Quantum [Un]speakables Springer-Verlag Berlin Heidelberg GmbH

ONLINE LIBRARY and Astronomy http://www.springer.de/phys/ R.A. Bertlmann A. Zeilinger Quantum [Un]speakables

From Bell to

With 141 Figures, 4 in Color

t Springer Professor Dr. Reinhold A. Bertlmann University of , Institute for Theoretical Physics Boltzmanngasse 5, 1090 Vienna, e-mail: [email protected] Professor Dr. , Institute for Experimental Physics Boltzmanngasse 5, 1090 Vienna, Austria e-mail: [email protected]

Library of Congress Cataloging-in-Publication Data Quantum [un]speakables : from Bell to quantum information I [edited by] R.A. Bertimann, A. Zeilinger. p. cm. Includes biblographical references and index. ISBN 3540427562 (acid-free pa• per) 1. Bell's theorem--Congresses. 3. Bell, J.S.--Congress. I. Bell, J.S. II. Bertlmann, Reinhold A. III. Zeilinger, Anton. QC174.17.B45 Q36 2002 530.12--dc21 2002021641

ISBN 978-3-642-07664-0 ISBN 978-3-662-05032-3 (eBook) DOI 10.1007/978-3-662-05032-2 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag Berlin Heidelberg GmbH. Violations are liable for prosecution under the German Copyright Law.

http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg N ew York in 2002 Softcover reprint of the hardcover 1St edition 2002 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant pro• tective laws and regulations and therefore free for general use.

Typesetting: Data conversion by LE-TEX Jelonek, Schmidt & Vockler GbR, Leipzig Cover design: design & production, Heidelberg

Printed on acid-free paper SPIN: 10958216 56/3111 5 4 3 2 1 John Bell @Renate Bertlmann, 1980 Preface - From Bell to Quantum Information

