred to as the “Old One,” was really a code name for the secrets—​the secrets of the Old One—​that we are allowed to glimpse. For Einstein, mere phenomenology was not enough. Science without this attempt to see what lies behind the mere phenomenology does not fulfill its purpose. It is interesting to note that until he created the general theory of relativity, Einstein was what I would call a phenomenologist. He won the Nobel Prize not for relativity but for his explanation of the experiments involving the photoelectric effect. Even his 1905 paper on special relativity is phenomenological. It begins: 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

178  Quantum Profiles 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 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.

This is pure phenomenology. General relativity was totally different. The phenomena came last. It was not that Einstein began with the problem of the anomalies in the orbit of the planet Mercury and looked for a way to explain them. He began with principles of symmetry and created out of pure thought a theory that explained the orbits of Mercury. This was an experience that Einstein never got over. He was sure that something like this must lie behind quantum theory—​another secret of the Old One which he could never find. The second part of the aphorism, “religion without science is blind,” is what caused all the trouble. I am not sure what he meant. He could have meant that if a structure like the general theory of relativity does not lead to experimental predictions, it is not a scientific theory. That certainly would not have inspired the polemics that were addressed against him. For the people who launched those, it was interpreted to mean that religion without scientific verification is handicapped. Put very bluntly, the existence of God must be scientifically verified, and that there are no miracles was intolerable to these critics. As I noted, I am not sure what he meant, and I am not sure that Jammer was sure, either, but he made a valiant effort to explain. Jammer’s masterwork was The Philosophy of Quantum Mechanics. It is a very large book of more than five hundred pages. It was published in 1974 and not recently reprinted. This is a pity, because little of it is dated. John Bell is there, and so are the many worlds of Hugh Everett III. Jammer seems to have read every publication in every language on the subject. What is more remarkable is that he had somehow found unpublished PhD theses in various languages that he thought had something significant to say. Let me give a specific example. When I went to the Institute for Advanced Study in the fall of 1957, another postdoc there in theoretical physics was Loyal Durand III,

Max Jammer  179 known as Randy. He was a couple of years younger than I was and had done his PhD at Yale. He wrote a thesis on a fairly standard subject but somehow had become interested in the foundations of quantum mechanics. At that time—​before Bell—​this was a very unusual thing for a young physicist to study. The subject was left to our elders such as Einstein and Niels Bohr. For all practical purposes—​FAPP in Bell’s acronym—​it did not matter. The only text where these things were discussed was the one written by David Bohm. In it, Bohm defended what was known as the Copenhagen interpretation—​ although Bohr never gave it that label or indeed any label. When Durand came to the Institute, he worked on this, and a preprint emerged in January 1958 titled “On the Theory and Interpretation of Measurement in Quantum Mechanical Systems.” This apparently caught the attention of Oppenheimer, and Durand was asked to present his paper at one of our weekly seminars. To understand what happened, I must describe the dynamics of these seminars. Oppenheimer sat in the center of the front row. I  think he may have smoked during the talks. (He would die of throat cancer.) He would constantly interrupt the speaker with questions, and after asking one, he would turn around and look at us to see if we had absorbed the brilliance of the question. Speakers reacted to this in different ways. The very young Freeman Dyson was reduced to silence when he tried to explain Richard Feynman’s electrodynamics. Oppenheimer thought that Julian Schwinger had a monopoly on the subject. The best was the very brilliant Swiss physicist, senior Res Jost. Jost had just gotten under way when Oppenheimer asked if he could explain so-​and-​so. Jost said yes and continued with his seminar. Then Oppenheimer asked again if he would explain so-​and-​so. Jost said no and continued with his seminar. Oppenheimer then asked why he wouldn’t explain so-​and-​so. Jost then answered, “It is because you won’t understand my answer and you will ask more questions and take up all of my time.” That silenced Oppenheimer. Now he started in on Durand. His basic point was that Durand was wasting his and our time by doing things that had already been done by Bohr. He kept interrupting, so Durand had no chance to finish his seminar. But Durand was made of strong stuff, and in 1960, he published a paper with the same title in the journal Philosophy of Science (17 [April]: 115). By this time, he had left the Institute and begun a distinguished career. Not only did Jammer discuss this paper, but he also discussed some papers that reacted to it and were published in even more obscure journals. Some of these papers were highly critical. Jammer left the reader to make up his or her mind.

180  Quantum Profiles Jammer’s Philosophy of Quantum Mechanics is organized into topical units, each one long enough to make a small book in itself. Typical is the one on Bell and his work. There is in it a historical note that took me completely by surprise. Indeed, at first, I  thought Jammer must have misunderstood something. Here is what he wrote: From the historical point of view it is interesting to note that the original idea of Bell’s result had been anticipated by T. D. Lee by about four years. Tsung-​Dao Lee, a native of Shanghai, studied at the universities of Kucichow and Kunming chang, largely guided Lee, and he soon transferred into the Department of Physics of National Che Kiang University, where he studied in 1943–​1944. However, again disrupted by a further Japanese invasion, Lee continued at the National Southwestern Associated University in Kunming the next year in 1945, where he studied with Professor Wu Ta-​You. China, obtained his PhD in 1950 working under Edward Teller at the University of Chicago, and has been at Columbia University since 1951. On May 28, 1960, three years after receiving with Chen-​Ning Yang, whose acquaintance he had made in Kuming, the Nobel Prize for his well-​known work on the breakdown of parity nonconservation, Lee gave a talk at Argonne National Laboratory on some striking effects of quantum mechanics in the large. In the course of this lecture he discussed certain correlations which exist, as he pointed out , between two simultaneously created neutral K-​mesons (kaons) moving off in opposite directions. Realizing that the situation under discussion is intimately related to the problem raised by Einstein, Podolsky and Rosen, he soon convinced himself that classical ensembles, for that matter systems with hidden variables, could never reproduce such correlations. But due to the complications caused by the finite lifetime of kaons—​for infinite lifetimes the situation would “degenerate” into that discussed by Bell—​ but he did not derive any conclusion equivalent to Bell’s inequality but assigned further elaboration of these ideas to Jonas Schurtz, who however soon began working on another project. (Jammer, Philosophy of Quantum Mechanics, 368)

Let me note for the record that Lee and Yang did not meet until they both got to Chicago. The first thought that occurred to me was why kaons? Why not neutral pions? Let me begin with a brief recapitulation of a situation

Max Jammer  181 where we know that Bell’s analysis applies. Let us imagine we have prepared two electrons in a spin singlet state ↑↓—​↓↑.

This is a very crude representation in which the arrows represent the spin, the first position is the first electron, and the second position is the second electron. It is in an “entangled” state—​to use Schrödinger’s term—​with a given electron having both directions of spin with equal weights simultaneously. This coherence persists even when the electrons are separated by any distance, so long as a perturbing force does not “decohere” them. One way to produce this decoherence is to measure the spin of one of the electrons. This can be done by having the observers prepare magnets that point in, say, the z direction. The spin magnetic moment of an electron will couple to this field, and the electron will follow one orbit or the other depending on its spin. Thus, we can infer the spin of the electron. Did the electron have this spin before the measurement? Not if we believe quantum mechanics. It had no particular spin but a fifty-​fifty mixture. But things get worse. Suppose the second observer located a huge distance away from the first observes the spin of the second electron also in the same singlet state. Suppose that later the two observers compare notes. They will find a perfect anti-​correlation. If one observer observes spin up for a given electron, the other will observe spin down for the companion electron. This is an example of what Einstein called “a spooky action at a distance.” But things get still worse. Suppose we rotate the magnets so they are oriented at an angle θ with respect to each other; then the correlation becomes –​cos(θ). How do the electrons know? This is a really spooky action at a distance. You might try to seek an “explanation.” Here is one possibility. Attached to each electron is a minuscule robot, and these robots can communicate instantaneously so that one can inform the other about the rotation of the magnet and what to expect. This an example of what is often referred to as a hidden variable, some classical variable that can reproduce the results of quantum mechanics. But in order for this to work in this case, the communication between the distant two robots must be essentially instantaneous. This is sometimes called non-​ locality, communications at speeds greater than light. What Bell showed was that no local hidden-​variable theory can reproduce the results of quantum mechanics. We can construct a measurement with the two magnets that this hidden-​variable theory cannot predict correctly. This is what Bell showed in

182  Quantum Profiles general. Then what did Lee do? Since he never published this work, we can only make an educated guess. By the way, Bell’s analysis has been applied to kaons, and there are whole conferences devoted to it. Lee is not mentioned, I think for good reason, and until I read Jammer’s book, I had no idea of his involvement. The analysis with the kaons is a much more complex situation than the coherent spins, and I will only sketch the general ideas and refer the reader to the literature. (See, for example, Reinhold A. Bertlmann and Beatrix C.  Hiesmayr, “Strangeness Measurements of Kaon Pairs, CP Violation and Bell Inequalities,” arxiv.org, 2006.) In order to set up a Bell situation, you must be able to produce a coherent state of two particles. It can be done for photon pairs using their polarizations, but this realization came after Bell’s original work and has nothing to do with what Lee did. Lee imagined that there could be a decay of a particle that produces a neutral kaon and its antiparticle. Here at once we must adumbrate. Many of the neutral particles we are familiar with, such as the photon and the neutral pion, are identical to their antiparticles. A neutral particle, such as the neutron, is not. But there is no known interaction that can mix these objects. The neutral kaon is quite different. Let me call the particle Ko and the antiparticle, for want of a better notation, Koc. These particles are produced in strong interactions that conserve a quantity called strangeness. The strangeness of the Ko is plus 1, while the strangeness of its antiparticle is minus 1. This might be uninteresting except that the interactions that cause these particles to decay do not conserve strangeness. This interaction can mix particle and antiparticle. We construct two states KL and KS where, for reasons that will become clear, L and S stand for long and short. Thus,

K S = K 0 − K oc

and

K L = K 0 + K oc .

