Between Quantum and Cosmos: Studies and Essays in Honor of John Archibald Wheeler 9781400886975

Table of contents :
Contents
Preface
John Archibald Wheeler: A Few Highlights of His Contributions to Physics
Early Estimates of the Strength of the Nuclear Spin-Orbit Force
Momentum Projection of Solitons Including Quantum Corrections
An S Matrix Theory for Classical Nonlinear Physics
Some Generalizations of the Virial Theorem
Does the Topology of Space Fluctuate?
Barrier Penetration and Initial Values in Kaluza-Klein Theories
Obvious, Incredible ...
Professor Wheeler and the Crack of Doom: Closed Cosmologies in the 5-d Kaluza-Klein Theory
Gravitation and Spontaneous Symmetry Breaking
The Birth of Time
Black Holes and Quantum Coherence
Heuristic Viewpoint Concerning the Thermal Ambience Relative to an Accelerated Frame
Test of the Gravitomagnetic Field via Laser-Ranged Satellites
Static Electromagnetic Geon
The Geometrodynamic Content of the Regge Equations as Illuminated by the Boundary of a Boundary Principle
Canonical Geometrodynamics and General Covariance
Boundary Terms in the Action Principles of General Relativity
Bianchi Identities and the Automatic Conservation of Energy-Momentum and Angular Momentum in General-Relativistic Field Theories
The Boundary of a Boundary Principle: A Unified Approach
The Gravitational Field at Spatial Infinity
Gravitational Radiation Reaction on the Motion of Particles in General Relativity
Equivalent Lagrangians in Classical Field Theory
p-Form Electrodynamics
General Covariance and Quantum Theory
Steering the Universe
On Observing the Absence of an Atom
How to Evade the Confrontation with the Uncertainty Relations
Are the Quantum Rules Exact? The Case of the Imperfect Measurements
The Problems in Quantum Foundations in the Light of Gauge Theories
Joint Wigner Distribution for Spin-1/2 Particles
Wedges I
The Measurement of Quantum Noise Reduction in Squeezed States
Quantum Mechanics without Probability Amplitudes
Quantum Mechanical Computers
Computability and Physical Theories
Computation and Physics: Wheeler’s Meaning Circuit?
On Wheeler's Notion of “Law without Law” in Physics
Existence of “Free Will” as a Problem of Physics
On the Nature and Origin of Complexity in Discrete, Homogeneous, Locally-Interacting Systems
Descriptions of Plates

Citation preview

Between Quantum and Cosmos

Between Quantum and Cosmos Studies and Essays in Honor of John Archibald Wheeler

Edited by Wojciech Hubert Zurek Alwyn van der Merwe Warner Allen Miller

Princeton University Press Princeton, New Jersey

Princeton Legacy Library edition 2017 Paperback ISBN: 978-0-691-60554-8 Hardcover ISBN: 978-0-691-62995-7 Arrangement and preface copyright © 1988 by Princeton University Press Published by FYinceton University Press. 41 William Street. Princeton. New Jersey 08540 In the United Kingdom: Princeton University Press, Guildford. Surrey The contents of this book were first published in six special issues of Foundations of Physics. Volume 16. Numbers 2 through 7 (February 1986 through July 1986). comprising invited papers in honor of John Wheeler. ® 1986 by Plenum Publishing Corporation. Reprinted by arrangement with Plenum Publishing Corporation. All Rights Reserved Library of Congress Cataloging in Publication Data Between quantum and cosmos : studies and essays in honor of John Archibald Wheeler / edited by Wojciech Hubert Zurek. Alwyn van der Merwe. and Wamer Allen Miller. p. cm. "The contents . . . were first published in six special issues of Foundations of physics"—T.p. verso. ISBN 0-691-08490-4 (alk. paper) 1. Physics. 2. Quantum theory. 3. Wheeler, John Archibald. 1911I. Wheeler. John Archibald. 1911- . II. Zurek. Wojciech Hubert. III. Van der Merwe. Alwyn. IV. Miller. Warner Allen. QC71.B45 1988 539—del 9