John Stewart Bell was certainly one of the really outstanding scientists of the Twentieth Century. The theorem named after him was most aptly called by Henry Stapp the most profound discovery since Copernicus. Born in Belfast in 1928, his scientific career up to his untimely death in 1990 covered not only the foundations of quantum , but also the areas of and the physics of accelerators, where he made outstanding contributions. So, the conference organized in his honor at the University of Vienna, 10-14 November 2000, to commemorate the Tenth Anniversary of his death brought together friends and colleagues working in all three areas. John Bell's scientific career began in Harwell and Malvern, where he made calculations of particle trajectories in accelerators and became an expert in high demand for the focusing of particle beams. During this time, he met his wife, Mary, who was also an accelerator . We were very happy and grateful to have Mary Bell as the Guest of Honor at the Vienna Conference. Later, while working on his thesis with Rudolf Peierls at Birmingham, he discovered independently from G. Liiders and W. Pauli the CPT theorem, one of the most basic theorems in physics. This is probably the most fundamental symmetry principle which states that the joint action of charge conjugation, inversion of parity and time reversal leaves any physical system unchanged. Of his contributions to quantum field theory, two others could be men• tioned. One is the discovery, together with Roman Jackiw, of what is to• day called the Bell-Jackiw-Adler anomaly. It explains some hitherto-not• understood decays by adding divergences of the quantum current to the description of the system. The other most important contribution of John Bell is his suggestion in 1967 that there should exist a gauge theory describing weak interactions. This idea had an immense influence on Martinus Veltman and Gerard 't Hooft and resulted in a full understanding of the weak force. Ultimately, gauge theories became the standard tool of modern . While it is difficult to underestimate the importance of John Bell's contri• butions to accelerator physics and to field theory, his most important contri• butions were certainly in the foundations of . Evidently, John Bell had been interested from a very early stage in the philosophical VIII Preface issues raised by quantum theory, a topic not very popular during his student days at Queen's University, Belfast. Apparently, John Bell, who had been interested in the Bohr-Einstein dialogue, always took the position of on philosophical issues. He also felt that a completion of quantum mechanics using so-called "hidden variables" would be highly desired, as it would help to regain a realistic and objective picture of the world. That way, Bell hoped one would be able to arrive at a physics where "measurement" would not play such a central role as in the Copenhagen interpretation of quantum mechanics. Then, a most interesting sequence of events set in. In 1952, David Bohm had achieved something which had earlier been proclaimed impossible. It had been proved by that no hidden variable theory could agree with quantum mechanics. Bohm actually formulated such a theory, where each particle at any time has both a well-defined position and a well• defined momentum. The conflict raised between von Neumann and Bohm was elegantly resolved by Bell, who showed that von Neumann's proof contained a physically unjustifiable assumption. So while John Bell had flung open the door widely for hidden variable theories, he immediately dealt them a major blow. In 1964, in his celebrated paper "On the Einstein-Podolsky-Rosen Paradox", he showed that any hidden variable theory, which obeys Einstein's requirement of locality, i.e. no influence travelling faster than the speed of , would automatically be in conflict with quantum mechanics. This is the celebrated Bell's theorem, which even found entrance into comics. Surprisingly, while quantum mechanics was already well established at the time of the publication of Bell's theorem, no experiments existed which definitely allowed one to rule out a local realistic interpretation. Which means that no experiment had measured for those specific two-particle correlations which are so necessary to demonstrate the violation of Bell's inequality, the quantitative measure of the border of the validity of local realism. Since then, experimentation has become better and better, and by now an impressive body of evidence has been collected, supporting quantum mechanics and being in conflict with local realism. While a very tiny loophole in principle remains for local realism, it is a very safe position to assume that quantum mechanics has definitely been shown to be the right theory. Thus, a very deep philosophical question, namely, whether or not events observed in the quantum world can be described by an underlying deterministic theory, has been answered by experiment, thanks to the momentous achievement of John Bell. This achievement is even more remarkable as he was able to rule out a gigantic class of theories, without having to know any details of the theories. Today, experimental development has gone far beyond this. Bell's in• equality and the underlying physics of entangled states have become cor• nerstones of the newly evolving technology of quantum information. There, information is encoded, transmitted and processed in completely novel ways Preface IX based on quantum laws. A bit of information can be encoded in a . Two quantum bits or q-bits can be entangled over long dis• tances, and entanglement can be used to encode information in a novel way unprecedented in classical physics. Experimentally, it has been shown that, using entanglement, one can encode more information than one bit in a two• state system, one can teleport a over large distances and one can use to provide a cryptographic method which is secure against eavesdropping by the laws of physics and not by a trick of the experimentalist. Finally, quantum computation promises exponential speed• up for certain problems, and first steps have been taken in the direction of quantum computation in various laboratories all over the world. It is most interesting to note that, despite his own theorem, John Bell continued to be an advocate of realistic hidden variable theories, which now, according to his own findings, have to be non-local. Therefore, he became an advocate of theories proposed by Ghirardi, Rimini, Weber, Peierls and Gisin, theories that, no matter how little, deviate from quantum mechanics and thus might be ruled out by experiment someday. Thus, even if John Bell in the end might not have turned out to be on the right side when it comes to the fundamentals of the interpretation of quantum mechanics, this should never be held against him. In contrast, he was one of the few, like Albert Einstein, who realized how extremely strange the consequences of quantum mechanics, if it finally should turn out to be the ultimate correct theory, are for our view of the world, and it is a sign of his high moral distinction that he was not at all willing to give in easily. In conclusion, it might very well turn out in the future that Bell's theorem paved the way to a momentous change of our conception of the world. Nobody has expressed his appreciation of John Bell, which we fully share, better than Jack Steinberger: "One of the greatest privileges of my rewarding life in physics has been the contact with ( ... ) John Bell. ( ... ) Trying to learn ( ... ) the behavior of neutral kaons in the light of CP violation, I had the pleasure of benefiting from John's penetrating understanding and insight, and of his readiness to share this. Bell was among the most brilliant I have known; in addition he had the very important human qualities of being accessible, unpretentious and kind to his less gifted colleagues." The organization of the conference in Vienna would have been impossible without the financial support of the Austrian Bundesministerium fiir Bildung, Wissenschaft und Kultur, the Stadt Wien, Wissenschafts- und Forschungs• forderung, the International Erwin Schrodinger Institut (ESI), the TMR• Network "The Physics of Quantum Information" and the University of Vi• enna. Many thanks also to Larissa Cox and Andrea Aglibut for handling the correspondence with the speakers and the editing of the present book, to Gabriele Zobl-Kratschmann and numerous other helpers for organizing X Preface the conference, to the Austrian Central Library for Physics for the video documentation and to Renate Bertlmann for taking a complete photographic record of the event.

