Making Sense of Quantum Mechanics

335 Pages·2016·4.34 MB·English

by  Jean Bricmont (auth.)

Jean Bricmont
Making Sense of
Quantum Mechanics
Making Sense of Quantum Mechanics
Jean Bricmont
Making Sense of Quantum
Mechanics
123
JeanBricmont
IRMP
UCLouvain
Louvain-la-Neuve
Belgium
ISBN978-3-319-25887-4 ISBN978-3-319-25889-8 (eBook)
DOI 10.1007/978-3-319-25889-8
LibraryofCongressControlNumber:2015956126
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Preface
This book is both apparently ambitious and modest in its aims. Ambitious, as it
attempts to achieve something that has been declared impossible by some of the
greatestphysicistssincethe1920s:makingsenseofwhatquantummechanicsreally
means.Butmodest,becausethatgoalwasactuallyalreadyattainedmanyyearsago
in the work of Louis de Broglie, David Bohm, and John Bell. I will simply try to
explain what they achieved.
Thisbookiswrittenespeciallyforallthosestudentswhofeelthattheyhavenot
understood the subject of quantum mechanics, not because they fail to master the
mathematics or because they cannot do the exercises, but because they do not see
what the theory means.
However, no prior knowledge of quantum mechanics is required. Most of the
technicalpartshavebeenputinappendices,whichcanbeskippedifoneiswilling
to take certain results for granted.
Hopefully this book should also interest philosophers and historians of science,
in particular Chaps. 1, 3, 7, and 8.
The analysis presented here has benefited from such a large number of discus-
sions,seminars,andexchangeswithsomanypeoplethatthankingthemallbyname
would scarcely be possible.
However, I must stress that I learned most of what I know about the subject
through discussions with Detlef Dürr, Tim Maudlin, Nino Zanghì, and especially
with Sheldon Goldstein.
Many readers ofparts ofthis bookhavemadeuseful comments andcorrections
and I wish to thank them: Xavier Bekaert, Serge Dendas, Lajos Diósi, Michel
Ghins, Michel Hellas, Dominique Lambert, Vincent Mathieu, Alexis Merlaud,
AmauryMouchet,andAlanSokal.MyspecialthankstoWardStruyveforhelping
mewithhisgreatscientificexpertiseonthetopicofthisbook.IthankalsoStephen
Lyle for his careful reading of the manuscript and many clarifying exchanges.
Needless to say, all remaining errors are mine.
v
vi Preface
I wish to thank Cathy Brichard warmly for her indispensable secretarial
help. And finally, heartfelt thanks to my editor Angela Lahee, without whom this
bookwouldnothaveseenthelightofday,forherencouragementandherpatience.
Contents
1 Physicists in Wonderland. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 What This Book Is About. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Back to Copenhagen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 What Do Physicists Say Now? . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 But There has Never Been a Consensus . . . . . . . . . . . . . . . . . 11
1.5 Why Bother?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.6 Outline of the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 The First Mystery: Interference and Superpositions . . . . . . . . . . . 21
2.1 The Spin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 The Mach–Zehnder Interferometer. . . . . . . . . . . . . . . . . . . . . 24
2.3 The Quantum Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4 How Does It Work?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 What Is the Meaning of the Quantum State?. . . . . . . . . . . . . . 33
2.5.1 The Measurement Process Within the Quantum
Formalism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.5.2 The “Naive” Statistical Interpretation . . . . . . . . . . . . . 41
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 “Philosophical” Intermezzo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.1 Realism and Idealism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Scientific Realism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.2.1 Underdetermination . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.2.2 Incommensurability of “Paradigms” . . . . . . . . . . . . . . 83
3.2.3 The Status of “Unobservable Entities” . . . . . . . . . . . . 86
3.3 Realism and Quantum Mechanics . . . . . . . . . . . . . . . . . . . . . 91
3.4 Determinism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4.2 Determinism and “Chaos Theory” . . . . . . . . . . . . . . . 98
3.4.3 Probabilities in Classical Physics . . . . . . . . . . . . . . . . 101
vii
viii Contents
3.4.4 The Law of Large Numbers and Scientific
Explanations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
3.4.5 “Randomness” and Deterministic Dynamical
Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3.4.6 Quantum Mechanics and Determinism . . . . . . . . . . . . 106
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4 The Second Mystery: Nonlocality. . . . . . . . . . . . . . . . . . . . . . . . . 111