88-1497

Clothbound editions of Princeton University Press books are printed on acid-free paper, and binding materials are chosen for strength and durability Printed in the United States of America by Princeton University Press. Princeton, New Jersey

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Between Quantum and Cosmos

14. Test of the Gravitomagnetic Field via Laser-Ranged Satellites Ignazio Ciufolini

188

15. Static Electromagnetic Geon Marek Demianski

196

16. The Geometrodynamic Content of the Regge Equations as Illuminated by the Boundary of a Boundary Principle Warner Allen Miller

201

17. Canonical Geometrodynamics and General Covariance Karel V. Kuchar

229

18. Boundary Terms in the Action Principles of General Relativity James H7. York, Jr.

246

19. Bianchi Identities and the Automatic Conservation of EnergyMomentum and Angular Momentum in General-Relativistic Field Theories Friedrich W. Hehl and J. Dermott McCrea

256

20. The Boundary of a Boundary Principle: A Unified Approach Arkady Kheyfets

284

21. The Gravitational Field at Spatial Infinity Matthew Alexander and Peter G. Bergmann

300

22. Gravitational Radiation Reaction on the Motion of Particles in General Relativity P. A. Hogan and I. Robinson

311

23. Equivalent Lagrangians in Classical Field Theory Sergio Hojman and L. C. Shepley

322

24. p-Form Electrodynamics Marc Henneaux and Claudio Teitelboim

340

25. General Covariance and Quantum Theory Bahram Mashhoon

366

26. Steering the Universe James lsenberg

384

27. On Observing the Absence of an Atom R. H. Dicke

400

28. How to Evade the Confrontation with the Uncertainty Relations V. B. Braginsky and F. Ya. Khalili

408

29. Are the Quantum Rules Exact? The Case of the Imperfect Measurements Bernard d'Espagnat

413

Contents

ix

30. The Problems in Quantum Foundations in the Light of Gauge Theories Yuval Ne'eman

424

31. Joint Wigner Distribution for Spin-1/2 Particles Leon Cohen and Marian O. Scully

442

32. WedgesI Cecile DeWitt-Morette, Stephen G. Low, Lawrence S. Schulman, and Anwar Y. Shiekh

459

33. The Measurement of Quantum Noise Reduction in Squeezed States W. G. Unruh

499

34. Quantum Mechanics without Probability Amplitudes William K. Wootters

507

35. QuantumMechanicalComputers Richard P. Feynman

523

36. Computability and Physical Theories Robert Geroch and James B. Hartle

549

37. Computation and Physics: Wheeler's Meaning Circuit? Rolf Landauer

568

38. On Wheeler's Notion of "Law without Law" in Physics David Deutsch

583

39. Existence of "Free Will" as a Problem of Physics Asher Peres

592

40. On the Nature and Origin of Complexity in Discrete, Homogeneous, Locally-Interacting Systems Charles H. Bennett

605

Descriptions of Plates

614

Preface The forty papers collected here honor one of the great twentieth-century scientists—John Archibald Wheeler. Preceding each paper is an original drawing by Wheeler (Wheeler's descriptions are provided at the end of the book). The papers and interwoven drawings capture and illuminate Wheeler's many contributions to physics, from his work with Niels Bohr in atomic and nuclear physics (the scattering matrix and liquid drop model) through his influential contributions to Albert Einstein's theory of gravity (black holes), his deep insights into quantum theory and measurement (the elementary quantum phenomenon), and his efforts to explain the origins of the quantum postulate and quantum gravity (the meaning circuit and the Wheeler-DeWitt Equation). The majority of the papers contained here are a reflection and sharpening of Wheeler's original and potentially earthshaking ideas. Many scientists are convinced that Wheeler's insights into the foundation of modern-day physics will spur a revolution in our perception of the universe. This book attempts to capture one man's rendering of the "big picture" by providing a glimpse of it through the eyes of his many colleagues. Rather than talk about John in this preface we have decided to let him speak for himself: quotations and, especially, the drawings illustrate the essence of the physics that forms the framework of his deep insight into the inner workings of nature. The contributed papers reveal this framework in a somewhat different, but no less dramatic, manner. The measure of the impact a scientist has on his field is best provided by the influence his ideas have on his colleagues. The contents of this volume—viewed in this light—speak for themselves. We wish to extend our gratitude to John Archibald Wheeler, not only for inspiring the papers in this book, but also for providing the drawings: they are intended by Professor Wheeler as an expression of his gratitude to his colleagues who have helped him celebrate his seventy-fifth birthday with this volume. We would also like to thank Zelda Davis for her indispensable help, the editors of Princeton University Press for the care with which this book was prepared, and the publishers of Foundations of Physics, in which the papers appeared in 1986, for their cooperation. We are particularly grateful to all the contributors. Los Alamos November 5, 1987