Vienna, Reinhold Bertlmann January 2002 Anton Zeilinger Contents

Part I John S. Bell - The Man

1 Some Reminiscences Mary Bell...... 3

2 John Bell in Belfast: Early Years and Education Andrew Whitaker...... 7 2.1 Introduction...... 7 2.2 Family and Early Life...... 7 2.3 Queen's University as a Technician ...... 8 2.4 A Student at Queen's...... 10 2.5 Early Ideas on Quantum Theory...... 14 2.6 John Bell and Michael Faraday...... 18

3 My Interaction with John Bell Bernard d'Espagnat ...... 21

4 Magic Moments: A Collaboration with John Bell Reinhold A. Bertlmann ...... 29 4.1 Prologue...... 29 4.2 Duality in Hadronic Reactions ...... 30 4.2.1 Hadron Production in e+e- Collisions...... 30 4.2.2 Duality...... 32 4.3 Nonrelativistic Potential Theory...... 32 4.3.1 Resume...... 34 4.4 Magic Moments ...... 35 4.4.1 Moments...... 37 4.4.2 Ground State ...... 38 4.4.3 Balance...... 39 4.5 Equivalent Potential...... 40 4.6 Epilogue...... 42 XII Contents

Part II Tests of Bell's Inequalities

5 John S. Bell: Some Reminiscences and Reflections Abner Shimony ...... 51 5.1 Why was Bell the Discoverer of Bell's Theorem? ...... 51 5.2 Some Reminiscences ...... 55 5.3 In What Direction Does Bell's Theorem Point? ...... 57

6 Early History of Bell's Theorem John F. Clauser ...... 61 6.1 Introduction...... 61 6.2 An Unresolved Issue Left by the Founding Fathers...... 63 6.3 An Untidy Legacy Left by the Founders of Quantum Mechanics.. 66 6.4 Evangelical Theoreticians Dominate ...... 69 6.5 The Development of a "Stigma" ...... 71 6.6 Challenging the Common Wisdom...... 74 6.7 John Bell Unravels the Confusion ...... 75 6.8 Theoretical Truth Versus Experimental Truth...... 77 6.9 Beware of the Experimentalists Lurking About...... 81 6.10 Generalization of the Bell and CHSH Results to Constrain Local Realism and Space-Time ...... 82 6.11 Common Confusion About Count-Rate Normalization ...... 87 6.12 Bell's Response to CH and "Local Beables" ...... 88 6.13 The Quantum-Optics Community Encounters Related Problems.. 89 6.14 Splitting ? ...... 91 6.15 Remaining Locality Loopholes...... 94 6.16 Conclusions...... 96

7 On Four Decades of Interaction with John Bell Michael Horne...... 99 8 Based Tests of the Bell Inequalities - the Legacy of John Bell Continues .. . Edward S. Fry and Thomas Walther ...... 103 8.1 Historical Overview ...... 103 8.2 The Bell-Clauser-Horne Inequality ...... 106 8.3 Loopholes ...... 107 8.3.1 The First Loophole ...... 107 8.3.2 The Second Loophole ...... 108 8.3.3 The Third Loophole ...... 108 8.4 Atom Based Experiments ...... 109 8.4.1 The Paris Experiments ...... 109 Contents XIII