Under CP—​charge conjugation and parity—​Ks goes into itself, while KL goes into its negative. The crucial point we have used here is that the neutral kaon is a spin-​0 pseudo-​scalar meson, so its intrinsic parity is negative. Now, if we

Max Jammer  183 have, say, a positively and negatively charged pion in a state with no orbital angular momentum, then this state goes into itself under CP, while if we have three pions, this will go into its negative. The decay rate for a two-​pion decay of the K0 is larger than that of a three-​pion decay, and hence the names long and short for the particles with definite lifetimes. They also have slightly different masses. This means that the two K0s, which can be rewritten in terms of the states with definite lifetimes, can mix, causing an oscillation between them as a function of time. A beam that begins as K0s will in the course of time contain Kocs. One can ask for the probability of finding, say, two Kocs at a later time. But the two states K and anti-​K are analogous to the two spin states up and down that we considered above. We can write the initial state as an entangled state involving the long-​and short-​lived mesons; symbolically. “long1short2–​short1long2.” Long and short are the analogies of spin up and spin down when we discussed the singlet state of two electrons. This enables us to carry out a Bell analysis to see what quantum mechanics implies for these correlations over time. For details, see the Bertlmann and Hiesmayr paper referred to above. This paper discusses the Bell inequalities for this process. While they have been studied experimentally for electrons and photons, I do not think that these experiments have been carried out for the K mesons. This is not what Lee and Yang did. A paper by T.  B. Day (“Demonstration of Quantum Mechanics in the Large,” Physical Review 121, no. 4 [1961]: 1204–​1206) makes this very clear. One gets the impression that Day actually heard Lee’s presentation. The question addressed by Lee and Yang is the probability of observing at some time after the creation of the K pairs an anti-​K in coincidence with a K or another anti-​K. Quantum mechanics gives a time-​dependent formula for this that is totally different from the classical answer. This is a manifestation of quantum entanglement. This has nothing to do with the question that Bell raises of whether this quantum answer can be derived from a local hidden-​variable theory. As Jammer noted, Lee did not claim that they derived anything like a Bell inequality. That is what the recent work I have referred to deals with. I have no understanding of what Lee meant when he said that for infinite lifetimes, the situation would “degenerate” into that of Bell. Once again, I wish I had had the opportunity to discuss this with Jammer. I want now to discuss two sections of Jammer’s book that deal with what is often called the quantum measurement problem. These two sections, one on Bohmian mechanics and the other on Everett’s many-​worlds interpretation, solve the problem by saying there isn’t one. Let me begin with something that

184  Quantum Profiles I would not describe as a problem, although Einstein did, but as a fact about quantum mechanics. Suppose we have a system described by a Hamiltonian H and we solve for the wave equation as a function of time. The formal solution is

ψ (x, t ) = e

−i

Ht 

( )

⋅ ψ x ,0 .

Here H is the Hamiltonian. There are two things to note. First, this equation is time-​reversible. We can go back to t = 0 by a suitable multiplication of an exponential. It is also completely deterministic. The future wave function is determined causally by the past. The probability interpretation is in a sense tacked on. It cannot be derived from any theory we know. Most of us just accept it because it works. Einstein didn’t and was sure that there must be some uhr theory to which quantum mechanics is a useful approximation. The second thing to note—​and this takes more explanation—​is that this equation cannot describe the measurements of quantum systems. This I will explain by using the example we have been discussing: the two electrons entangled in a singlet state. Their joint wave function can be solved for in the region where the electrons encounter their respective magnets. One can put in reasonable parameters and note that when this wave function is used to derive the expectation value of something, there are cross terms that implicate the two electrons. These cross terms have giant numbers in the exponential, which means that the corresponding trigonometric functions oscillate wildly, so in an integral, one can set them approximately to zero. The wave function is said to decohere. It is important to note that this is an approximation. But it is the approximation that describes the measurement. Indeed, the measurement selects—​projects out—​one of these terms, after which the wave function has no memory of the other term. This process is reversible so long as one does not drop the cross terms, but once this happens, it cannot be reversed to construct the original wave function, and hence it cannot be described by ordinary quantum mechanics—​the Schrödinger equation. That is the quantum measurement problem. Everett and Bohm, using different mechanisms, “solve” the problem by introducing formalisms where it does not arise. The reader must decide whether this game is worth the candle. In particular,

Max Jammer  185 there is the matter of relativity. Neither the collapse of the wave function nor either of the two methods I am going to discuss for solving the measurement problem is consistent with relativity. One would be entitled to dismiss the whole enterprise as academic, but quantum theory without particle production is not consistent with relativity. When the kinetic energies of particles become comparable to the masses of various particles, they will be produced. However, one might—​and I do—​take the position that these attempts might offer clues to how they could be generalized in a quantum field theory that would be consistent with relativity. I will begin with Bohm. I first became aware of his work on quantum theory when I made use of his textbook to supplement the material in an introductory course I was taking with Schwinger. As I mentioned earlier, there is no hint of Bohmian mechanics in Bohm’s book. Indeed, Einstein read it and asked Bohm, who was at Princeton, to come and see him to talk about quantum theory. I  once wrote a letter to Bohm to ask if this discussion had influenced him to try a new direction, but I did not get an answer. I did read his first paper, which came out in 1952, and decided that it was too complicated to work on. I had a chance to mention this to Schwinger, who said that as far as he was concerned, it was too simple. This also seems to have been Einstein’s view, and indeed, he wrote to Max Born, “Have you noticed that Bohm believes (as de Broglie did, by the way, 25 years ago) that he is able to interpret the quantum theory in deterministic terms? That way seems too cheap to me. But you, of course, can judge this better than I.” Later, Einstein even claimed that Bohm’s physics was wrong, which provoked a firm rebuttal by Bohm. A reader of this chapter may not be familiar with Bohmian mechanics, so here is a brief primer. The Schrödinger wave function ψ can be written as:

Ψ = R exp(iS / ).

Here R and S are real functions of space and time. Using the Schrödinger equation

i∂Ψ / ∂t = − 2 / 2 m ∇2 Ψ + V (x )Ψ,

186  Quantum Profiles we have

∂R / ∂t = − 1 / 2m[R ∇2 S + 2 ∇ R • ∇S].

If we let the probability Ψ Ψ be called P then R = P1/​2 or from the above,

∂P / ∂t + ∇ • (P∇S / m) = 0,

which suggests that if we identify ∇S / m with a velocity and call j = P∇ S / m the current, we have a continuity equation. We will soon see what velocity is to be so identified. There is a second equation that reads

∂ S / ∂ t + (∇ S)2 / 2m + V (x ) − 2 / 4m(∇ 2 P / P −1 / 2(∇ P )2 / P 2 ) = 0

where we have made use of the Schrödinger equation with the potential V. So far, there is no new interpretation of quantum theory involved. All we have done is to replace the Schrödinger equation with two equations for the modulus and phase of the wave function. It is the next step that suggests this interpretation. To see this, we call the quantum mechanical potential U(x) with



U (x ) = − 2 / 4m(∇2 P / P − 1 / 2(∇P )2 / P 2 ) = 2 / 2m(∇2 R / R)

If we set ћ = 0, this equation is just the classical Hamilton-​Jacobi equation, which can be derived from Newton’s law. We have here a sort of quantum-​ mechanical Hamilton-​Jacobi equation. But let us suppose that we take the • continuity equation seriously and identify ∇S / m with Q the velocity of a real particle of mass m. Then the “Newton’s law” is ••



mQ = − ∇(V (Q) + U (Q)).

This is Newton’s law with the extra-​quantum-​mechanical potential. This is the form of the equations of motion for the Bohmian particles that you will

Max Jammer  187 find in Bohm. Most other authors present a first-​order equation from which this equation can be deduced. This is what de Broglie did. Bell may have been the first of the modern authors to write the equations in this first-​order form. Thus, in our previous notation, the first-​order equation for the time evolution of Q is •



Q = j(Q, t ) / P (Q, t ) = 1 / m∂ / ∂Q(Im log ψ (Q, t )).

In writing the second part of this equation, we have used the fact that j can be written as

(

)

j = 1/ m Im Ψ † (Q, t )∂ / ∂QΨ(Q, t ) .



As a consequence of the continuity equation, the probability density of the 2 particle position (or configuration) will be Ψ(t ) at all times t, assuming (as we do) that it is so distributed initially. Before we launch into the deep end of how Bohm’s interpretation deals with the issues of quantum theory, let’s begin with the simplest example imaginable. In this example, I will set ћ = 1. Our modus operandi is first to solve the Schrödinger equation for the ψ we are going to insert into the expression for the quantum potential. The solution to the Schrödinger equation in this case is a free-​particle solution in which the normalization is irrelevant, since it cancels in the expression for the quantum potential. The solution to the Schrödinger equation in this case is with Planck’s constant set equal to one

ψ ( x.t ) = exp(i ( px − ωt )).



•

If we insert this, we get Q = p / m , which tells us that in this case, the Bohmian particle moves in a straight line with no change of speed. A more interesting example to work out is the one-​dimensional simple harmonic oscillator. The wave function for the ground state is, with A the normalization,

Ψ =  exp(− x 2 / 2a2 )exp(−iω 0t / 2),

with a = ( / m ω 0 )1/2 .

