Interpreting Quantum Theories

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ISBN: 9780199535408 | 019953540X
Cover: Hardcover
Copyright: 7/21/2011

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Traditionally, philosophers of quantum mechanics have addressed exceedingly simple systems: a pair of electrons in an entangled state, or an atom and a cat in Dr. Schrodinger's diabolical device. But recently, much more complicated systems, such as quantum fields and the infinite systems at the thermodynamic limit of quantum statistical mechanics, have attracted, and repaid, philosophical attention.Interpreting Quantum Theorieshas three entangled aims. The first is to guide those familiar with the philosophy of ordinary QM into the philosophy of 'QM infinity', by presenting accessible introductions to relevant technical notions and the foundational questions they frame. The second aim is to develop and defend answers to some of those questions. Does quantum field theory demand or deserve a particle ontology? How (if at all) are different states of broken symmetry different? And what is the proper role of idealizations in working physics? The third aim is to highlight ties between the foundational investigation of QM infinity and philosophy more broadly construed, in particular by using the interpretive problems discussed to motivate new ways to think about the nature of physical possibility and the problem of scientific realism.

Preface	p. xi
List of Abbreviations	p. xv
List of Symbols	p. xvi
Exegesis Saves: Interpreting Physical Theories	p. 1
Why be so particular?	p. 1
Interpreting physical theories	p. 5
In praise, and in defense, of the standard account	p. 10
Criteria of adequacy for interpretations	p. 10
Realism and pristine interpretation	p. 12
Interpreting QM_∞	p. 14
Quantizing	p. 19
Rival quantum theories?	p. 20
Physical equivalence and unitary equivalence	p. 24
The Stone-von Neumann uniqueness theorem	p. 30
Mechanics: classical to quantum	p. 30
Classical theories as symplectic vector spaces	p. 33
Hamiltonian quantization	p. 35
The Stone-von Neumann theorem	p. 37
Uniqueness illustrated	p. 42
Pause	p. 45
Beyond the Stone-von Neumann Theorem	p. 46
Suspending weak continuity	p. 46
The position and momentum representations	p. 46
Are they ôphysicalö?	p. 50
Non-vanilla configuration spaces	p. 53
Mr. Heisenberg's group	p. 54
Phase spaces of other topologies	p. 57
Infinitely many degrees of freedom	p. 59
The thermodynamic limit: the infinite spin chain	p. 59
QFT: the Klein-Gordon field	p. 65
Conclusion	p. 72
Representation Without Taxation: An Unstrenuous Tour of Algebraic Notions	p. 73
What an algebra is	p. 73
C^* algebras, abstractly	p. 75
C^* algebras, concretely	p. 77
The representation of a C^* algebra	p. 82
Faith and reducibility	p. 84
Unitary equivalence of representations	p. 85
Von Neumann algebras	p. 86
States on C^* algebra	p. 89
The GNS representation	p. 89
Foliums	p. 94
Von Neumann factors	p. 98
Conclusion and précis	p. 99
Axioms for QM_∞	p. 102
A declaration of sentiment	p. 102
Axioms for QFT	p. 104
Entanglement and locality in QFT	p. 109
Motivating the Microcausality axiom	p. 109
Entanglement in QFT	p. 113
Axioms for QSM	p. 114
Conclusion	p. 116
Interpreting QM_∞: Some Options	p. 117
What are we interpreting?	p. 119
Hilbert Space Conservatism	p. 122
Some privileging strategies	p. 123
Underprivileged?	p. 124
Overprivileged?	p. 125
DHR selection theory	p. 127
Motivation and set up	p. 127
Reservations	p. 131
Algebraic Imperialism	p. 132
Apologetic Imperialism	p. 133
Bold Imperialism	p. 136
Instantiation and necessity	p. 139
Imperialism: excess and deficiency	p. 142
Mixed strategies	p. 143