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.2 Einstein’s Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.3 What Is Nonlocality? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.4 A Simple Proof of Nonlocality . . . . . . . . . . . . . . . . . . . . . . . 118
4.4.1 An Anthropomorphic Thought Experiment . . . . . . . . . 118
4.4.2 A Real Quantum Situation . . . . . . . . . . . . . . . . . . . . 121
4.4.3 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5 The de Broglie–Bohm Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.1 The Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.1.1 The Equations of the Theory. . . . . . . . . . . . . . . . . . . 130
5.1.2 How Does the de Broglie–Bohm Dynamic Work? . . . . 134
5.1.3 What About the Statistical Predictions of Quantum
Mechanics?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.1.4 Measurements of “Observables” in the de Broglie–
Bohm Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.1.5 “Contextuality” and Naive Realism About
Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1.6 What About the Collapse of the Quantum State? . . . . . 152
5.1.7 WhatAretheMeaningandtheOriginoftheStatistical
Assumptions on the Initial Conditions in the de
Broglie–Bohm Theory?. . . . . . . . . . . . . . . . . . . . . . . 155
5.1.8 Heisenberg’s Relations and Absolute Uncertainty. . . . . 159
5.1.9 What Is the Relationship Between the de
Broglie–Bohm Theory and Ordinary Quantum
Mechanics?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
5.2 Some Natural Questions About the de Broglie–Bohm
Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.2.1 How Does the de Broglie–Bohm Theory Account
for Nonlocality?. . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
5.2.2 What About Relativity? . . . . . . . . . . . . . . . . . . . . . . 169
5.2.3 What About the Classical Limit? . . . . . . . . . . . . . . . . 173
5.3 Other Objections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5.3.1 Isn’t This a Return to Classical Mechanics?. . . . . . . . . 175
5.3.2 Isn’t the Theory Too Complicated? . . . . . . . . . . . . . . 176
Contents ix
5.3.3 What About the Symmetry Between Position
and Momentum? . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5.3.4 What About the No Hidden Variables Theorems? . . . . 178
5.3.5 If the Predictions of the de Broglie–Bohm Theory
Are the Same as Those of Quantum Mechanics,
What Is the Point of the de Broglie–Bohm Theory?. . . 179
5.3.6 Why Isn’t there an Action–Reaction Principle
in the de Broglie–Bohm Theory?. . . . . . . . . . . . . . . . 179
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
5.4.1 Trouble in Paradise?. . . . . . . . . . . . . . . . . . . . . . . . . 180
5.4.2 The Merits of the de Broglie–Bohm Theory . . . . . . . . 183
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6 Are There Any Alternative Theories?. . . . . . . . . . . . . . . . . . . . . . 199
6.1 The Many-Worlds Interpretation . . . . . . . . . . . . . . . . . . . . . . 200
6.1.1 The Naive Many-Worlds Interpretation. . . . . . . . . . . . 200
6.1.2 A Precise Many-Worlds Interpretation . . . . . . . . . . . . 207
6.1.3 The Pure Wave Function Ontology . . . . . . . . . . . . . . 209
6.2 The Spontaneous Collapse Theories. . . . . . . . . . . . . . . . . . . . 213
6.3 The Decoherent Histories Approach. . . . . . . . . . . . . . . . . . . . 216
6.4 QBism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
Appendices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
7 Revisiting the History of Quantum Mechanics. . . . . . . . . . . . . . . . 233
7.1 The Bohr–Einstein Debate. . . . . . . . . . . . . . . . . . . . . . . . . . . 234
7.1.1 What Was the Debate Really About? . . . . . . . . . . . . . 234
7.1.2 The 1927 Solvay Conference. . . . . . . . . . . . . . . . . . . 236
7.1.3 The Photon and the Box Experiment . . . . . . . . . . . . . 238
7.1.4 The Einstein–Podolsky–Rosen Argument . . . . . . . . . . 241
7.1.5 Who Won the Bohr–Einstein Debate?. . . . . . . . . . . . . 244
7.2 Born and Einstein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
7.3 What Did Schrödinger Really Worry About?. . . . . . . . . . . . . . 249
7.4 The von Neumann No Hidden Variables Theorem. . . . . . . . . . 253
7.5 Misunderstandings of Bell. . . . . . . . . . . . . . . . . . . . . . . . . . . 258
7.6 The Non-reception of de Broglie’s and Bohm’s Ideas. . . . . . . . 264
7.6.1 Reactions to de Broglie. . . . . . . . . . . . . . . . . . . . . . . 264
7.6.2 Reactions to Bohm. . . . . . . . . . . . . . . . . . . . . . . . . . 269
7.7 Quantum Mechanics, “Philosophy”, and Politics . . . . . . . . . . . 275
7.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
8 Quantum Mechanics and Our “Culture”. . . . . . . . . . . . . . . . . . . . 285
8.1 The Trouble with Quantum Mechanics. . . . . . . . . . . . . . . . . . 286
8.2 A Plea for “Copenhagen” . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
x Contents
8.3 But What About Now?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
8.4 Understanding Quantum Mechanics: An Unfinished Story. . . . . 292
Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327