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. Schrödinger'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 Theories has 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 xi

List of Abbreviations xv

List of Symbols xvi

1. Exegesis Saves: Interpreting Physical Theories 1

1.1. Why be so particular? 1

1.2. Interpreting physical theories 5

1.3. In praise, and in defense, of the standard account 10

1.4. Criteria of adequacy for interpretations 10

1.5. Realism and pristine interpretation 12

1.6. Interpreting QM_∞ 14

2. Quantizing 19

2.1. Rival quantum theories? 20

2.2. Physical equivalence and unitary equivalence 24

2.3. The Stone–von Neumann uniqueness theorem 30

      2.3.1. Mechanics: classical to quantum 30

      2.3.2. Classical theories as symplectic vector spaces 33

      2.3.3. Hamiltonian quantization 35

      2.3.4. The Stone–von Neumann theorem 37

      2.3.5. Uniqueness illustrated 42

2.4. Pause 45

3. Beyond the Stone–von Neumann Theorem 46

3.1. Suspending weak continuity 46

      3.1.1. The position and momentum representations 46

      3.1.2. Are they “physical”? 50

3.2. Non-vanilla configuration spaces 53

      3.2.1. Mr. Heisenberg's group 54

      3.2.2. Phase spaces of other topologies 57

3.3. Infinitely many degrees of freedom 59

      3.3.1. The thermodynamic limit: the infinite spin chain 59

      3.3.2. QFT: the Klein–Gordon field 65

3.4. Conclusion 72

4. Representation Without Taxation: An Unstrenuous Tour of Algebraic Notions 73

4.1. What an algebra is 73

4.2. C* algebras, abstractly 75

4.3. C* algebras, concretely 77

4.4. The representation of a C* algebra 82

      4.4.1. Faith and reducibility 84

      4.4.2. Unitary equivalence of representations 85

4.5. Von Neumann algebras 86

4.6. States on C* algebra 89

      4.6.1. The GNS representation 89

      4.6.2. Foliums 94

4.7. Von Neumann factors 98

4.8. Conclusion and précis 99

5. Axioms for QM_∞ 102

5.1. A declaration of sentiment 102

5.2. Axioms for QFT 104

5.3. Entanglement and locality in QFT 109

      5.3.1. Motivating the Microcausality axiom 109

      5.3.2. Entanglement in QFT 113

5.4. Axioms for QSM 114

5.5. Conclusion 116

6. Interpreting QM_∞: Some Options 117

6.1. What are we interpreting? 119

6.2. Hilbert Space Conservatism 122

      6.2.1. Some privileging strategies 123

      6.2.2. Underprivileged? 124

      6.2.3. Overprivileged? 125

6.3. DHR selection theory 127

      6.3.1. Motivation and set up 127

      6.3.2. Reservations 131

6.4. Algebraic Imperialism 132

      6.4.1. Apologetic Imperialism 133

      6.4.2. Bold Imperialism 136

      6.4.3. Instantiation and necessity 139

      6.4.4. Imperialism: excess and deficiency 142

6.5. Mixed strategies 143

6.6. Universalism 145

6.7. Unpristine approaches 146

7. Extraordinary QM 148

7.1. Typing von Neumann factors 149

      7.1.1. Dimension functions and subtypes 154

7.2. Atomlessness and normality 155

7.3. KMS states 159

7.4. A modicum of modular theory 162

7.5. Extraordinarily physical 166

      7.5.1. Non-atomic von Neumann algebras in QFT 166

      7.5.2. Non-atomic von Neumann algebras in QSM 167

7.6. Interlude 168

8. Interpreting Extraordinary QM 169

8.1. Preparation 170

8.2. The MBA and ordinary QM 173

      8.2.1. Characterizing the MBA 174

      8.2.2. Lattice entertain you 177

      8.2.3. A scheme and some instances 179

8.3. The MBA and QM_∞ 181

      8.3.1. Hope 182

      8.3.2. Tempered 183

      8.3.3. Interpretation unbound? 186