8.4.2 The Boulder Experiments ...... 110 8.4.3 The Texas A&M Experiment ...... 111 8.5 Summary ...... 116

9 Bell's Theorem: The Naive View of an Experimentalist ...... 119 9.1 Introduction ...... 119 9.2 Why Have Supplementary Parameters? The Einstein~Podolsky~Rosen~Bohm Gedankenexperiment ...... 121 9.2.1 Experimental Scheme ...... 121 9.2.2 Correlations ...... 122 9.2.3 Difficulty of an Image Derived from the Formalism of Quantum Mechanics ..... 123 9.2.4 Supplementary Parameters ...... 124 9.3 Bell's Inequalities ...... 125 9.3.1 Formalism ...... 125 9.3.2 A (Naive) Example of the Supplementary-Parameter Theory ...... 126 9.3.3 The Inequalities ...... 127 9.4 Conflict with Quantum Mechanics ...... 128 9.4.1 Evidence ...... 128 9.4.2 Maximum Conflict ...... 129 9.5 Discussion: The Locality Condition ...... 130 9.6 Gedankenexperiment with Variable Analyzers: The Locality Condition as a Consequence of Einstein's Causality. 131 9.7 From Bell's Theorem to a Realistic Experiment ...... 133 9.7.1 Experimentally Testing Bell's Inequalities ...... 133 9.7.2 Sensitive Situations Are Rare ...... 133 9.7.3 Production of Pairs of Photons in an EPR State ...... 134 9.7.4 Realistic Experiment ...... 135 9.7.5 Timing Conditions ...... 136 9.8 First-Generation Experiments ...... 136 9.8.1 Experiments with a One-Channel Polarizer ...... 136 9.8.2 Results ...... 137 9.9 Orsay Experiments (1980~ 1982) ...... 138 9.9.1 The Source ...... 138 9.9.2 Detection~Coincidence Counting ...... 139 9.9.3 Experiment with One-Channel Polarizers ...... 140 9.9.4 Experiment with Two-Channel Analyzers ...... 141 9.9.5 Timing Experiment ...... 143 9.10 Third Generation: Experiments with Pairs of Photons Produced in Parametric Down Conversion ...... 146 9.11 Conclusion ...... 149 XIV Contents

10 Bell's Theorem for Space-Like Separation Gregor Weihs ...... 155 10.1 From Gedanken to Real Experiments ...... 155 10.2 Efficiency ...... 156 10.2.1 Reducing the Required Efficiency ...... 157 10.2.2 State of the Art and Development of Optical Experiments 158 10.2.3 A Proposal Using Mercury ...... 158 10.2.4 Closure of the Detection Efficiency Loophole with an Ion Trap Experiment ...... 159 10.3 Locality ...... 159 10.3.1 Experiments with Large Separation Between Measurement Stations ...... 160 10.3.2 Analyzer Switching ...... 161

11 The EPR Paradox in Massive Systems or about Strange Particles Reinhold A. Bertlmann, Walter Grimus and Beatrix C. Hiesmayr 163 11.1 Introduction ...... 164 11.2 The Bell-CHSH Inequality for Photons and for Kaons ...... 164 11.3 A Neutral Kaon Introduces Itself ...... 167 11.4 The Experiment at CERN and Possible Decoherence ...... 169 11.5 The Generalized Bell Inequality and Unitary Time Evolution .... 175 11.5.1 The Choice of the Strangeness Eigenstate ...... 178 11.5.2 The Choice Sensitive to the CP Violating Parameter, c .. 178 11.6 Connection of the Bell Inequality and the Decoherence Approach. 179 11.7 Final Remark ...... 180