188  Quantum Profiles Here the factorization into the R and exp(iS) is given to us on a platter. But notice that in this case, S is independent of x. This means that the particle momentum is zero. We are indeed dealing with a stationary state in the sense that there is no motion. To see that this is consistent with “Newton’s law,” the reader is invited to work out the quantum potential. You will find that this cancels against the classical potential, leaving behind a constant term—​the ground-​0state energy ћω/​2—​which does not generate a force since it has zero gradient. This picture may or may not agree with one’s intuition, but intuition is hard to objectify. I would like to end this chapter with two issues discussed by Jammer in some detail; I will not give anything like the detail one finds in his book. First, how does the model escape the general strictures put on hidden-​variable theories? And then, what does the model say about the quantum measurement problem? Someone first exposed to Bohmian mechanics may well wonder why it is a hidden-​variable theory at all. The Newtonian particles it deals with are there for all the world to see. But one must recall that to define a solution to Newton’s equation, one must specify initial conditions. This is true of Bohmian mechanics with its Newton’s law. But what gives it its hidden-​ variable character is the fact that the initial conditions are distributed statistically as weighted by the square of the wave function at this point in space-​time. These initial conditions are the hidden variables. Bell’s stricture on such theories is that they cannot be local. But the minute you introduce two interacting particles, you find that they must be linked by instantaneous communication. The theory is non-​local in the worst possible way. Signals must travel at speeds greater than that of light. Hence, Bell’s stricture does not apply. There are others that the theory also evades, and once again, I recommend Jammer’s book as a way of learning about them. The best illustrative example is the notorious double-​slit experiment. A beam of electrons, one at a time, passes through first a single slit and then a double slit. The diffraction patterns are completely different, and a question naturally arises for someone—​say, a student—​hearing about this for the first time: if the electrons pass through the slits one at a time, how does the electron “know” the difference between the two cases? The answer given is that in quantum mechanics, everything is governed by probabilities. Here you have a sum of probabilities that must be squared, and this is what accounts for the interference. That is just how quantum theory works. In Bohmian mechanics, things are totally different. The electrons follow trajectories that are derived from the quantum potential. The lines can pass through both slits,

Max Jammer  189 but the electron following one of the paths can travel through only a single slit. This demystifies the whole business but at the cost of some heavy-​duty mathematics. Again, one must ask if the game is worth the candle. If you take this example as a form of quantum measurement, you see that there is no collapse of the wave function, and the whole problem has disappeared. I am well aware that I have oversimplified the issues, and I can assure you that Jammer did not. In the preface to his magnificent book, Jammer wrote: “In spite of its significance for physics and philosophy alike, the interpretative problem of quantum mechanics has rarely, if ever, been studied sine ira et studio from a general historical point of view. The numerous essays and monographs published on this subject are usually confined to specific aspects in defense of a particular view. No comprehensive scholarly analysis of the problem in its generality and historical perspective has heretofore appeared. The present historic-​critical study is designed to fill this lacuna.” And so it does.

10 Robert Serber

Robert Serber

I do not remember how Bob Serber and I became friends. It was a somewhat unlikely friendship. He was twenty years older than I, and we never taught in the same institutions. But it happened that I last spoke to him in the hospital, where as it turned out he was making an unsuccessful recovery from brain surgery. He died at home on June 1, 1997, at the age of eighty-​eight. Serber was born in Philadelphia on March 14, 1909. He took his undergraduate degree at Lehigh and received his doctorate at the University of Wisconsin in 1934. He won a rare fellowship in those Depression days and planned to go to Princeton, but on the way he stopped at Ann Arbor, Michigan, where there

Robert Serber  191 was a celebrated summer school in physics. One of the lecturers was J. Robert Oppenheimer, and Serber was so impressed that he followed Oppenheimer back to Berkeley. They wrote some papers together and became close friends. In 1938, Serber took a job at the University of Illinois. He recalled that from the summer of 1942 until March 1943, he and Oppenheimer basically constituted the entire theoretical part of the atomic-​bomb program in the United States. The British had a more advanced program. In March 1943, Los Alamos got started. Serber moved there with his wife, Charlotte, who came to run the technical library, and Oppenheimer moved there with his wife, Kitty. Serber became Oppenheimer’s assistant, a job that took various forms. When the laboratory went full out on implosion, the design and construction of the gun-​assembly device that was eventually dropped untested on Hiroshima was left to Serber. (He would be the first physicist to visit the Japanese city after the explosion. He took a Geiger counter, but there was no radioactive fallout.) While at Los Alamos, Oppenheimer gave Serber and his wife the task of going to Santa Fe on a Saturday night to throw people off by planting the rumor that they were working on a novel submarine on the mesa, only to discover that no one cared, although several men enjoyed dancing with Charlotte Serber. Many gifted technical people began arriving at Los Alamos, but almost none of them knew anything about nuclear weapons. Oppenheimer assigned Serber the job of teaching them. Serber gave a series of five lectures for an audience of about fifty people. The lectures were written up and then classified until 1965. Now they are available as a small book, The Los Alamos Primer, with Serber’s wonderful annotations. It is the best source I  know for anyone with a little technical background to learn about the physics of these weapons. I want to focus here on the first part of the first lecture, where Serber introduced the units that measure the explosive energy of a nuclear weapon. These units have been with us ever since. He considered a kilogram (2.2 pounds) of uranium and asked how much energy would be liberated if the entire kilogram was fissioned. I want to note two things. Uranium is considerably denser than lead. If one made a kilogram sphere, it would have a diameter of less than two inches. If you had such a sphere, it would not do anything much. You would need a critical mass, which for U235 is 52 kilograms, a sphere with diameter of about seven inches. So Serber was conducting a thought experiment. We need to know how many nuclei are in our kilogram sphere and what each fission provides in terms of energy. I will begin with the latter. In terms

192  Quantum Profiles of units that may be unfamiliar, it is about 200 million electron volts per fission. The electron volt—​I will spare you the definition in terms of electrons and volts—​is the practical energy unit for atomic and nuclear physics. For example, you would have to supply about 14 electron volts to extract the most tightly bound electron from the hydrogen atom. But as a practical unit of energy for real life, it is useless. A better unit is the joule. That is what it would take to lift an average tomato by a meter. The electron volt is 1.6 × 10-​19 joules. So 200 million electron volts is about 3 × 10-​11 joules. There are about 2.6 × 1024 uranium nuclei in a kilogram, so if they all fissioned, we would produce about 1013 joules. If you read Serber’s notes, you will see that he expressed things in terms of ergs and not joules. Since a joule is 107 ergs, we can write this energy release as about 7 × 1017 ergs per gram, where I have carried out the multiplications in the factors that come with the powers. But TNT produces about 4 × 1010 ergs per gram, a factor about 107 times smaller. If we reexpress this in terms of kilotons, where 1 kt = 109 grams, we see that the practical unit for expressing the explosive power of fission is in terms of an equivalent number of kilotons of TNT it would take to produce the same explosive energy. That is what it means when one says that a certain nuclear test has a yield of, say, 100 kilotons. This equivalence is clearly spelled out in Serber’s primer. I have invented a unit that I think is even more graphic. I call my unit the Ryder truck. On April 19, 1995, Timothy McVeigh detonated a rented Ryder truck packed with 2.5 tons of ammonium nitrate fertilizer in front of the Alfred P.  Murrah Federal Building in Oklahoma City, killing 168 people and shocking the country. So it would require 400 Ryder trucks to produce a kiloton or 8,000 to produce the blast energy of the Nagasaki explosion. I leave it to the reader to produce the number of Ryder trucks needed to generate the energy of a megaton hydrogen bomb. As I have said, I do not remember how I first met Serber. I do remember going to a couple of his parties. Charlotte, his wife, tended to fill whatever space was available with her personality, and Serber was pretty laconic in her presence. She died in 1967, as did Oppenheimer. Serber and Kitty Oppenheimer decided to live together. Part of living together meant sailing. Serber had a boat, and he often sailed in the Caribbean. The pair decided they would sail around the world. They had gotten as far as the Panama Canal when Kitty became fatally ill. She died on October 27, 1972, in Panama City. I would like to finish this chapter with a couple of anecdotes.

Robert Serber  193 I did a profile of Hans Bethe for the New Yorker. He told me about something that happened at Los Alamos. On December 31, 1943, Bohr arrived accompanied by his son Aage and General Leslie Groves, who ran the Manhattan Project. Groves was very exercised by something Bohr apparently showed him. It was a drawing of what Bohr thought was a design for a German nuclear weapon, and it was somehow associated with Werner Heisenberg. Groves insisted that Oppenheimer assemble some of his senior staff on New Year’s Day to discuss the drawing. Bethe immediately understood that it was a drawing of a reactor design and indeed not a very good design. It did not occur to Bethe or anyone else at the meeting that the Germans might be planning to use a reactor to make plutonium. This would have alarmed them, but they simply wrote the whole thing off. I mentioned this briefly in my New Yorker profile of Bethe and forgot about it. I was surprised when I was informed that the historian and writer Thomas Powers, based on my profile, was claiming that this was another example of Heisenberg’s defiance of the government and was done at great risk of giving away nuclear secrets. I was sure that this was nonsense, but I felt that I should reinvestigate the matter. To this end, I attempted to contact everyone still alive who I thought might have attended this meeting. At the top of my list was Aage Bohr. He categorically denied that Heisenberg ever gave his father a drawing. Working down the list, I came to Serber. He told me that he had come a little late to the meeting, and when shown the drawing, he realized at once that it was of a poorly designed reactor. He also sent me a copy of a report prepared by Bethe and Edward Teller which showed that this reactor could not blow up like a bomb. Here the matter rested for a couple of years. But then a colleague of Serber at Columbia, Mal Ruderman, solved the riddle. During the time he had been on the faculty at Berkeley, the German Nobelist J. Hans D. Jensen came to dinner. Somehow the subject turned to the war, and Jensen said he had made two trips to Copenhagen to see Bohr. On one of them, he gave Bohr the drawing of Heisenberg’s reactor. Finally, I would like to deal with something that involves memory—​always perilous. Sometime in the spring of 1963, Murray Gell-​Mann gave a lecture at Columbia on his recently constructed classification scheme of the elementary particles. It was a useful approximation to assume that they were classified in multiplets of related particles. The multiplet with the least number of particles at the time was an octet with eight. At one point, Serber raised his hand and asked about the triplet, the smallest multiplet possible in the scheme. Where was it? This much I am sure of. What happened next I am not

194  Quantum Profiles sure of. I do not remember Gell-​Mann’s answer, but I am sure we discussed the scheme at the Chinese lunch that followed. I do not remember if anyone, including Serber, mentioned that if you composed ordinary particles out of such triplets, the triplets would have to bear fractional electric charges. They would be totally bizarre, and so they were when Gell-​Mann presented them as quarks.

