The Ultimate Constituents of the Material World (eBook)

Part I Ontology and Quantum Field Theory 13
Chapter 1 Introduction 15
Chapter 2 Philosophical Background 21
2.1 Atomism in the History of Philosophy 22
2.2 Philosophical Versus Scientific Atomism 27
2.3 Atomism and Reductionism 28
Chapter 3 Ontology and Physics 31
3.1 Some Main Themes in Ontology 31
3.2 A Brief History of Ontology 33
3.3 The Analytical Tradition of Ontology 35
3.4 No-Go Theorems as Tools for the Ontological Practician 37
3.5 Symmetries, Heuristics and Objectivity 38
Chapter 4 History and Basic Structure of QFT 41
4.1 The Early Development 41
4.2 The Emergence of Infinities 45
4.3 The Taming of Infinities 46
4.4 The Lagrangian Formulation of QFT 49
4.5 Interaction 52
Chapter 5 Alternative Approaches 55
5.1 Deficiencies of the Standard Formulation of QFT 55
5.2 The Algebraic Point of View 56
5.3 Basic Ideas of AQFT 58
Chapter 6 The Ontological Significance of QFTand AQFT 61
6.1 QM Versus QFT 61
6.2 AQFT and the Ideal Language Philosophy 65
6.3 QFT Versus AQFT 69
6.4 The Philosophical Interest in (A)QFT 72
Part II Classical Ontologies 75
Chapter 7 Classical vs. Revisionary Ontologies 77
7.1 Introduction 78
7.2 Aristotle’s Theory of Substances 81
7.3 Substance Ontologies 86
7.4 Substances Under Attack 91
7.5 Substance Ontology and Quantum Physics 93
7.5.1 Incompatible Observables 93
7.5.2 Non-Vanishing Vacuum Expectation Values 95
Chapter 8 Particle Interpretation of QFT 97
8.1 The Particle Concept 98
8.1.1 General Features 98
8.1.2 Wigner’s Analysis of the Poincar´e Group 101
8.2 Theory and Experiment in Elementary Particle Physics: Is a Particle Track a Track of a Particle? 108
8.3 Localization Problems 112
8.3.1 The Clash of Causality and Localizability 113
8.3.2 Locating the Origin of Non-Localizability: A Comparative Study 118
8.4 Further Problems for a Particle Interpretation of QFT 124
8.5 Results 126
Chapter 9 Field Interpretations of QFT 127
9.1 The Field Concept 128
9.2 Fields as Basic Entities of QFT 129
9.2.1 The Role of Field Operators in QFT 129
9.2.2 Indirect Evidence for Fields 131
9.3 Fields Versus Algebras 132
Part III Revisionary Ontologies 133
Chapter 10 Process Ontology 135
10.1 The Strands of Process Ontology 135
10.2 Why Process Ontology in QM and QFT? 136
10.3 A Case Study: Consequences of the Ontological Hypotheses for the Interpretation of Feynman Diagrams 139
10.4 Evaluation of the Case Study 145
10.5 Remaining Problems 146
Chapter 11 Trope Ontology I: The Ontological Status of Properties 149
11.1 The Problem of Universals 150
11.2 The Traditional Responses 152
11.3 A New Solution: Trope Ontology 155
11.4 An Evaluation of the Debate 159
11.5 Conclusion and Outlook 162
Chapter 12 Trope Ontology II: Properties and Things 165
Part IV The Trope Bundle Interpretation 169
Chapter 13 Dispositional Trope Ontology 171
13.1 Introduction 171
13.2 Trope Bundles and Many-Particle Systems 173
13.2.1 ‘Elementary Particles’ 173
13.2.2 Individuality of Quantum Objects 174
13.2.3 Dispositions and Tropes 178
13.2.4 An Example 181
13.3 The Trope Bundle Interpretation of AQFT 183
13.3.1 AQFT as a Model of Trope Ontology 184
13.3.2 An Algebraic Argument for the Bundle Conception 185
13.3.3 Representations and Properties/Tropes 188
13.3.4 Outlook on Potential Problems and Further Work 192
13.3.5 The Explanatory Power of the Trope Bundle Interpretation 193
13.4 Summing Up 195
Part V Concluding Remarks 197
Chapter 14 Physics and Philosophy 199
Chapter 15 Summing Up 201
15.1 General Remarks 201
15.2 Comparison of Ontologies for QFT 203
15.2.1 Particles Versus Fields 203
15.2.2 Processes Versus Tropes 206
15.2.3 The Merits of Dispositional Trope Ontology 208
Part VI Appendices 211
Abbreviations and Notation 213
Appendix A Special Relativity Theory: Some Notation and Required Results 215
Appendix B Ontologically Oriented Survey of Quantum Mechanics 217
B.1 The Hilbert Space Formalism 219
B.1.1 States and Observables 219
B.1.2 Probability Interpretation 221
B.1.3 Dynamics 226
B.2 Problems for an Ontology of QM 227
B.2.1 The Problem of Individuation 228
B.2.2 The Problem of Reidentifiability 230
B.2.3 The Measurement Problem 232
Appendix C 
235 
C.1 Gauge Invariance 235
C.2 Effective Field Theories and Renormalization 237
C.3 String Theory 239
Appendix D Assumptions and Results of AQFT 241
D.1 Assumptions of AQFT 241
D.2 Representations and States 245
D.3 Superselection Sectors 248
Bibliography 255
Physics Glossary 273
Philosophy Glossary 287