Part III Quantum Information

12 Are There Measurements? Stig Stenholm ...... 185 12.1 An Encounter with John Bell ...... 185 12.2 Measurements or Not? ...... 187 12.3 Describing a Measurement ...... 189 12.4 How to Map Reality ...... 193 12.5 Conclusion ...... 196

13 Sundays in a Quantum Engineer's Life Nicolas Gisin ...... 199 13.1 I am a Quantum Engineer, but on Sundays I Have Principles .... 199 13.2 on Sundays ...... 199 13.3 Let's Assume That the Collapse Is Real ...... 201 Contents XV

13.4 ... and Relativity? ...... 204 13.5 Conclusion ...... 206 14 Secret Sides of Bell's Theorem ...... 209 14.1 Is the Bell Theorem of any Practical Use? ...... 209 14.2 Is There a Perfect Cipher? ...... 210 14.3 Quantum Key Distribution ...... 213 14.4 Eavesdropping Revisited ...... 216 14.5 Quantum Privacy Amplification ...... 218 14.6 Concluding Remarks ...... 219

15 An Impossible Necklace Lev Vaidman ...... 221

16 Multi- Entanglement and Quantum Non-Locality Jian-Wei Pan and Anton Zeilinger ...... 225 16.1 Introduction ...... 225 16.2 The GHZ Theorem ...... 226 16.3 Experimental Multi-Photon GHZ Entanglement ...... 229 16.4 Experimental Test of Quantum Non-Locality ...... 233 16.5 Discussions and Prospects ...... 237

17 Bell's Theorem, Information and Quantum Physics Anton Zeilinger ...... 241 17.1 Introduction ...... 241 17.2 Information and Interference ...... 242 17.3 Information and Entanglement ...... 244 17.4 Bell's Theorem, Quantum Communication and Quantum Information ...... 246 17.4.1 Quantum Dense Coding ...... 246 17.4.2 ...... 248 17.4.3 Teleportation of Entanglement ...... 249 17.4.4 Quantum Cryptography ...... 251 17.5 John Bell's Desiderata and the Interpretation of Quantum Mechanics...... 252

Part IV Quantum Ideas

18 The Geometry of the Quantum Paradoxes John Conway and Simon Kochen ...... 257 18.1 Introduction ...... 257 18.2 Old Paradoxes ...... 258 XVI Contents

18.3 New Paradoxes and Their Geometry ...... 262 18.4 Reconstructing Quantum Mechanics ...... 267

19 Whose Knowledge? N. David Mermin ...... 271

20 The History of the G HZ Paper Daniel M. Greenberger ...... 281

21 and the Dynamical Reduction Program GianCarlo Ghirardi ...... 287 21.1 John Stewart Bell and His Role ...... 288 21.2 His Role Before 1985 ...... 289 21.3 The Birth of Dynamical Reduction Theories ...... 291 21.3.1 Stochastic Equations for the Description of Decay Processes ...... 291 21.3.2 Stochastic Differential Equations ...... 291 21.3.3 The Breakthrough- Quantum Mechanics with Spontaneous Localizations . . . . . 292 21.4 His Role Immediately After the Publication of Our Paper ...... 293 21.4.1 The Letter ...... 294 21.4.2 The Paper: Are There Quantum Jumps? ...... 296 21.4.3 The Relativistic Issue ...... 297 21.5 From QMSL to Continuous Spontaneous Localization (CSL) ..... 298 21.6 The Subsequent Role of J.S. Bell in the Dynamical Reduction Program ...... 301 21.6.1 Problems of Interpretation ...... 301 21.6.2 The Relativistic Program ...... 302 21. 7 Concluding Remarks ...... 303

22 How Does God Play Dice? (Pre-) Determinism at the Planck Scale Gerard 't Hooft ...... 307 22.1 Dice ...... 307 22.2 Quantum Interference ...... 314 22.3 Quantum Coherence and Entanglement ...... 314 22.4 The Einstein-Rosen-Podolsky Paradox and the Violation of the Bell Inequalities ...... 315 Contents XVII