Notes Chapter 3 1. The details appeared in a paper published the following year. Erwin Schrödinger, “An Undulatory Theory of the Mechanics of Atoms and Molecules,” Physical Review 28, no. 6 (1926): 1049–​1070. 2. Albert Einstein to Max Born, December 4, 1926, in The Born–​Einstein Letters, trans. Irene Born (London: Macmillan, 1971), 91. 3. A remarkable group photograph taken at the conference shows the greatest physicists of their generation gathered together. Einstein is, of course, in the first row, along with Hendrik Lorentz, Marie Curie, and Max Planck. Paul Dirac is seated behind Einstein in the second row. Niels Bohr is at one end of the second row beside Max Born. Wolfgang Pauli, Werner Heisenberg, and Erwin Schrödinger are all standing in the back row. To view the photograph online, see Wikipedia, “Solvay Conference.” 4. A wonderful discussion of this can be found in Bohr’s contribution to Albert Einstein, Philosopher Scientist, edited by Paul Arthur Schilpp (New York: MFJ Books, 1969). 5. Eventually, this is going to enter into the position-​momentum uncertainty relation, but here I want to use it for another purpose. 6. Erwin Schrödinger, “The Present Status of Quantum Mechanics,” Naturwissenchaften 23, no. 48 (1935). 7. In my view, this is not a paradox. An example of a paradox is a Cretan holding a sign that reads “All Cretans are liars.” This is a paradox in language. I have yet to encounter anyone who can tell me what the paradox is in the cat paradox. Describing a cat using a wave function goes against every notion we have of what a cat is. That is perhaps the paradox, but it is only a paradox in the theory of cats. 8. George Greenstein and Arthur Zajonc, The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics (Sudbury, MA: Jones and Bartlett, 1997), 157. 9. Albert Einstein, Boris Podolsky, and Nathan Rosen, “Can Quantum-​Mechanical Description of Physical Reality Be Considered Complete?” Physical Review 47, no. 777 (1935). 10. Schrödinger, “The Present Status,” n. 2. 11. Einstein to Born, September 7, 1944, in The Born–​Einstein Letters, 149. 12. I regret even more not asking him if the discovery of DNA’s structure had caused him to change any of the views expressed in his masterpiece What Is Life? I did not know enough to ask or to tell him that people like Francis Crick had moved from physics to biology in some measure because of his book. Erwin Schrödinger, What Is Life? The Physical Aspect of the Living Cell (Cambridge: Cambridge University Press, 1944).

196 Notes 13. Albert Einstein, “On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses,” Annals of Mathematics 40, no. 4 (1939): 922–​936. 14. J.  Robert Oppenheimer and Hartland Snyder, “On Continued Gravitational Contraction,” Physical Review 56 (1939): 455–​459. 15. Albert Einstein, “Die Feldgleichungen der Gravitation,” Sitzungsberichte der Preußischen Akademie der Wissenschaften zu Berlin (1915):  844–​ 847. See also an English translation that appears in The Collected Papers of Albert Einstein (Princeton: Princeton University Press, 1998), vol. 6, 117–​120. 16. Schwarzschild’s letter to Einstein ends: “As you see, it means that the friendly war with me, which, in spite of your considerable protective fire throughout the terrestrial distance, allows this stroll in your fantasy land.” Karl Schwarzchild to Albert Einstein, December 22, 1915, in The Collected Papers, vol. 8a, 224–​225. Translation by the author. 17. Albert Einstein to Karl Schwarzschild, Berlin, January 9, 1916, in The Collected Papers, vol. 8, 239. Translation by the author. In the original German: Ihre Arbeit habe ich mit größtem Interesse durchgesehen. Ich hätte nicht erwartet, dass man so einfach die strenge Lösung der Aufgabe formulieren könne. Die rechnerische Behandlung des Gegenstandes gefällt mir ausgezeichnet. Nächsten Donnerstag werde ich die Arbeit mit einigen erläuternden Worten der Akademie übergeben. 18. For details of the derivation, see Schwarzschild’s paper or the excellent pedagogical treatment in Wolfgang Rindler, Relativity:  Special, General and Cosmological (New York: Oxford University Press, 2001). 19. For more details, see Rindler, Relativity. 20. Albert Einstein, “On a Stationary System,” 936. 21. More generally, such objects can have both angular momentum and electric charge, but that does not change the discussion. 22. Oppenheimer and Snyder, “On Continued Gravitational Contraction,” 456. 23. Schwarzschild’s son Martin grew up to become a noted astronomer, ending his career as a professor at Princeton. Martin was born in 1912 and must have barely known his father. 24. Albert Einstein, “On the Electrodynamics of Moving Bodies,” in Arthur J.  Miller, Einstein’s Special Theory of Relativity (Reading, MA: Addison-​Wesley, 1981), 415. 25. Pierre Speziali, ed., Albert Einstein, Michele Besso:  Correspondance, 1903–​ 1955 (Paris: Hermann, 1979). 26. Prior to Besso’s birth, his family had lived in Italy for several generations. The family name is likely a derivation of basso, meaning “small” or “low.” True to their name, the Bessos were indeed short. Einstein was five feet nine inches tall, and Besso, judging from photographs of the two standing together, was clearly several inches shorter. 27. The pair eventually became distantly related by marriage. Before attending the Poly, Einstein had spent a year living with the Winteler family in Aarau, Switzerland. They were a musical family with charming children. Einstein introduced Besso to them, and Besso eventually married one of the daughters, while Einstein’s sister Maja married one of the Winteler sons.

Notes  197 28. Einstein to Besso, Berne, Thursday (January 1903), in Albert Einstein, Michele Besso, 3. Translation by the author. In the original French: Je suis donc maintenant un homme marié et je mène avec ma femme une vie fort agréable. Elle s’occupe parfaitement de tout, elle fait une bonne cuisine et se montre toujours gaie. 29. By the time the letters began again, Einstein had experienced the miracle year of 1905, in which he created modern physics. See Richard Panek, “The Year of Albert Einstein,” Smithsonian Magazine (June 2005). 30. Philipp Frank, Einstein: His Life and Times, translated by George Rosen, edited by Shuichi Kusaka (New York: Alfred A. Knopf, 1947), 113. 31. Einstein to Besso, Berlin, October 31, 1916, in Albert Einstein, Michele Besso, 51. Translation by the author. In the original French:  Quant au divorce, j’y ai renoncé définitivement. Passons maintenant aux questions scientifiques! 32. Albert Einstein to Mileva Einstein-​Marić, Berlin, January 31, 1918, in The Collected Papers, 456. 33. Einstein to Besso, Berlin, March 9, 1917, in Albert Einstein, Michele Besso, 61. Translation by the author. In the original French: L’état de mon cadet me cause beaucoup de soucis. Il est exclu qu’un jour il puisse devenir un homme les autres. Qui sait, peut-​être serait-​il mieux pour lui de quitter ce monde avant d’avoir connu la vie. Pour la première fois dans ma vie, je me sens responsable et je me fais des reproches. 34. Besso to Einstein, Geneva, January 29, 1955, in Albert Einstein, Michele Besso, 311. Translation by the author. In the original French:  Ce qui est important pour moi personnellement, c’est le refus tranchant que mon père opposait à toute représentation ou même dénomination de Dieu (en quoi sa pensée était tout à fait conforme à la Thora . . . “Tu ne te feras pas d’image ni aucune représentation . . .”); il ne subsiste alors que le seul concept de loi naturelle, ce qui revient pour moi à donner un sens à la recherche en elle-​même, à reconnaître à côté de l’expérience immédiate des sens une valeur à la représentation libre de toute contradiction qu’ils nous donnent, à poser en face de l’Être englobant toutes choses, mesuré à son aune et à celle de notre critique, notre propre être spirituel . . . porte ouvert sur une Beauté reconnue, Joie . . . Reconnaissance, Bonté . . . sur d’autres genres de Vérité, de Bonté et de Beauté. 35. Einstein to Vero and Bice Rusconi, Princeton, March 21, 1955, in Albert Einstein, Michele Besso, 312. Translation by the author. In the original French: Il était vraiment très aimable de votre part de me donner, en ces jours si pénibles, tant de détails sur la mort de Michele. Sa fin a été harmonieuse à son l’image de sa vie entière, à l’image aussi du cercle des siens. Le don de mener une vie harmonieuse est rarement doublé d’une intelligence si aiguë, surtout au degré où cela se rencontrait chez lui. Mais ce que j’admirais le plus chez Michele, en tant qu’homme, c’est le fait d’avoir été capable de vivre tant d’années avec une femme, non seulement en paix, mais aussi dans un accord constant, entreprise dans laquelle j’ai lamentablement échoué par deux fois. . . . Voilà qu’il m’a de nouveau précédé de peu, en quittant ce monde étrange. Cela ne signifie rien. Pour nous, physiciens croyants, cette séparation entre passé, présent et avenir, ne garde que la valeur d’une illusion, si tenace soit elle.

198 Notes

Chapter 5 1. Karl Sigmund, Exact Thinking in Demented Times. 2. Ernst Mach, The Science of Mechanics (Open Court, 1960), 272. 3. Sigmund, Exact Thinking, 10. 4. Sigmund, Exact Thinking, 33. 5. Here is an exchange in which Wittgenstein makes some remarks about Gödel’s undecidability theorem: In the discussions of the provability of mathematical propositions it is sometimes said that there are substantial propositions of mathematics whose truth or falsehood must remain undecided. What the people who say that don’t realize is that such propositions, if we can use them and want to call them “propositions,” are not at all the same as what are called “propositions” in other cases; because a proof alters the grammar of a proposition. You can certainly use one and the same piece of wood first as a weathervane and then as a signpost; but you can’t use it fixed as a weathervane and moving as a signpost. If some one wanted to say “There are also moving signposts” I would answer “You really mean ‘There are moving pieces of wood.’ ” I don’t say that a moving piece of wood can’t possibly be used at all but only that it can’t be used as a signpost.” Ludwig Wittgenstein, Philosophical Grammar, 367. Has Wittgenstein lost his mind? Does he mean it seriously? He intentionally utters trivially nonsensical statements.” Kurt Gödel, in Hao Wang, A Logical Journey, 179. 6. Every once in a while, Sigmund shows his hand as a mathematician, such as when he invites the reader to find two irrational numbers x and y such that xy is rational. He discusses the answer as an illustration of the method of mathematical proof.

