Quantum Mechanics: An Empiricist View www.com This page intentionally left blank www.com Quantum Mechanics: An Empiricist View Bas C. van Fraassen CLARENDON PRESS · OXFORD www.com Great Clarendon Street, Oxford OX2 6DP 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 in Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo Toronto Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Bas C. van Fraassen 1991 The moral rights of the authors have been asserted Database right Oxford University Press (maker) 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, or under terms agreed with the appropriate reprographcs rights organization.
Enquiries 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 book in any other binding or cover and you must impose this same condition on any acquirer ISBN 0-19-824861-X (hb) ISBN 0-19-823980-7 (pb) www.com Que, touchant les choses que nos sens n'aperçoivent point, il suffit d'expliquer comment elles peuvent être. René Descartes, Principes, iv.com This page intentionally left blank www.com Preface Quantum theory grew up, from Planck to Heisenberg and Schroedinger, in response to a welter of new experimental phenomena: measurements of the heat radiation spectrum, the photoelectric effect, specific heats of solids, radioactive decay, the hydrogen spectrum, and confusingly much more. Yet this theory, emerging from the mire and blood of empirical research, radically affected the scientific world-picture. If it did describe a world ‘behind the phenomena’, that world was so esoteric as to be literally unimaginable.
The very language it used was broken: an analogical extension of the classical language that it discredits, and redeemed at best by the mathematics that it tries to gloss. Interpretation of quantum theory became genuinely feasible only after von Neumann's theoretical unification in 1932. Von Neumann himself, in that work, attempted to codify what he took to be the common understanding. Astonishingly, the attempt led him to assert that in measurement something happens which violates Schroedinger's equation, the theory's cornerstone.
As he saw very clearly, interpretation enters a circle when its main principle is Born's Rule for measurement outcome probabilities, while at the same time measurements are processes in the domain of the theory itself. Behold the enchanted forest: every road leads into it, and none leads out—or does the hero's sword cleave the wood by magic? An empiricist bias will be evident throughout this book, but my own interpretation of quantum mechanics does not begin until Chapter 9. The first three chapters provide philosophical background; though they overlap my Laws and Symmetry, I have tried to make them interesting in their own right. The next four chapters mainly outline the achievements of foundational research, though with an eye to the philosophical issues to come.
The negative part is to show that the phenomena themselves, and not theoretical motives, can suffice to eliminate Common Cause models of the observable world. The positive part is the conclusion that there are adequate descriptions of www.com viii PREFACE measurement—in the sense required for Born's Rule—internal to quantum theory. To make the book relatively self- contained, Chapters 6 and 7 introduce all the quantum mechanics needed for the philosophical discussions to come. From a purely philosophical point of view, the most important clarification reached since 1925 concerns the criteria of adequacy for interpretations of quantum mechanics.
It appears at present that more than just one tenable interpretation, already in process of development, can meet those criteria. I regret that I may have done little justice to the promising interpretations now underway which differ from my own, although I have tried to point to them as often as I could. I regard every interpretation as increasing our understanding, and believe that an awareness of what rival interpretations may be tenable is crucial to clarity. But that attitude already needs defence, for it involves views on what science is, and what philosophy can hope for.
I have also tried to take the philosophical debates somewhat further, into the fascinating cluster of problems that concern quantum-statistical mechanics and identical particles. At every point, but here especially, I was acutely aware of rapid progress in foundational research and of the kaleidoscopically changing philosophical debates. It is true that interpretation focuses on a single theory at one more or less definite historical stage—and yet, what we try to interpret is not static. Every time we understand a little more, we change what we are trying to understand.
It is not surprising that scientists often become impatient with philosophy: what is ever achieved if every generation has to face the same questions again, with a new understanding of what is being asked, unable to rest on past answers? But philosophy does not create our predicament. It is only a myth that modern science had arrived at a clear and well-integrated world- picture, or that contemporary science has already effectively given us a new one. At best, we are in process of replacing what never has existed by something that never will. It is only in this unendliche Aufgabe, this reaching for what we cannot finally have or hold, that understanding consists.
The pleasures of acknowledgement are always accompanied by a good deal of soul-searching. Debts are subtle, and always www.com PREFACE ix so numerous that only a few can be avowed, for philosophy is a thoroughly historical and communal enterprise. For the first part of the book, devoted to general philosophical background, my debts are largely acknowledged already in my previous books. But I must thank above all my teachers Adolf Grünbaum, who led me into the intricacies of determinism and indeterminism, and Wilfrid Sellars, who would not allow me to treat those or any other subjects in isolation.
To Henry Margenau I believe I am indebted in two ways, first through what I received from him through Grünbaum, who was his student and my teacher, and then directly as he drew me into his quantum-mechanical questioning during my two years at Yale. In the next year at Indiana University Wesley Salmon took me in, as it were, to instil a preoccupation with causality, probability, and frequency. Salmon was the first to comment on my fledgling ideas about identical particles. It was also around then that I participated in a symposium with Hilary Putnam, who challenged me with a new way to see quantum logic.
