FOUNDATIONS OF QUANTUM MECHANICS AND INFORMATION

By S. ALMIN

1 Pre-Quantum Theories 1 11 Newtonian Mechanics 1 12 Maxwellian Electrodynamics 5 13 Locality 8 14 Bell’s Formulation of “Locality” 13 15 Ontology 18 16 Measurement 22 17 Abstract Spaces 25 References 31 2 Quantum Examples 33 21 Overview 33 22 Particle-in-a-Box 36 23 Free Particle Gaussian Wave Packets 38 24 Diffraction and Interference 44 25 Spin 47 26 Several Particles 51 References 57 3 The Measurement Problem 59 31 The Quantum Description of Measurement 59 32 Formal Treatment 64 33 Schrödinger’s Cat and Einstein’s Bomb 69 34 Hidden Variables and the Ignorance Interpretation 74 35 Wrap-Up 79 References 85 4 The Locality Problem 87 41 Einstein’s Boxes 87 42 EPR 96 43 Einstein’s Discussions of EPR 100 44 Bohm’s Reformulation 104 45 Bell’s Re-Telling 107 References 113 5 The Ontology Problem 115 51 Complexity and Reality 115 52 Configuration Space 118 53 Ontology, Measurement, and Locality 122 54 Schrödinger’s Suggestion for a Density in 3-Space 129 55 So Then What? 133 References 139 6 The Copenhagen Interpretation 141 61 Bohr’s Como Lecture 142 62 Heisenberg 148 63 Bohr on Einstein’s Diffraction Example 154 64 The Photon Box Thought Experiment 160 65 Bohr’s Reply to EPR 166 66 Contemporary Perspectives 169 References 174 7 The Pilot-Wave Theory 177 71 Overview 178 72 Particle in a Box 182 73 Other Single Particle Examples 185 74 Measurement 188 75 Contextuality 194 76 The Many-Particle Theory and Nonlocality 199 77 Reactions 205 References 212 8 Bell’s Theorem 215 81 EPRB Revisited 215 82 A Preliminary Bell Inequality 218 83 The Real Bell (and the CHSH) Inequality 222 84 Experiments 227 85 What Does It Mean? 231 86 (Bell’s) Locality Inequality Theorem 236 References 243 9 The Spontaneous Collapse Theory 245 91 Ghirardi, Rimini, and Weber 246 92 Multiple Particle Systems and Measurement 254 93 Ontology, Locality, and Relativity 259 94 Empirical Tests of GRW 265 References 271 10 The Many-Worlds Theory 273 101 The Basic Idea 274 102 Probability 280 103 Ontology 286 104 Locality 291 References 302 Afterword 303