Index Academy of Arts and Sciences, 148 accelerators. See also CERN designing,  8–​9 strong focusing principle, 12–​13 “The Added Cubit” (Oppenheimer), 154 Advance Publications, 73 Albert Einstein: Philosopher Scientist (Pais), 30, 176 American Association for the Advancement of Science, 105 American Physical Society, 35, 59, 86 Ames, Joseph Sweetman, 84 amplification, quantum theory and, 77–​ 78, 106, 111 Ananda Ashram, 4 Anderson, Carl, 39 angular momentum. See spin and angular momentum Annalen der Physik, 21 Annals of Mathematics, 121 antimatter, 39 anti-​Semitism, 151–​152, 160–​161 apparatus, importance of in quantum theory,  41–​42 Archibald, John Christy, 80 Ashbel Smith and Roland Blumberg Professorship, 105 Aspect, Alain, 60–​61 astronomy locality and, 57 measuring speed of light, 56 atomic bomb research and testing, 91–​92, 95, 140, 153, 161, 191, 193. See also Los Alamos atomic clocks, 34 Atomic Energy Commission, 102–​103, 157–​158 Atomic Energy Research Establishment,  11–​13 atomic spectra, 25, 40

atoms atomic theory of matter, 43 Bohr’s “planetary” model, 22–​23 liquid-​drop model of nuclei, 88–​89, 95 Rutherford’s work with nuclei, 22 “An Attempt at a Visualization of the Structure of Space-​Time” (Besso), 126 Auden, W. H., 152   Balanchine, George, 158–​159 Baldwin, Lydia, 82 Baltimore City College, 82 Baltimore Federation of Church and Synagogue Youth, 86 Bar-​Ilan University, 175 BBC, 3 Belfast Technical High School, 9 Bell, John Stewart, 178–​182. See also Bell, Mary background of, 9 Bell’s inequality, 5, 58–​62, 106 bicycle analogy, 68 Bohm’s work analyzed by, 52–​53, 57–​58 Bohr evaluated by, 41–​42 classical vs. quantum world, 40–​42,  67–​68 Copenhagen interpretation, 42, 50, 55 correlations, 6, 50 death of, 74 education of, 9–​11, 13, 39–​40 Einstein-​Podolsky-​Rosen experiment, 4–​6,  35–​36 Einstein’s abandonment of quantum theory, 67 genetic determinism, 50 Heisenberg evaluated by, 42 hidden variables, 51–​54, 188 image of, 1 impact of work on nonscientists, 61–​63

200 Index Bell, John Stewart (cont.) impossibility proof, 58 influential professors of, 10–​11 introduction to physics, 10 introduction to quantum theory, 39–​40 locality, 54, 57 marriage to Mary, 13 New Yorker profile of, 73–​74 Pauli evaluated by, 42 personality and descriptions of, 5–​8, 54, 67, 69–​70, 74 philosophy and, 10 religion and, 10, 64–​67 reservations about quantum theory, 5–​6, 15–​16, 67–​68,  110 Schrödinger’s cat, 40–​41 strong focusing principle, 12–​13 TCP theorem, 13–​14 uncertainty principle, 40–​41 visiting Stanford, 54 visit to LEP, 68–​71 von Neumann evaluated by, 51–​52 Wheeler and, 77–​78, 110 work as laboratory assistant, 10 work at Atomic Energy Research Establishment,  11–​15 work at CERN, 13–​15 work with Peierls, 13, 53 Bell, Mary (Ross), 5–​6 death of John, 74 education of, 12 family background of, 11–​12 marriage to John, 13 personality and descriptions of, 7–​8 retirement of, 8 visit to LEP, 69–​71 visit to Stanford, 54 work at Atomic Energy Research Establishment, 12, 14–​15 work at CERN, 8, 15, 69 Bell’s inequality, 5, 58–​62, 106 Beowulf, Wheeler’s writing compared, 105, 109 Bertlmann, Reinhold, 5 “Bertlmann’s Socks and the Nature of Reality” (Bell), 5–​6 Besso, Michele Angelo background of, 127, 196n26

correspondence with Einstein, 126–​130 death of, 126, 129 friendship with Einstein, 127–​128 height of, 196n27 retirement of, 129 Speziali and, 126 work at patent office, 127–​129 Besso, Vero, 126, 129 Bethe, Hans, 73, 160–​161, 193 Big Bang theory, 65, 76 Birkbeck College of the University of London, 45 black-​body (cavity) radiation, 16–​21 black hole research Einstein and, 121–​125 Oppenheimer and Snyder, 95, 104, 121, 123–​125, 152, 156–​157 Wheeler and, 79, 95, 104, 152 Bohm, David, 39, 179 determinism and hidden variables, 43, 51–​52,  57–​58 Einstein and, 45, 57, 185 Einstein-​Podolsky-​Rosen experiment, 42–​43, 45, 48–​49, 60 political difficulties, 45 quantum field theory consistent with relativity, 185–​187 quantum measurement problem, 184–​185 von Neumann’s proof, 44–​45 Wheeler and, 106 Bohr, Aage, 111, 193 Bohr, Eric, 90 Bohr, Niels, 2–​3, 30, 160, 195n3 Bell’s evaluation of, 41–​42 Bell’s inequality, 5 Bohr orbits, 23–​24, 46 collaboration with Wheeler, 87–​88, 91–​92, 95, 101–​102 complementarity principle, 33, 38 debates on quantum theory with Einstein, 30–​38, 78 debates with Schrödinger, 44 discussion with Roosevelt, 99 division of classical and quantum worlds,  41–​42 dizziness thinking about quantum mechanics, 16, 47

Index  201 double-​slit experiment, 33 Eastern religions and, 64 Einstein-​Podolsky-​Rosen experiment,  36–​38 impossible return to classical physics, 5 influence on Wheeler, 78, 87–​88, 106 liquid-​drop model, 88–​89, 95 nuclear fission research, 89–​91 personality and descriptions of, 87, 91 planetary atomic model, 22–​23, 40 quantum electrodynamics at high energies,  87–​88 Rutherford and, 84–​85, 87 unsettling nature of quantum theory, 16 visit to Los Alamos, 193 visit to Soviet Union, 87 Wheeler’s evaluation of, 87 Bohr orbits, 23–​24, 46 Boissevain, Menso, 166 Boltzmann, Ludwig, 43, 144–​148, 172 Born, Max, 51, 195n3 correspondence with Einstein, 38, 52, 61, 185 wave theory, 27–​30 Weisskopf and, 160 Boston University, 60 Brahe, Tycho, 122 Breit, Gregory, 86–​88 Bridgman, Percy, 151–​152 Brownian motion, 2, 43, 144 Brown University, 81 Bruner, Jerry, 153 Buddhism, 62, 64–​66, 105 Buhler-​Broglin, Manfred,  69–​70 Bureau of Standards, 103   Caen, Herb, 166 Caltech, 158 Cambridge University, 22, 132, 135, 140, 147 Camp Androscoggin, 167 “Can Quantum-​Mechanical Description of Physical Reality Be Considered Complete?” (Einstein, Podolsky, and Rosen),  35–​36 Capp, Al, 164–​165 Carnap, Rudolf, 147–​148

Carnegie Institute for Terrestrial Magnetism, 85 CERN (Conseil Européen pour la Recherche Nucleaire), 161 Bell’s work at, 5, 8–​9 informal dress at, 54 Large Hadron Collider, 8 LEP (Large Electron-​Positron Collider), 7–​8,  68–​71 location and size of, 7, 14 lunch traditions at, 7 member states, 14 newcomers to, 15 New Yorker profile of Bell, 73 origin of, 14 Proton Synchrotron, 13 theoretical division, 8, 15 visit of Dalai Lama, 64–​65 Weisskopf and, 160 Z0 particle, 71–​72 CERN Courier, 64 Charles-​Ferdinand University, 127 chemical bonding, quantum theory and, 39 Christofilos, Nicholas, 12 Clarke, Arthur C., 73 Clauser, John, 60 Cocteau, Jean, 116 Cohen, I. Bernard, 140–​142 Cohn, Roy, 135 Colgate, Sterling, 83 Columbia University, 75, 154, 193 complementarity principle, 33, 38, 43, 49 Compton, Arthur, 95–​96 computers, 4, 12 development of, 86 solid-​state theory, 21 Conant, James Bryant, 140 Concepts of Force (Jammer), 170 Concepts of Mass (Jammer), 170 Concepts of Simultaneity (Jammer), 170 Concepts of Space (Jammer), 169–​175 The Conceptual Development of Quantum Mechanics (Jammer), 170 “Concerning a Heuristic Point of View about the Creation and Transformation of Light” (Einstein), 19

202 Index Condon, E. U., 89 Confidential Guide of College Courses, 140 Congress of Cultural Freedom, 159 conjugate quantities, 28. See also momentum; position Conseil Européen pour la Recherche Nucleaire. See CERN Copenhagen interpretation gravitation, 55 planetary atomic model, 22–​23 quantum theory, 42, 50, 179 Cornell University, 161 correlations Bell’s inequality, 58–​60, 62 Bertlmann’s socks, 6 parapsychology and, 63 spin concept and, 48–​49 split coin analogy, 36 twins analogy, 50 cosmology, 72 Einstein and, 174 Wheeler and, 76, 104, 108 Coulomb, Charles-​Augustin de, 55 Courant, Ernest, 12 Crease, Robert, 154 Crick, Francis, 25, 195n12 Curie, Marie, 195n3 Czernowitz university, 26   Dalai Lama, 64–​65 The Dancing Wu Li Masters (Zukav), 4, 61, 64, 105 Dancoff, Sidney, 137 dark energy, 174 Davisson, C., 11, 24 Day, T. B., 183 The Day after Trinity (film), 153 de Broglie, Louis, 23–​24, 26, 43–​44, 115 de Broglie, Maurice, 23 DePauw University, 132 Descartes, René, 54 determinism, 27–​28, 51–​53,  57–​58 deuterons, 138 DeWitt, Bryce, 108 Dirac, Paul, 2, 26, 39, 94, 152, 195n3 Discourses and Mathematical Demonstrations concerning Two New Sciences (Galileo), 55