8.4. Conclusion 188

9. Is Particle Physics Particle Physics? 190

9.1. Particle physics 191

9.2. Particle interpretations 193

9.3. Pro particles 195

      9.3.1. Fock space, heuristically 195

      9.3.2. The particle notion as fundamental 199

9.4. Anti particles: an argument, and a loophole 204

9.5. Closing the loophole: incommensurable particle notions 206

      9.5.1. Fock space without the heuristic 206

      9.5.2. Unitary inequivalence and incommensurability 211

9.6. The incommensurability of Jack's and Jill's particle notions 214

      9.6.1. Jill's spacetime 214

      9.6.2. Jack's notion, and Jill's 215

9.7. Operationalizing the particle notion? 216

9.8. The Unruh effect without particles 218

9.9. Conclusion: the case against, restated and extended 219

10. Particles and the Void 221

10.1. Extended particle notions 222

      10.1.1. An appeal to exfoliated predictions 222

      10.1.2. An appeal to Fell's theorem 225

      10.1.3. Universalizing 226

10.2. Spacetime matters 229

      10.2.1. Killing particles and μ-born particles 229

      10.2.2. Adulteration? 232

10.3. Matter matters 234

      10.3.1. For Jack 235

      10.3.2. More adulteration? 237

10.4. Coherent states 239

      10.4.1. One degree of freedom 240

      10.4.2. n degrees of freedom 241

      10.4.3. QFT 242

      10.4.4. Some properties of coherent representations 243

      10.4.5. Coherence: what is it good for? 244

10.5. Conclusion 246

11. Phenomenological Particle Notions 247

11.1. Particle physics, redux 249

      11.1.1. The interaction picture and Haag's theorem 250

      11.1.2. Hope: Haag–Ruelle? 253

      11.1.3. The (ø~ 4)_2 theory 255

11.2. Cosmological particle creation 256

11.3. Conclusion 260

12. A Matter of Degree: Making Sense of Phase Structure 261

12.1. The thermodynamic limit: why go there? 262

      12.1.1. Ergodicity 263

      12.1.2. Phase structure 268

      12.1.3. Broken symmetry 270

12.2. Phase structure: a closer look 272

      12.2.1. Pure phases 272

      12.2.2. The set of equilibrium states 277

12.3. Extremist obstructions to explanation 281

      12.3.1. The phase argument 281

      12.3.2. The W* argument 284

12.4. Complicating content 288

13. Interlude: Symmetry Breaking in QSM 291

13.1. Introduction: Coalesced Structure 291

13.2. Symmetry and the Sharp Distinction 292

13.3. Broken symmetry in QM_∞ 300

      13.3.1. The individual sense 300

      13.3.2. The decompositional sense 301

      13.3.3. Comparing the accounts 303

13.4. The decompositional account illustrated 305

      13.4.1. The ferromagnet 305

      13.4.2. Superconductivity 306

13.5. Coalesced structures in broken symmetry 309

14. Broken Symmetry and Physicists' QFT 312

14.1. Introduction 312

14.2. Broken symmetry in QFT 314

      14.2.1. Overview 315

      14.2.2. An example: the massless Klein–Gordon field 317

14.3. Goldstone bosons 320

14.4. The Higgs mechanism 324

      14.4.1. The saga of the electroweak theory 325

      14.4.2. The abelian Higgs model 328

14.5. Coalesced structures in QFT? 330

      14.5.1. Promissory notes 330

      14.5.2. Unphased 332

14.6. A Sounder Principle? 336

15. Re: Interpreting Physical Theories 340

15.1. An anatomy of scandal 340

15.2. Realism sophisticated 344

      15.2.1. The global argument 344

      15.2.2. Structural Realism 346

15.3. QM_∞ and the morals 349

15.4. Law and possibility 351

15.5. Virtue reconceived 354

15.6. Fundamental physics 355

References 357

Index 371

中科院文献情报中心