Epistemology and Probability (eBook)

Preface 6
Acknowledgments 27
Contents 29
Abbreviations 32
Introduction-Epistemology and Probability in Quantum Theory: Physics, Mathematics, and Philosophy 33
1.1 Classical and Nonclassical Epistemology 33
1.2 Nonclassical Epistemology and Quantum Probability 44
1.3 Physics, Mathematics, and Philosophy in Quantum Theory 53
1.4 The Architecture of Quantum-Theoretical Concepts 58
1.5 Epistemology and Interpretation 71
Quantum Phenomena and the Double-Slit Experiment 77
2.1 The Double-Slit Experiment: From an (Almost) Classical to a Nonclassical View 77
2.2 The Double-Slit Experiment, the Uncertainty Relations, and Probability 89
2.3 The Delayed-Choice Experiment 97
2.4 The Quantum Eraser 102
2.5 Repetition and Erasure, Classical and Quantum 105
Heisenberg’s Revolutions: New Kinematics, New Mathematics, and New Philosophy 108
3.1 ‘‘A Step of Probably Fundamental Importance’’: From Bohr to Heisenberg 109
3.2 The Founding Physical and Philosophical Principles of Heisenberg’s Quantum Mechanics 123
3.3 The Correspondence Principle Between Physics and Mathematics 131
3.4 ‘‘Ensembles of Quantities’’: From Experiment to Mathematics to Physics 138
From Geometry to Algebra in Physics, with Heisenberg 145
4.1 ‘‘A Purely Algebraic Method of Description of Nature’’ 145
4.2 ‘‘A New Era of Mutual Stimulation of Mechanics and Mathematics’’ 158
Schrödinger’s Waves: Propagation and Probability 167
5.1 Quantum Waves and Quantum Probability 168
5.2 ‘‘The Wave Radiation Forming the Basis of the Universe’’ 174
5.3 Schrödinger’s Equation 185
5.4 Wave Mechanics Between Optics and Mechanics 191
5.5 Quantum Mechanics Beyond Mechanics and Optics 195
5.6 The Ends of the Wave Function: From Quantum States to Entangled Knowledge 201
Bohr’s Como Argument: Complementarity and the Problem of Causality 208
6.1 Complementarity: Between Concepts and Experiments 208
6.2 The Quantum Postulate: Discontinuity and Irrationality 215
6.3 Complementarity and Causality 220
6.4 Quantum Causality in Dirac, Heisenberg, and von Neumann 231
6.5 A Brief History of Quantum Causality 243
From Como to Copenhagen: Renunciations 247
Can Quantum-Mechanical Description of Physical Reality Be Considered both Complete and Local? 264
8.1 Correlations, Completeness, and Locality 265
8.2 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? EPR’s Argument 275
8.3 Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? Bohr’s Argument 279
8.4 Can Quantum-Mechanical Description of Physical Reality Be Considered Local? 295
Essential Ambiguity and Essential Influence: Reading Bohr’s Reply to EPR 305
9.1 Framing the Argument 305
9.2 Measurement and Complementarity 310
9.3 Restaging the EPR Experiment 320
9.4 Essential Ambiguity and Essential Influence 327
9.5 From Temporality to Relativity 332
Mysteries Without Mysticism, Correlations Without Correlata, Epistemology Without Ontology, and Probability Without Causality 338
10.1 Mysteries Without Mysticism 338
10.2 Correlations Without Correlata 348
10.3 Epistemology Without Ontology 352
10.4 Probability Without Causality 361
Conclusion: ‘‘The Mere Touch of Cold Philosophy’’ 378
References 393
Name Index 403
Subject Index 407