DNA, 195n12 Domash, Larry, 67 Doppler effect, 172, 174 double-​slit experiment, 31–​33, 112, 188–​189 Dukas, Helen, 126, 176–​177 du Pont, Éleuthère Iréné, 96 Du Pont Company, 96–​98 Durand, Loyal, III, 178–​179 Dyson, Freeman, 11, 105, 150, 152–​153, 156, 158, 179   Eastern religions, 4, 64–​67, 105 Eban, Aubrey, 164 Economist,  3–​4 Eddington, Arthur, 141 Ehrenfest, Paul, 46–​47, 85 Einstein, Albert, 2, 35, 116, 195n3 abandonment of quantum theory, 29, 115 black-​body radiation,  18–​21 black holes, 121–​125 Bohm and, 45, 52–​53, 185 Born and, 30, 115, 120 breakdown of classical physics, 18 Brownian motion, 43–​44 children of, 127–​128 correspondence and friendship with Besso, 126–​130 cosmology, 174 death of, 125, 130, 145 debates on quantum theory with Bohr, 30–​38, 78, 115, 117 de Broglie’s thesis, 24, 115 dice-​playing analogy, 29, 31, 94, 112, 115, 120 Dirac’s book, 39 Einstein-​Podolsky-​Rosen experiment, 6, 35–​36,  38–​39 feelings about quantum theory, 33–​35,  38–​39 Gödel and, 112–​114 Habicht and, 1–​2 heat absorption theory, 21 height of, 196n26 hidden-​variable theory, 43 incompleteness of quantum theory, 5 light quanta theory, 20–​21

Index  203 local realism, 58, 61, 67 Mach and, 172–​173 “madmen” and quantum theory, 16 marriage to Mileva, 127–​128 military work, 62 Newton and, 171 Olympia Academy, 1 origin of term quanta, 18 1905 papers, 2, 18–​21, 56, 177–​178 phenomenology, 177–​178 relativity theory, 2, 18, 21, 24–​25, 34–​ 35, 56, 121–​122, 141, 143, 173–​174, 177–​178 religion and, 175–​176 response to Feynman’s thesis, 94–​95, 112, 116 Rupp and, 175 Schrödinger and, 116, 118–​120 Schwarzschild and, 121–​122, 196n16 smoking, 154 solid-​state theory, 21 Solovine and, 1–​2 speed of light, 143 “spooky actions at a distance,” 35, 48–​ 50, 58, 120, 181 statistical mechanics, 20 uncertainty principle, 34, 116–​117 unified field theory, 89 views on quantum theory, 115–​121 von Neumann’s proof, 44 wave mechanics, 26, 115–​116 wave theory, 19–​21, 26–​27 Wheeler and, 104 Wolfson and, 170 work at patent office, 127 Einstein, Eduard, 128 Einstein, Elsa, 176 Einstein, Hans Albert, 128 Einstein, “Lieserl,” 127 Einstein and Religion (Jammer), 170–​171, 175–​178 Einstein: His Life and Times (Frank), 142 Einstein-​Podolsky-​Rosen (EPR) experiment, 4–​6, 35–​39, 42–​43, 45, 48–​49, 58, 60–​62, 111–​112, 180 Electric Company (television series), 167 electrodynamics, 55, 87–​88, 132, 137 electron microscopes, 24

electron-​positron collider, 7–​8,  68–​69 electrons atomic spectra, 25, 40 spin concept, 46 “state” of, 77–​78 Thomson family’s discoveries, 11 uncertainty principle, 28–​29 wave nature of, 23–​24, 26–​27, 115 electrostatics, 55, 63 elementary-​particle physics, 70 Bell and, 5, 15 Wheeler and, 106 Elements of Electricity (Thomson), 11 Emeleus, Karl, 11 epicycles, 142–​143 EPR. See Einstein-​Podolsky-​Rosen experiment Ernst Mach Society, 148 ether,  54–​55 Euclid, 173 Everett, Hugh, III, 178, 183–​184 Ewald, Peter Paul, 11 Exact Thinking in Demented Times (Sigmund), 139 excited states, 22–​23   fallout shelters, 104 Federal Office for Intellectual Property, 127 Feigl, Herbert, 148 Feinberg, Gerald, 56–​57, 76 Fermi, Enrico, 51, 88–​89, 134 nuclear fission, 89–​90 nuclear reactor research, 95–​96, 98 quantum theory at nuclear dimensions, 39 Feynman, Richard, 3, 61, 160 atomic bomb research, 97 Einstein’s response to thesis, 94–​95, 112, 116 Feynman diagrams, 132–​133 jellyfish neurology experiment, 93 lawn sprinkler experiment, 93 marriage to Arline, 94 PhD thesis, 94 post at Princeton University, 92–​95 principle of least action, 94 reservations about quantum theory, 61 Wheeler and, 79, 87, 92–​94

204 Index Fierz, Markus, 161 “Fight Fiercely Harvard” (Lehrer), 163 Finley, John, 163–​165 Forrestal Center, 102 four-​dimensional space-​time geometry, 107 Frank, Margot, 143 Frank, Philipp, 15–​16, 25, 127, 139–​149 Boltzmann and, 144 death of, 145 Einstein and, 142–​145 geometry, 143 image of, 140 Institute for the Unity of Science, 148 Mach and, 172–​173 personality and descriptions of, 142 planetary motion, 142–​143 relativity theory, 143 Schrödinger and, 139, 145 Vienna Circle, 139, 147 Franz Josef (emperor), 146 Frazer, James, 177 Freedman, Stuart, 60 Freud, Sigmund, 146 Frisch, Otto, 89 Fuchs, Klaus, 101 Furry, Wendell, 131–​138 background of, 131–​132 examination of author’s thesis, 131, 137–​138 image of, 131 investigation over Communist Party membership, 131, 135–​136 neutrinoless double beta decay, 133–​134 personality and descriptions of, 135 radar research, 135 theorem in quantum electrodynamics, 132 Weisskopf ’s mistake, 133 work at Harvard, 131–​137   Galileo Galilei, 2, 55–​56, 172 game theory, 139 Gamow, George, 44 Gauss, Carl Friedrich, 173 Gell-​Mann, Murray, 45, 139, 156, 162, 193–​194 General Motors, 86

genetic determinism, 50, 67 Gerlach, Walter, 47–​48 German Charles-​Ferdinand University in Prague, 127, 142, 145–​146 Germer, L., 24 Gleason, Andrew, 166 Gödel, Kurt, 112–​114, 139, 147, 198n5 The Golden Bough (Frazier), 177 Gottlieb, Robert, 73 Goudsmit, Samuel, 46–​47 Graves, George, 99 gravitation early research on, 54–​55 quantum theory and, 34 Greenbaum, Arline, 94 Gropius, Walter, 166 ground states, 23, 138 Groves, Leslie, 99, 151, 158, 193 Gruppentheorie und Quanten-​mechanik (Weyl), 84 Guggenheim Fellowship, 101   Habicht, Conrad, 1–​2, 43 Hafstead, Larry, 85–​86 Hagner, Janette, 86, 88, 109 Hahn, Otto, 89 Hamilton-​Jacobi equation, 186 Hanford Engineering Works, 97–​100 Hapgood (Stoppard), 3 Harrer, Heinrich, 64 Hartle, Jim, 108 Harvard Crimson, 166 Harvard University, 131–​132, 135–​ 136, 139–​140, 145, 148, 151, 160, 163–​164,  169 Hawking, Stephen, 108 Hebrew University in Jerusalem, 175 Heisenberg, Werner, 44, 195n3. See also uncertainty principle absurdities of quantum theory, 2–​3 criticism of wave mechanics, 26 impossible return to classical physics, 5 matrix mechanics, 24–​26 nuclear reactor research, 193 quantum theory at nuclear dimensions, 39 Weisskopf and, 160 Herzfeld, K. F., 84–​85

Index  205 hidden-​variable theory, 27, 43–​45, 50–​53, 60, 112, 181, 188 Higgs boson, 8 Hitler, Adolf, 92 holistic medicine, 4, 63 Holt, Richard, 60 Holton, Gerald, 149 Home, Michael, 60 Hoover, J. Edgar, 151 Horace Mann high school, 167 House Un-​American Activities Committee, 45, 131, 135–​136 Hubble, Edwin, 174 Huxley, Aldous, 152 Huygens, Christaan, 18, 172 hydrogen bomb research, 102–​104, 153   I Am News, 4 IBM, 103 IMB (Irvine, Michigan, Brookhaven) detector, 70 “Information, Physics, Quantum” (Wheeler), 109 Ingenious Mechanisms and Mechanical Devices, 79 Institute for Advanced Study (Dublin), 25 Institute for Advanced Study (Princeton), 30, 89, 103, 113, 119, 150, 152–​154, 156–​158, 176–​178 Institute for the Study of Twins, 50 Institute for the Unity of Science, 148 interference, 19, 32–​33, 188 International Encyclopedia of Unified Sciences, 148 Irvine, Michigan, Brookhaven (IMB) detector, 70   Jammer, Max, 169–​189 background of, 170 death of, 171 Einstein and cosmology, 174 Einstein and religion, 175–​178 image of, 169 Mach and, 172–​173 Newton and absolute space and motion, 171–​172 parity, 174–​175

post at Harvard, 169–​170 quantum mechanics, 178–​189 Riemann’s differential geometry, 173–​174 writing of, 170 Jauch, Josef, 54 Jeans, James, 18 Jefferson, Thomas, 96, 99 Jensen, J. Hans D., 193 Johns Hopkins Hospital, 86 Johns Hopkins University, 78, 83 Joliot-​Curie, Irène, 89 Jost, Res, 179 A Journey into Gravity and Spacetime (Wheeler), 109 J. Robert Oppenheimer: A Life (Pais and Crease), 154 Juhos, Bela, 149 Juilliard String Quartet, 158   Kamin, Leon, 135 kaons, 180, 182–​183 Kennedy, John F., 54 Kepler, Johannes, 122 Keynes, John Maynard, 172 Kirchoff, Gustav, 17 Klein, Abraham, 137–​138 Kramers, Hendrik, 133 Krohn, Ellen, 166 Kronig, Ralph, 46 Kuhn, Thomas, 18, 21   Landau, Lev, 44 Langevin, Paul, 24, 115 Lawrence, Ernest, 158 Lee, T. D., 72–​73, 156, 180, 182–​183 Lehigh University, 190 Lehrer, Tom, 163–​168 academic posts, 167 background of, 166–​167 first record, 166 at Harvard, 163–​165, 167 last public performance, 167 military service, 166 The Physical Revue, 165 radio program, 165 writing of, 163–​167 Leibniz, Gottfried, 106, 172