In the individual chapters I have tried as much as possible to indicate my more specific debts, for example to Enrico Beltrametti and Gianni Cassinelli, whose book became one of my bibles, to my frequent collaborator, R. Hughes, and to Jeffrey Bub, Nancy Cartwright, Roger Cooke, Maria Luisa Dalla Chiara, Arthur Fine, Clifford Hooker, Simon Kochen, Pekka Lahti, James McGrath, Peter Mittelstaedt, and Brian Skyrms, among others. Alan Hajek and R. Hughes read large parts of the manuscript and gave many helpful comments.
Almost every section of each chapter benefited from the close reading and comments by Sara Foster. The National Science Foundation and Princeton University steadfastly supported my research, while Anne Marie De Meo typed the results and helped me generously through many practical difficulties.com This page intentionally left blank www.com Summary Table of Contents 1. What Is Science? 1 PART I. DETERMINISM AND INDETERMINISM IN CLASSICAL PERSPECTIVE 19 2.
Indeterminism and Probability 49 PART II. HOW THE PHENOMENA DEMAND QUANTUM THEORY 77 4. The Empirical Basis of Quantum Theory 79 5. New Probability Models and their Logic 106 PART III.
The Basic Theory of Quantum Mechanics 139 7. Composite Systems, Interaction, and Measurement 193 PART IV. QUESTIONS OF INTERPRETATION 239 8. Critique of the Standard Interpretation 241 9.
Modal Interpretation of Quantum Mechanics 273 10. EPR: When Is a Correlation Not a Mystery? 338 11. The Problem of Identical Particles 375 12. Identical Particles: Individuation and Modality 434 NOTES 483 BIBLIOGRAPHY 502 INDEX 529 www.com This page intentionally left blank www.
What Is Science? 1 1. Two views about science 1 2. Theories and models 4 3. Interpretation: science as open text 8 4.
Models and scientific practice 12 5. More about empiricism 15 PART I. DETERMINISM AND INDETERMINISM IN CLASSICAL PERSPECTIVE 19 2. How symmetry is connected to determinism 21 2.
State-space models and their laws 26 3. Symmetry, transformation, invariance 33 4. Symmetries of time: classical (in)determinism 39 5. Conservation laws and covariance 44 3.
Indeterminism and Probability 49 1. Pure indeterminism and the modalities 49 2. Probability as measure of the possible 53 3. Symmetry and a priori probability 57 4.
Permutation symmetry: De Finetti's representation theorem 61 5. Ergodic theory: underlying determinism 65 6. A classical version of Schroedinger's equation 68 7. Holism: indeterminism in compound systems 73 PART II.
HOW THE PHENOMENA DEMAND QUANTUM THEORY 77 4. The Empirical Basis of Quantum Theory 79 1. Threat of indeterminism 79 www.com xiv CONTENTS 2. Causality in an indeterministic world 81 3.
Deduction of Bell's Inequalities 85 4. General description of causal models 99 6. Does locality really play a role? 102 5. New Probability Models and their Logic 106 1.
When are values indeterminate? 106 2. General and geometric probability models 112 3. The end of counterfactual definiteness 122 5. Models of measurement: a trilemma for interpretation 125 6.
Introduction to quantum logic 128 7. Is quantum logic important? 134 PART III. The Basic Theory of Quantum Mechanics 139 1. Pure states and observables 139 2.
Pure states, observables, and vectors 141 3. Observables and operators 147 4. Mixed states and operators 157 5. Gleason's theorem and its implications 165 6.
Symmetries and motion: Schroedinger's equation 177 7. Symmetries and conservation laws 181 8. The radical effect of superselection rules 185 7. Composite Systems, Interaction, and Measurement 193 1.
Interaction and the ignorance interpretation of mixtures 206 4. The quantum-mechanical theory of measurement 208 5. Preparation of state 233 PART IV. QUESTIONS OF INTERPRETATION 239 8.
Critique of the Standard Interpretation 241 1. What is an interpretation? 241 www.com CONTENTS xv 2. Two forms of indeterminism 244 3. What happens in measurement? von Neumann's answer 245 4.
Von Neumann's first defence: consistency of measurement 250 5. Von Neumann's second defence: repeatable measurement 252 6. Hughes's argument from conditional probability 259 7. Two cat paradoxes and the macro world 261 8.
Macroscopic character and superselection rules 264 9. Modal Interpretation of Quantum Mechanics 273 1. The modal interpretation 274 2. The modal account developed 279 3.
What happens in a measurement? 283 4. Puzzle: how far does holism go? 290 5. Puzzle: is there chaos behind the regularities? 294 6. The resources of quantum logic 299 7.
The modal interpretation, quantum-logically 306 8. Modal interpretation of composition and reduction 327 9. Consistency of the description of compound systems 330 10. Interpretation and the virtue of tolerance 335 10.
EPR: When Is a Correlation Not a Mystery? 338 1. The paper by Einstein, Podolsky, and Rosen 338 2. Initial defence of the argument 341 3. The step to empirical testability 344 4.
How are correlations explained? 349 5. Attempts at perfect explanation 354 6. Sinister consequences and spooky action at a distance 363 7. The end of the causal order? 372 11.
The Problem of Identical Particles 375 1. Elementary particles: aggregate behaviour 375 2. Permutation invariance and the Dichotomy Principle 381 3. The Exclusion Principle 384 4.
Blokhintsev's proof of the fermion–boson dichotomy 389 5. Permutations as superselection operators 396 www.com xvi CONTENTS 6. Quantum-statistical mechanics 403 7.