Part V Quantum Specials

23 John Bell, State Reduction, and Quanglement ...... 319 23.1 Encounters with John Bell ...... 319 23.2 Gravitationally Induced State Reduction: A Minimalist View .... 321 23.3 Quanglement ...... 326

24 Interferometry with Macromolecules: Quantum Paradigms Tested in the Mesoscopic World Markus Arndt, Olaf Nairz, Anton Zeilinger ...... 333 24.1 A Prototype Quantum Experiment ...... 333 24.2 Interference of ...... 336 24.3 Decoherence ...... 340 24.3.1 Vibrational Transitions ...... 342 24.3.2 Emission of Blackbody Radiation ...... 343 24.3.3 Absorption of Blackbody Radiation ...... 344 24.3.4 Rayleigh Scattering of Thermal Radiation ...... 344 24.3.5 Fragmentation and Ionization ...... 345 24.3.6 Influence of Collisions with the Residual Gas ...... 345 24.3.7 Quasi-Static Interactions ...... 346 24.3.8 Magnetic Interactions ...... 346 24.3.9 Electric Interactions ...... 347 24.3.10 Inertial Forces ...... 347 24.3.11 Which-Way Information in Internal Clocks ...... 348 24.4 Conclusion ...... 349

25 Towards More Quantum Complete Experiments Helmut Rauch ...... 351 25.1 Introduction - Basic Relations ...... 351 25.2 Classic Neutron Interference Experiments ...... 355 25.2.1 Gravity Experiments ...... 355 25.2.2 Neutron Fizeau Effect ...... 356 25.2.3 41f Spinor Symmetry ...... 356 25.2.4 Spin Superposition ...... 357 25.2.5 Neutron Josephson Effect ...... 359 25.2.6 Stochastic Versus Deterministic Beam-Path Detection .... 360 25.3 Postselection Experiments ...... 362 25.3.1 Postselection of Momentum States ...... 362 25.3.2 Contrast Retrieval by Phase Echo ...... 366 25.4 Phase-Space Coupling ...... 366 25.5 Topological Effects ...... 368 25.6 Discussion ...... 370 XVIII Contents

Part VI Particles and Fields

26 John Bell's Observations on the Chiral Anomaly and Some Properties of Its Descendants Roman Jackiw ...... 377 26.1 John Bell and the Chiral Anomaly ...... 377 26.2 Descendants of the Anomaly ...... 379

27 Fractional Charge R. Rajaraman ...... 383 27.1 Introduction ...... 383 27.2 Fractional Charge in Field Theory ...... 384 27.2.1 Vacuum Sector ...... 385 27.2.2 Soliton Sector ...... 387 27.3 Polyacetylene ...... 389 27.4 Eigenvalue or Expectation Value? ...... 391 27.4.1 Polyacetylene Re-Visited ...... 396 27.5 Conclusion ...... 397

28 Thermal Excitations of Accelerated Electrons Jon Magne Leinaas ...... 401 28.1 Electrons as a Thermometer ...... 401 28.2 Linear Acceleration and the Unruh Effect ...... 403 28.3 Stationary World Lines ...... 406 28.4 Electrons in a Storage Ring ...... 407 28.5 Concluding Remarks ...... 411

29 Bell's Spaceships and Special Relativity Franco Selleri ...... 413 29.1 The Generalised Transformations ...... 413 29.2 Michelson-Type Experiments ...... 416 29.3 Jupiter's Satellites Occultations ...... 417 29.4 Aberration ...... 419 29.5 Radar Ranging of Planets ...... 420 29.6 Proofs of Absolute Simultaneity ...... 421 29.7 The Inertial Transformations ...... 425

30 John Bell and the Ten Challenges of Subnuclear Physics Antonino Zichichi ...... 429 30.1 Introduction ...... 429 30.2 The Remarkable Value of John Bell's Support to My Physics .... 431 30.3 The LAA Project in a Few Words ...... 447 30.4 Facilities and the Basic Steps ...... 448 Contents XIX