206 Index light complementarity principle, 33 diffraction and interference, 19, 32 Galileo’s research, 55–​56 particle theory, 18–​19 photon polarization, 60–​61, 182 speed of, 55–​57, 143 superluminal phenomena, 56–​57, 62 wave theory, 18–​20, 31–​32 Li’l Abner (comic strip), 164 Lippold, Richard, 166 liquid-​drop atomic model, 88–​89, 95 The Little Primer of Positivism (von Mises), 148 Livingston, M. Stanley, 12 locality, 54, 57–​58, 60, 181 local realism, 58–​59, 61, 67 Loomis, F. Wheeler, 132 Lorentz, Hendrik, 24, 46, 83, 195n3 Los Alamos, 45, 83, 94, 100–​103, 135, 153, 158, 161, 166, 191, 193 The Los Alamos Primer, 191 Lüders, Gerhard, 14 Lüders-​Pauli theorem, 14   Mach, Ernst, 144–​148, 171–​174 Mach’s principle, 173–​174 magnetism, 19, 36, 39, 55 Maharishi Mahesh Yogi, 64, 66–​67 Majorana, Ettore, 134 Manchester University, 22 Mandl, Franz, 52 Manhattan Project. See Los Alamos Marić, Mileva, 127–​128 Mathematical Foundations of the Quantum Theory (von Neumann), 44 Matthews, Paul, 13 Mauchly, John, 86 Maxwell, James Clerk, 19, 43, 55 Mayer, Maria, 133 McCarthy, Joseph, 131, 135–​137 McConnell, R. A., 63 McGovern, George, 167 McVeigh, Timothy, 192 The Meaning of Relativity (Einstein), 141 Mechanics, Molecular Physics, Heat and Sound (Millikan, Roller, and Watson), 11

Meitner, Lise, 89 “The Merely Very Good” (Bernstein), 152 Mermin, David, 62 Merton, Robert, 154 mesons, 88, 134, 138 Metallurgical Laboratory (University of Chicago),  95–​96 Minkowski, Hermann, 173–​174 Minsky, Marvin, 72–​73 Misner, Charles, 113 MIT, 92, 160–​161, 167 Moke, Verdet, 82 Møller, Christian, 88 momentum double-​slit experiment, 33 Einstein-​Podolsky-​Rosen experiment and,  36–​38 Einstein’s thought experiments, 116–​118 quantum mechanics, 28, 38, 47 spin and angular momentum, 46–​47 uncertainty principle, 28–​29, 40 Morgenstern, Oskar, 114 Morton Salt Company, 70 Murray, Bob, 86 My View of the World (Schrödinger), 64   Nabokov, Nicolas, 159 Nabokov, Vladimir, 159 Nagel, Ernst, 148 National Research Council Fellowship, 85, 87, 132 National Security Agency (NSA), 166 Natural Philosophy of Cause and Chance (Born), 51 Nature, 37 Naturwissenchaften, 118 Needham, Joseph, 65–​66 Nernst, Walther, 21–​22 neutrinos, 70–​72, 133–​134, 175 New Age mysticism, 4, 105 Newhouse, Samuel, 73 Newton, Isaac, 122 gravitation, 54–​55, 143–​144 nature of light and, 18 space and time, 171–​173 New Yorker, 72–​73, 160, 176, 193 New York Times, 3

Index  207 New York University, 86–​87 Nicolaisen, Ida, 154 Nobel Prize Bell, 74 Bohr, Aage, 111 Born,  29–​30 Davisson, 11 de Broglie, 24 Einstein, 21, 177 Feynman, 79, 160 Gell-​Mann,  156 Heisenberg, 29–​30, 35 Jensen, 193 Lee, 72, 156, 180 Ramsey, 136, 165 Schrödinger, 35 Schwinger, 155, 160 Thomson, G. P., 11 Thomson, J. J., 11 Tomonaga, 153, 160 Yang, 72, 156, 180 nonlocality, 57–​58, 62–​63, 181 Nova (television series), 109 nuclear fission research, 79, 89–​92 nuclear power plants, 14, 97–​101 nuclei liquid-​drop model, 88–​89, 95 Rutherford’s work with, 22 slow neutron absorption by, 88   O’Hara, John, 156 Oklahoma City bombing, 192 Olympia Academy, 1 “On a Stationary System with Spherical Symmetry Consisting of Many Gravitating Masses” (Einstein), 121, 123 “On Continued Gravitational Contraction” (Oppenheimer and Snyder), 121 “On the Einstein-​Podolsky-​Rosen Paradox” (Bell), 4–​6 “On the Theory and Interpretation of Measurement in Quantum Mechanical Systems” (Durand), 179 Oppenheimer, J. Robert, 84, 86, 102–​103, 110, 150–​160 atomic bomb research, 153, 191

Atomic Energy Commission hearings, 157–​158 biography by Pais, 150–​158 black hole research, 95, 104, 121, 123–​125, 152, 156–​157 Bohm and, 45 Congress of Cultural Freedom, 159 death of, 3, 125, 192 Durand and, 179 on epoch of discovery of quantum theory, 3, 30 first name, 151, 154–​155 illness and death of, 158–​159 marriage to Kitty, 153 personal identity and anti-​Semitism, 151–​152 personality and descriptions of, 153–​155 questioning during lectures, 179 Reith Lectures, 3, 30 Serber and, 191 smoking, 154–​155 Upanishads, 4 views of own scientific accomplishments, 152, 157 work with Furry, 132–​133 Oppenheimer, Kitty, 153, 156, 191–​192 Optiks (Newton), 18   Pais, Abraham, 30–​31, 33–​34, 150–​158 parapsychology, 63, 104–​105 parity violation, 86 Parsons, Estelle, 167 particle theory of light, 18–​19, 33 Pasteur, Louis, 83 Pauli, Wolfgang, 2, 14, 61, 195n3 division of classical and quantum worlds, 42 Eastern religions and, 64 spin concept, 46 Weisskopf and, 160 Pauling, Linus, 39 Peebles, Jim, 113–​114 Peierls, Rudolf, 11, 13, 53, 101 phenomenology, 177–​178 philosophy, 10, 76–​77, 105. See also Eastern religions; reality The Philosophy of Quantum Mechanics (Jammer), 170–​171, 178

208 Index Philosophy of Science, 179 photoelectric effect, 21, 177 photons, 111–​112. See also light Physical Review, 35, 37, 51, 59, 95 The Physical Revue (performance), 165 Physics, 5, 59 Physics Today, 92 Picasso, Emilio, 69 pions, 182–​183 Placzek, George, 91 Planck, Erwin, 16 Planck, Max, 116, 195n3 appeal of physics, 16–​17 black-​body radiation, 16–​18,  20–​21 criticism of Einstein, 21 derivations from Wien’s formula (Planck law), 17–​18 Planck’s constant, 28, 94, 187 planetary atomic model (Bohr atom),  22–​23 plutonium, 91, 97, 99 Podolsky, Boris, 6, 35–​36, 119 popular culture, quantum theory and, 3–​5,  61–​62 position double-​slit experiment, 33 Einstein-​Podolsky-​Rosen experiment and,  36–​38 Einstein’s thought experiments, 116–​118 quantum mechanics, 28, 38, 47 uncertainty principle, 4, 28, 34, 40, 117–​118,  195n5 wave theory, 27 Positivism (von Mises), 145 positrons, 39, 152 Powers, Thomas, 193 preferred sense of rotation of galaxies, 113 “The Present Status of Quantum Mechanics” (Schrödinger), 118 Princeton University, 45, 79, 113, 153, 190. See also Institute for Advanced Study Principia (Newton), 171 “A Principle of Least Action in Quantum Mechanics” (Feynman), 94 probability amplitudes, 94 hidden variables, 51, 184

wave function, 27, 30 Problems of Modern Physics (Lorentz), 83 Project Matterhorn, 102–​104 “Proposed Experiment to Test Local Hidden-​Variable Theories” (Clauser, Home, Shimony, and Holt), 60 Proust, Marcel, 153 Prussian Academy of Sciences, 121   quanta black-​body radiation,  20–​21 double-​slit experiment, 32 origin of term, 18 polarization, 60 Quantrill, William C., 80 quantum electrodynamics, 87–​88, 132, 137 quantum measurement problem, 119, 183–​185 quantum mechanics. See quantum theory Quantum Mechanics (Dirac), 39 Quantum Profiles (Bernstein), 74 Quantum Theory (Bohm), 39, 42 quantum theory (quantum mechanics). See also names of specific theorists absurdities of, 2–​4 Bell’s inequality and, 5, 59–​60, 106 Bohm’s interpretation of, 42–​43,  51–​53 chemical bonding and, 39 clarifications of mathematical foundations,  44–​45 classical vs. quantum world, 40–​42 conjugate quantities, 28 criticisms of, 15–​16 Eastern religions and, 4, 64–​67, 105 Einstein and, 2, 16 as explanation of everything, 39 genetic determinism and, 50 hidden variables and, 27, 43–​45, 50 idea that something is missing, 61 increased acceptance of, 39 kaons, 182–​183 locality and, 54, 57–​58 local realism and, 58–​59 old vs. new, 23, 25, 46, 48 origins of, 1–​3 “participator” aspects of, 105