WOJCIECH HUBERT ZUREK ALWYN VAN DER MERWE WARNER ALLEN MILLER

Between Quantum and Cosmos

Plate 1

John Archibald Wheeler: A Few Highlights of His Contributions to Physics Compiled and edited by Kip S. Thorne1 and Wojciech H. Zurek2 Received October 28, 1985 The following quotations describe in "nutshells" a few highlights of John Archibald Wheeler's contributions to physics. The contributions are arranged in roughly the following order: (i) concrete research results, (it) innovative ideas that have become foundations for the research of others, (iii) insights that give guidance for the development of physics over the coming decades. Since most of Wheeler's work contains strong elements of two or even all three of these charac­ teristics, the editors have not attempted to delineate the dividing lines between the three categories.

A description of the nucleus which regards the neutrons and protons as spending part of their time in configurations corresponding, for example, to interacting alpha-particles, part of their time in other groupings, already takes into account to a large extent that intimate interaction between nuclear particles which is so entirely different from the situation in atomic struc­ ture ... The method of "resonating group structure" builds up a wave function for the whole nucleus out of partial wave functions which describe the close interactions within the individual groups.—Wheeler (1937). [Wheeler's method of "resonating group structure," introduced in this paper, was called "clustering theory" by some later researchers, and was the direct ancestor of the "method of generator coordinates" developed later by Wheeler and D. L. Hill.]

' Division of Physics and Astronomy, California Institute of Technology, Pasadena, California 91125. 2 Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545.

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Between Quantum and Cosmos

The c s form a unitary [scattering] matrix ... The equality which must exist between the numbers of incoming and outgoing groups in the [givenJ state ...for arbitrary choices of the a's ... is just the necessary and sufficient condition for unitary character. ... [Time-reversal invariancej shows that IjcmnII is a symmetrical matrix, and ... each element of the matrix is deter­ mined up to a factor ± 1.—Wheeler (1937). [The matrix \\cmn\\ introduced for the first time in this paper was later given the name "scattering matrix" or "S-matrix" and has come to play a major role in nuclear physics and elementary particle physics.] On the basis of the liquid drop model of atomic nuclei, an account is given of the mechanism of nuclear fission. In particular, conclusions are drawn regarding the variation from nucleus to nucleus of the critical energy required for fission, and regarding the dependence of the fission cross section for a given nucleus on the energy of the exciting agency."—Bohr and Wheeler (1939). [This paper, written only a few months after the discovery of nuclear fission, gave the definitive theory of fission. It even enabled Bohr and Wheeler to predict that the yet-to-be-discovered nucleus plutonium-239 would have a very large cross section for fission when bombarded by slow neutrons—a cross section that would make it the chosen fuel for the first American atomic bomb.] [Describing the first, abortive attempt on September 27, 1944 to operate at full strength the Hanford Washington reactor that was to produce Plutonium-239, Wheeler says]: 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 decayed, could give rise to another one which could absorb the neutrons. When [the reactivity of the reactor mysteriously began to fall] and then, a few hours later, ... began rising again, I was sure that this was what had happened. Now the second nucleus had decayed into a third one which did not absorb the neutrons; ... the culprit had to be Xenon-135.— Wheeler (1985). [Thanks to Wheeler, the Hanford reactor had already been designed to deal with the possibility of such "poisoning" by fission product nuclei with high neutron capture cross sections. Some months earlier he had started to warn of the possibility of cross sections far higher than the typical 10 barns that had been measured up to that time; perhaps even as high as 1 to 25 million barns. The reactor had been redesigned at the last minute to allow for this possibility; and this permitted it, with the readjustement of the safety rods, to handle Xenon-135 whose cross section turned out to be 3 million barns.]