30.5 The Ten Challenges ...... 451 30.5.1 The Physics of Imaginary Masses (SSB) ...... 451 30.5.2 Matter- Symmetry ...... 454 30.5.3 Supersymmetry ...... 455 30.5.4 Non-perturbative QCD ...... 457 30.5.5 Anomalies and Instantons ...... 458 30.5.6 Flavour Mixing in the Sector ...... 462 30.5.7 Flavour Mixing in the Leptonic Sector ...... 464 30.5.8 The Problem of the Missing Mass in the Universe ...... 466 30.5.9 The Problem of Hierarchy ...... 468 30.5.10 The Physics at the Planck Scale: The Gap and the Number of Expanded Dimensions ...... 469 30.6 The ELN Project in a Few Words ...... 471 30.7 ConcI usions...... 473

Subject Index ...... 479 List of Contributors

Markus Arndt Edward S. Fry Institute of Experimental Physics Department of Physics University of Vienna Texas A&M University Vienna, Austria College Station, TX, USA Alain Aspect GianCarlo Ghirardi Laboratoire Charles Fabry Dipartimento di Fisica Teorica Institut d'Optique Theorique et Dell' Universita' degli Studi di Appliquee Trieste, Italy Orsay Cedex, France Nicolas Gisin Mary Bell Group of Applied Physics Geneva, Switzerland University of Geneva Geneva, Switzerland Reinhold A. Bertlmann Institut of Theoretical Physics Department of Physics University of Vienna CCNY Vienna, Austria New York, NY, USA John F. Clauser Walter Grimus J.F. Clauser & Assoc. Institut of Theoretical Physics Walnut Creek, CA, USA University of Vienna John Conway Vienna, Austria Department of Mathematics Beatrix C. Hiesmayr Princeton University Institut of Theoretical Physics Princeton, NS, USA University of Vienna Artur Ekert Vienna, Austria Centre for Quantum Computation Gerard 't Hooft Clarendon Laboratory Institute for Theoretical Physics Oxford University University of Utrecht Oxford, UK Utrecht, The Bernard D'Espagnat Michael Horne Professeur emerite de l'Universite de Physics Department Paris-Sud, Membre de l'Institut Stonehill College Paris, France Easton, MA, USA XXII List of Contributors Roman Jackiw Franco Selleri Center for Theoretical Physics Universita di Bari Massachusetts Institute of Dipartimento di Fisica Technology Bari, Italy Cambridge, MA, USA Abner Shimony Simon Kochen Cupertino, CA, USA Princeton University Department of Mathematics Jack Steinberger Princeton, NJ, USA CERN Geneva, Switzerland Jon Magne Leinaas Department of Physics Stig Stenholm University of Oslo Royal Institute of Technology Kansli Blindern, Oslo, Norway Stockholm,

N. David Mermin Lev Vaidman Laboratory of Atomic and Solid Faculty of Exact Sciences, Physics State Physics Tel Aviv University Tel Aviv, Ithaca, NY, USA Thomas Walther Olaf Nairz Department of Physics Institute of Experimental Physics Texas A&M University University of Vienna College Station, TX, USA Vienna, Austria Gregor Weihs Jian-Wei Pan Institute of Experimental Physics Institute of Experimental Physics University of Vienna University of Vienna Vienna, Austria Vienna, Austria Roger Penrose Andrew Whitaker The Mathematical Institute Department of Physics Queen's University Belfast Oxford, UK Belfast, Northern R. Rajaraman Anton Zeilinger School of Physical Sciences Institute of Experimental Physics Jawaharlal Nehru University University of Vienna New Delhi, Vienna, Austria Helmut Rauch Antonino Zichichi Atominstitut der Osterreichischen CERN Universitaten EP Division Vienna, Austria Geneva, Switzerland