Universalism	p. 145
Unpristine approaches	p. 146
Extraordinary QM	p. 148
Typing von Neumann factors	p. 149
Dimension functions and subtypes	p. 154
Atomlessness and normality	p. 155
KMS states	p. 159
A modicum of modular theory	p. 162
Extraordinarily physical	p. 166
Non-atomic von Neumann algebras in QFT	p. 166
Non-atomic von Neumann algebras in QSM	p. 167
Interlude	p. 168
Interpreting Extraordinary QM	p. 169
Preparation	p. 170
The MBA and ordinary QM	p. 173
Characterizing the MBA	p. 174
Lattice entertain you	p. 177
A scheme and some instances	p. 179
The MBA and QM_∞	p. 181
Hope	p. 182
Tempered	p. 183
Interpretation unbound?	p. 186
Conclusion	p. 188
Is Particle Physics Particle Physics?	p. 190
Particle physics	p. 191
Particle interpretations	p. 193
Pro particles	p. 195
Fock space, heuristically	p. 195
The particle notion as fundamental	p. 199
Anti particles: an argument, and a loophole	p. 204
Closing the loophole: incommensurable particle notions	p. 206
Fock space without the heuristic	p. 206
Unitary inequivalence and incommensurability	p. 211
The incommensurability of Jack's and Jill's particle notions	p. 214
Jill's spacetime	p. 214
Jack's notion, and Jill's	p. 215
Operationalizing the particle notion?	p. 216
The Unruh effect without particles	p. 218
Conclusion: the case against, restated and extended	p. 219
Particles and the Void	p. 221
Extended particle notions	p. 222
An appeal to exfoliated predictions	p. 222
An appeal to Fell's theorem	p. 225
Universalizing	p. 226
Spacetime matters	p. 229
Killing particles and µ-born particles	p. 229
Adulteration?	p. 232
Matter matters	p. 234
For Jack	p. 235
More adulteration?	p. 237
Coherent states	p. 239
One degree of freedom	p. 240
n degrees of freedom	p. 241
QFT	p. 242
Some properties of coherent representations	p. 243
Coherence: what is it good for?	p. 244
Conclusion	p. 246
Phenomenological Particle Notions	p. 247
Particle physics, redux	p. 249
The interaction picture and Haag's theorem	p. 250
Hope: Haag-Ruelle?	p. 253
The (¿⁴)₂ theory	p. 255
Cosmological particle creation	p. 256
Conclusion	p. 260
A Matter of Degree: Making Sense of Phase Structure	p. 261
The thermodynamic limit: why go there?	p. 262
Ergodicity	p. 263
Phase structure	p. 268
Broken symmetry	p. 270
Phase structure: a closer look	p. 272
Pure phases	p. 272
The set of equilibrium states	p. 277
Extremist obstructions to explanation	p. 281
The phase argument	p. 281
The W^* argument	p. 284
Complicating content	p. 288
Interlude: Symmetry Breaking in QSM	p. 291
Introduction: Coalesced Structure	p. 291
Symmetry and the Sharp Distinction	p. 292
Broken symmetry in QM_∞	p. 300
The individual sense	p. 300
The decompositional sense	p. 301
Comparing the accounts	p. 303
The decompositional account illustrated	p. 305
The ferromagnet	p. 305
Superconductivity	p. 306
Coalesced structures in broken symmetry	p. 309
Broken Symmetry and Physicists' QFT	p. 312
Introduction	p. 312
Broken symmetry in QFT	p. 314
Overview	p. 315
An example: the massless Klein-Gordon field	p. 317
Goldstone bosons	p. 320
The Higgs mechanism	p. 324
The saga of the electroweak theory	p. 325
The abelian Higgs model	p. 328
Coalesced structures in QFT?	p. 330
Promissory notes	p. 330
Unphased	p. 332
A Sounder Principle?	p. 336
Re: Interpreting Physical Theories	p. 340
An anatomy of scandal	p. 340
Realism sophisticated	p. 344
The global argument	p. 344
Structural Realism	p. 346
QM_∞ and the morals	p. 349
Law and possibility	p. 351
Virtue reconceived	p. 354
Fundamental physics	p. 355
References	p. 357
Index	p. 371
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Interpreting Quantum Theories

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