John Archibald Wheeler

5

A quantitative formulation of [the absorber as the mechanism of radiation] is given here on the basis of the following postulates: (I) An accelerated charge in otherwise charge-free space does not radiate energy. (2) The fields which act on a given particle arise only from other particles. (3) These fields are represented by one-half the retarded plus one-half the advanced Lienard-Wiechert solutions of Maxwell's equations. In a system containing particles sufficient in number ultimately to absorb all radiation [these postulates produce the standard radiation-reaction phenomena in the emitterJ ... Radiation is [thereby] concluded to be a phenomenon as much of statistical mechanics as of pure electrodynamics.—Wheeler and Feynman (1945). [Feynman (1966) in his Nobel Prize lecture describes the genesis of this work, his interactions with Wheeler during its development, and its considerable influence on Feynman's subsequent Nobel-prize-winning contributions to quantum electrodynamics.] ... by far the dominating type of annihilation is that in which the positron combines with an electron whose spin forms a singlet state with respect to the positron. Associated with this selection of pairs which have zero relative angular momentum, before the annihilation process, is an analogous polarization phenomenon in the two quanta which are left at the end of the process. According to the pair theory, if one of these photons is linearly polarized in one plane, then the photon which goes off in the opposite direc­ tion with equal momentum is linearly polarized in the perpendicular plane.—Wheeler (1946). [This paper, in addition to developing the theory of electron-positron atoms, also laid the foundations (in the above quote) for the now-mostfamiliar variant of the Einstein-Podolsky-Rosen paradox.] Ignorance of the deeper relation between nucleons and mesons makes it especially appropriate at this time to investigate those features of the behavior of mesons which are largely independent of uncertainties about the nature of elementary particles. Fortunately, a number of conclusions may be drawn about the interaction between the meson and the nucleus when we assume little more than the laws of electrodynamics, elementary notions of nuclear structure, the principle of microscopic reversibility, and the simplest ideas of quantum theory. Thus, it has become clear not only that the meson possesses characteristic Bohr orbits of its own around the nucleus, but also that trapping into these orbits via ordinary atomic interactions is the precur­ sor of any specific reaction with the nucleus. ... Also interesting are the energy levels and interlevel transitions of the meson, the first experimental evidence for which is given by W. Y. Chang in a following paper. Among the

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Between Quantum and Cosmos

possible transitions are not only those in which a photon is emitted or an atomic electron is ejected, but also processes of pair creation and mesoninduced fission. ... An attempt is made to analyze these questions in the present paper.—Wheeler (1949). [This paper developed the definitive theory of mu-mesic atoms.] Analyzing different formulations of conditions for validity of the disper­ sion formula relating absorption and refraction of light, especially the con­ dition that no wave be scattered before arrival of the primary wave (Kronig) we conclude: it is reasonable to apply the dispersion formula for arbitrarily high frequencies.—Toil and Wheeler (1951). [This work showed for the first time that dispersion theory could be extended into the relativistic domain by a proper application of the principle of causality.] Associated with an electromagnetic disturbance is a mass, the gravitational attraction of which under appropriate circumstances is capable of holding the disturbance together for a time long in comparison with the characteristic periods of the system. Such gravitational-electromagnetic entities, or "geons," are analyzed via classical relativity theory. They furnish for the first time a completely classical, divergence-free self-consistent picture of the Newtonian concept of body...—Wheeler (1955). [This paper introduced the concept of "geon" into physics, and in analyzing geons it introduced the concept of two-lengthscale perturbative expansions into general relativity. Such expansions, in the hands of Wheeler's subsequent students and their students, have become the key foundation for the theory of the interaction of propagating gravitational waves with the "background" curvature of space-time.] We consider a number of mass concentrations so distributed in space and of such relative magnitudes, that the zone of influence of each can be reasonably approximated by a sphere. Inside each cell [sphere] we replace the actual gravitational potentials by the expressions of Schwarzschild. ... The mass concentrations on either side of a cell boundary accelerate toward that boundary at such a rate as to nullify the discontinuity in matching of the normal derivative of the gravitational potentials that would otherwise occur. ... [This] expresses the equation of motion of the mass at the center of a cell as a dynamic condition on the boundary of the cell. ... The whole of the expansion and subsequent contraction [of the universe] is derived [in this way] from the elementary static Schwarzschild solution.—Lindquist and Wheeler (1957). [This paper introduced into general relativity a technique for matching together two different space-time geometries. This matching