Index  209 popular culture and widespread interest in, 3–​4,  61–​62 precision testing, 60–​61 probability amplitudes, 94 quantum entanglement, 183 quantum measurement problem, 183–​185 “reality” of, 35–​38, 48–​49 solid-​state theory, 21 spin and angular momentum, 45–​48 statistical interpretation (wave function),  29–​30 TCP theorem, 13–​14 uncertainty principle, 28–​29 unsettling nature of, 15–​16 wave and matrix mechanics and, 25–​26 wave function as probability, 27, 30 Wheeler’s views, 78, 105–​106 Quantum Theory and Measurement (Wheeler and Zurek), 6 quarks, 52, 71, 162 Queen’s University, 10–​11, 40 “The Queerness of Quanta” (Economist),  3–​4 Quine, Willard, 148   Rabi, I. I., 48, 73, 75, 84, 151, 157, 161 radioactivity, spin concept and, 48 Ramsey, Norman, 136, 165 Rayleigh, John William Strutt (lord), 18, 20 Rayleigh-​Jeans law, 18, 20 reality and quantum theory, 35–​38, 48–​49, 112. See also locality philosophical aspects of physics, 76–​77 spin concept and, 112 split coin analogy, 36 Reichenbach, Hans, 148 Reidermeister, Kurt, 147 relativity theory, 24–​25, 141, 143, 173–​174, 177–​178 black hole research, 104 debates between Einstein and Bohr,  34–​35 Einstein’s 1905 paper on, 2, 18, 21 locality and, 56–​57 quantum measurement problem, 185 speed of light and, 56

religion Bell and, 10, 64–​67 Eastern religions, 4, 64–​67, 105 Einstein and, 175–​178 Pauli’s views, 42 Remington Rand, 86 Requiem Canticles (Stravinsky), 158 Reviews of Modern Physics, 91 Riemann, Bernhard, 173–​174 Rockefeller Institute for Medical Research, 102 Roemer, Ole, 56 Roosevelt, Franklin D., 99 Roosevelt, Theodore, 81 Rosen, Nathan, 6, 35–​36, 119 Rosenfeld, Leon, 34, 36–​37, 90 Royal Prussian Academy of Sciences, 21 Ruark, Arthur, 88 Rubens, Heinrich, 17 Ruderman, Mal, 154, 193 Rupp, Emil, 175 Rusconi, Bice, 129 Russell, Bertrand, 147 Rutherford, Ernest, 22, 84–​85, 87, 151 Rye Country Day School, 86   Sacks, Oliver, 164 San Francisco Chronicle, 166 Schlick, Moritz, 147 Schrödinger, Erwin, 2, 195n3 death of, 120 debates with Bohr, 44 Eastern religions and, 64 Einstein and, 116, 118–​120 Frank and, 139, 145 misgivings over quantum mechanics, 44 modesty, 121 Schrödinger equation, 27, 77, 119, 184–​187 Schrödinger’s cat, 40–​41, 118–​119, 121, 195n7 spin concept, 119–​120 wave mechanics, 25–​27, 115–​116, 118–​119,  185 Weisskopf and, 160 Schwarzschild, Karl, 196n16 death of, 125 relativity theory, 121–​122

210 Index Schwarzschild, Karl (cont.) Schwarzschild black holes, 124 Schwarzschild metric, 122–​125 Schwarzschild, Martin, 196n23 Schwinger, Julian, 134–​135, 137, 155, 160, 179, 185 The Science of Mechanics (Mach), 144, 171, 173 The Scientific World View, 148 semi-​empirical mass formula, 90 Serber, Charlotte, 191–​192 Serber, Robert, 190 atomic bomb research, 191, 193 background of, 190 death of, 190 Heisenberg’s nuclear reactor, 193 image of, 190 lectures, 191 Oppenheimer and, 191 quarks, 193–​194 sailing, 192 units of explosive energy, 191–​192 Seven Years in Tibet (Harrer), 64 Shawn, William, 73 Shimony, Abner, 60 Sigmund, Karl, 139, 145–​146, 148–​149,  198n6 Simon, Walt, 99 Skitt, David, 64, 66 Snyder, Hartland, 12, 95, 104, 121, 124–​125,  156 solid-​state (condensed-​matter) theory, 21 Solovine, Maurice, 1–​2 Solvay, Ernest, 30 Solvay Congresses, 31, 33, 116–​117, 195n3 Sondheim, Stephen, 167 Songs by Tom Lehrer (Lehrer), 166 space quantization, 47–​48 Speakable and Unspeakable in Quantum Mechanics (Bell), 5 Spender, Stephen, 152 Speziali, Pierre, 126–​127, 129 spin and angular momentum, 45–​49, 119, 181 Spinoza, Baruch, 170, 177 Spitzer, Lyman, 102 “spooky actions at a distance,” 35, 48–​50, 58, 120, 181

“Stability of Perturbed Orbits in the Synchrotron” (Bell), 13 Stanford Linear Accelerator, 54 State University of New York at Albany, 81 statistical mechanics, 20, 51 stellarator, 79, 102 Stern, Otto, 47–​48, 61 Stoppard, Tom, 3 Strassman, Fritz, 89 Strauss, Lewis, 157–​158 Stravinsky, Igor, 158 string theory, 68 strong focusing principle, 12–​13 “A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables” (Bohm), 51 “Surely You’re Joking, Mr. Feynman!” (Feynman), 79 Surprises in Theoretical Physics (Peierls), 53 Sweeney Todd (musical), 167 Swiss Federal Polytechnic School, 127 Szilard, Leo, 92   tachyons,  56–​57 Tamm, Igor, 137 Tamm-​Dancoff expansion, 137–​138 TCP theorem, 13–​14 telepathy, 63 Teller, Edward, 103, 157, 180, 193 Thatcher, Margaret, 71 thermodynamics, 17, 43, 51 Thirring, Walter, 153 Thomson, G. P., 11, 24 Thomson, J. J., 11, 22 Thorne, Kip, 113 three-​dimensional geometries, 26–​27, 107 Time, 135 Toll, John, 103 Tolman, Richard, 158 Tolman, Ruth, 158 Tomonaga, Sin-​Itiro, 153, 160 Tractatus Logico-​Philosophicus (Wittgenstein), 144, 147 Transradio Studio, 166 Trinity College, 11 Trump, Donald, 135 Turner, Louis, 91 twins analogy, 50

Index  211 Uhlenbeck, George, 46–​47 Ulam, Stanislaw, 103 ultraviolet catastrophe, 18, 20 umpire analogy and quantum theory, 78, 95, 109 uncertainty principle, 28–​29, 33–​34, 120 Bell and, 40–​41 Einstein’s thought experiments, 116–​118 popular culture and, 3–​5 spin concept and, 47 Z0 particle, 71 unified field theory, 89 UNIVAC, 86, 103 University of Berlin, 17 University of California, Berkeley, 60, 191, 193 University of California, Santa Cruz, 167 University of Chicago, 95–​96 University of Copenhagen, 22 University of Geneva, 126 University of Glasgow, 12 University of Illinois, 132, 191 University of Istanbul, 148 University of Kansas, Lawrence, 80 University of North Carolina, Chapel Hill, 88 University of Pittsburgh, 63 University of Rochester, 161 University of São Paulo, 45, 51 University of Texas, Austin, 76 University of Vienna, 139, 144–​146, 149, 172 University of Western Ontario, 60 University of Wisconsin, 89, 190 Upanishads, 4 uranium, 91, 98, 191–​192   Vienna Circle, 139, 147–​149 Vindicator, 81 von Mises, Richard, 145, 147–​148 von Neumann, John, 44–​45, 51–​54 von Weizsäcker, C. F., 90   Weisskopf, Victor, 133, 160–​162 atomic bomb research, 161 background of, 160 death of, 162

humor, 161–​162 work at MIT, 160–​161 work with Pauli, 160 Weyl, Hermann, 84, 110–​111 “What Do You Care What Other People Think?” (Feynman), 94 What Is Life? (Schrödinger), 25, 195n12 Wheeler, Ezekiel, 80 Wheeler, James English, 88–​89 Wheeler, Joe, 81 Wheeler, John Archibald, 6 atomic bomb research, 91–​92, 95 birth and childhood of, 81–​83 black hole research, 79, 95, 104, 152 Bohr’s influence on, 78, 87–​88, 106 bypass surgery, 109 Center for Theoretical Physics, 76 collaboration with Bohr, 87–​88, 91–​92, 95, 101–​102 death of, 114 diagrams and drawing, 78–​79 discussing Bell, 110–​111 educational career of, 79 education of, 82–​85 Einstein evaluated by, 89, 112 fallout shelters, 104 family background of, 79–​81 Feynman and, 79, 87, 92–​94 Foundation Problems of Physics course, 75–​77, 106, 109 Fuchs and, 101 geon experiments, 106–​107 Gödel and, 113–​114 Guggenheim Fellowship, 101 hydrogen bomb research, 102–​104 image of, 75 interest in explosives, 82–​83 introduction to quantum theory, 84 lectures, 76, 78, 101 marriage to Janette, 87–​88, 109 National Research Council Fellowship, 85, 87 nuclear fission research, 79, 89–​92 nuclear fusion power research, 102–​103 nuclear reactor research, 95–​98, 100–​101 personality and descriptions of, 76, 109–​110

212 Index Wheeler, John Archibald (cont.) PhD thesis, 84–​85 philosophical aspects of physics, 76–​77,  105 post at Columbia University, 75–​76, 106 post at New York University, 86–​87 post at Princeton University, 89–​93, 100–​104,  109 post at University of North Carolina,  88–​89 post at University of Texas, 76, 104–​105, 108–​109 quantum theory interpretation, 77 retirement of, 108–​109 social life, 86 terminology invented by, 79 umpire analogy, 78, 95, 109 views on quantum theory, 106–​108, 111 work at Hanford Engineering Works,  97–​100 Wheeler, Mary, 81 Wheeler, Robert, 81 Wheeler, Thomas, 80

Wheeler Lamston, Alison, 89 Wheeler-​Moke Safe and Gun Company, 82 Wheeler Ufford, Letitia, 88–​89 Wien, Wilhelm, 17, 20 Wigner, Eugene, 89, 92, 111 Williams, E. J., 87–​88 Williams, Roger, 96–​97 Winteler family, 196n27 Witten, Edward, 169 Wittgenstein, Ludwig, 139, 147, 198n5 Wolfson, Harry Austryn, 169–​170 World Tree (Lippold), 166 Wu Ta-​You, 180   Yale University, 86, 139, 162, 179 Yang, C. N., 72–​73, 156, 180, 183 Young, Thomas, 19, 24, 31–​32   Z0 particle, 71–​72 Zeitschrift für Physik, 84, 175 Zukav, Gary, 4, 61–​62, 64, 105 Zurek, Wojciech, 6