John Archibald Wheeler

7

technique, in the hands of Wheeler's students and colleagues, has become a foundation for modern analyses of the laws of motion and precession of black holes and other relativistic bodies.] Space tells matter how to move, ... and matter tells space how to curve.—Misner, Thome, and Wheeler (1973). ... we examined the consequences of an equation of state that attempts to span the whole region from normal densities to supranuclear densities. We assume: (1) Cold matter ideally catalyzed to the end point of thermonuclear evolution. ... (2) General relativity equations of hydrostatic equilibrium. ... The numerical integrations show for the first time both crushing points [white dwarf and neutron star] on a single curve for mass as a function of central density. [The form of this curve emphasizes that] assembly of an amount of mass that exceeds in order of magnitude the mass of the sun and catalysis of this matter to the endpoint of energy evolution results in a condition which lies at the untamed frontier between elementary particle physics and general relativity. Of all the implications of general relativity for the structure and evolution of the universe, this question of the fate of great masses is one of the most challenging.—Harrison, Wakano, and Wheeler (1958). [With these words Wheeler began the quest to understand the fates of great masses, a quest that led him a decade later to formulate the concept of a black hole.] Energy of rotation [of a central neutron star] appears not yet to have been investigated as a source of power [for the Crab nebula]. Presumably this mechanism can only be effective—if then—when the magnetic field of the residual neutron star is well coupled to the surrounding ion clouds."—Wheeler (1966). [This statement, published one year before the discovery of pulsars, was the closest anybody ever came before pulsars to the correct explanation of what powers the Crab nebula.] We write down ... the linear differential equations for small first-order departures from the Schwarzschild metric. ... It is shown that a Schwarzschild singularity /""black hole" in the terminology of the 1980s] ... will undergo small vibrations about the spherical form and will therefore remain stable if subjected to a small nonspherical perturbation.—Regge and Wheeler (1957). [This was the pioneering analysis of the pulsations and stability of black holes, performed a decade before the concept of a black hole was fully understood.]

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Between Quantum and Cosmos

... by reason of its faster and faster infall [the surface of a collapsing star] moves away from the observer more and more rapidly. The light is shif­ ted to the red. It becomes dimmer millisecond by millisecond, and in less than a second too dark to see... [ The starJ like the Cheshire cat fades from view. One leaves behind only its grin, the other, only its gravitational attraction. Gravitational attraction, yes; light, no. No more than light do any particles emerge. Moreover, light and particles incident from outside ... go down the black hole only to add to its mass and increase its gravitational attrac­ tion.—Wheeler (1968). [With these sentences, Wheeler coined the name "black hole" thereby catalyzing a major change in viewpoint on something that previously had gone under such names as "Schwarzschild singularity," "collapsed star," and "frozen star." Note that, in typical Wheelerian style, he does not tell us that he is coining a new name for and viewpoint on a fundamental concept in physics; rather, he writes as though this name and viewpoint had always been used—and almost overnight all other researchers in "black-hole physics" embrace them.] A black hole has no hair.—Rufiini and Wheeler (1971). [This phrase epitomized a result of which hints existed at the time Wheeler coined the phrase; and like so many of Wheeler's pithy phrases, it acted as a stimulus for further research by Wheeler's colleagues, former students and students of students—research that ultimately gave strong validity to the phrase.] On an atomic scale the metric appears flat, as does the ocean to an aviator far above. The closer the approach, the greater the degree of irregularity. Finally, at distances o f the order L * [ = ( h G / c 2 )= 1.6 χ IO-33 cm], the fluctuations in the typical metric component, gIJV, become of the same order as gμμ themselves. Then the character of the space undergoes an essential change ... Multiple connectedness develops, as it does on the surface of an ocean where waves are breaking.—Wheeler (1957). [Wheeler's intuitive insight that space-time may be multiply connected (foam-like) on the scale L* has received considerable substantiation from recent research on the quantum theory of gravity. The lengthscale L* is called by Wheeler the "Planck length" and by others the "Planck-Wheeler length," in recognition that Wheeler was the first to understand clearly its significance. ] Along with the fluctuations of the metric there occur fluctuations in the electromagnetic field. In consequence the typical multiply connected space ... has a net flux of electric lines of force passing through the "wormhole." These

9

John Archibald Wheeler

lines are trapped by the topology of space. These lines give the appearance of a positive charge at one end of a wormhole and a negative charge at the other."—Wheeler (1957). The quantum mechanical state of the metric field is a functional of the three-dimensional geometry cS intrinsic to a spacelike surface σ Ψ= ψ(9) The probability amplitude Ψ typically falls off rapidly for large scale depar­ tures from a smoothly behaved metric, but falls off very little for departures from smoothness which are of the scale L* = (hG/c2) = 1.6 χ 10~~ 33 cm or less.—Wheeler (1960). [This line of thought led, within the next few years, to the DeWitt-Wheeler formulation of quantum gravity, which in the hands of Hartle, Hawking, and others has recently achieved considerable success in understanding the initial conditions of the universe.] ... one feels that one has, at last in gravitational collapse, a phenomenon where general relativity dramaticaly comes into its own, and where its fiery marriage with quantum physics will be consummated.—Wheeler (1964a). The law of conservation of baryons must be abandoned for a star that exceeds the critical baryon number.—Wheeler (1964b). [This conclusion, forced on Wheeler by a long struggle to understand the fate of great masses, became a central issue in the 1970s with the discovery by Hawking that black holes can evaporate. This conclusion also led Wheeler to speculate, as an inspiration for future research, about the mutability of all conservation laws—and indeed of all the laws of physics—in the big bang and big crunch of the universe.] ... These advances in cosmology and black hole physics lend new emphasis to some of the most remarkable consequences of Einstein's standard theory: ... nature conserves nothing; there is no constant of physics that is not transcended; or, in one word, mutability is a law of nature."—Wheeler (1979a). Law without Law. "Physical space-time is not mathematical spacetime" is the one lesson of mutability; the other, "Physical law is not ideal mathematical law." Law that comes into being at the beginning of time and fades away at the end of time cannot be forever 100 % accurate. Moreover, it must have come into being without anything to guide it into being.—Wheeler (1980).

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Between Quantum and Cosmos

Not only particles and the fields of force liave to come into being at the big bang, but the laws of physics themselves, and this by a process of higgledy-piggledy as genetic mutation or the second law of thermo­ dynamics.—Wheeler (1982). Time is defined so that motion looks simple.—Misner, Thorne, and Wheeler (19731 Time ends. That is the lesson of the "big bang." It is also the lesson of the black hole.—Wheeler (1981a). Time is not a primary category in the description of nature. It is secon­ dary, approximate, and derived.—Wheeler (1982). [Wheeler is also fond of the phrase "Time is God's way of keeping things from happening all at once" (anonymous graffiti, discovered by him on the wall of Pecan Street Cafe in Austin, Texas).] No account of existence that presupposes the concept of lime can ever account for either time or existence.—Wheeler (1982). No elementary phenomenon is a phenomenon until it is an observed phenomenon.—Wheeler (1979b). [This phrase, and variations on its theme, paraphrase the central point of Niels Bohr. They serve Wheeler and his colleagues both as a point of departure and as a motto in the struggle to understand the relation between the quantum and measurements.] ... if one really understood the central point and its necessity in the con­ struction of the world, one ought to be able to state it in one clear, simple sentence. Until nc see the quantum principle with this simplicity we can well believe that u? do not know the first thing about the universe, about our­ selves. and about our place in the universe.—Wheeler (1979a). The final story of the relation between the quantum and the universe is unfinished business. We can well believe that we will first understand how simple the universe is when u'