Chance in physics: Foundations and perspectives

Title page......Page 3
Table of Contents......Page 5
1 Introduction......Page 11
2 Two Notions of Probability......Page 12
3 Typicality, Scientific Explanations, and Statistical Mechanics......Page 15
4 A Simple Example: The Kac Ring Model......Page 18
5 A Mechanical Example......Page 22
6 Probabilities and Chaotic Dynamical Systems......Page 24
7 Bohmian Mechanics and Quantum Equilibrium......Page 26
References......Page 29
2 The Rise of Statistical Mechanics......Page 30
1 Introduction......Page 44
2 The Easy Part......Page 46
Boltzmann\'s Entropy......Page 47
The Relevance of Ergodicity and Mixing......Page 49
Boltzmann\'s Entropy Versus the Gibbs Entropy......Page 52
3 The Hard Part......Page 54
4 Typicality and Explanation......Page 57
References......Page 59
4 Microscopic Time Reversibility and the Boltzmann Equation......Page 60
1 Does Time Have a Direction?......Page 65
2 Some Time-Directed Processes......Page 66
3 The Dynamical Laws......Page 68
4 Probabilities: The Mathematical Model......Page 71
5 Physical Probabilities......Page 73
6 The Common Cause Principle......Page 76
7 Quantum Mechanics......Page 80
8 Conclusion......Page 82
References......Page 85
1 Introduction......Page 87
2 Is the Boltzmann Entropy of the Universe Finite?......Page 88
3 Relativistic Dynamics of Interacting Particle Systems......Page 96
References......Page 103
1.1 Postulates of Quantum Mechanics......Page 105
1.3 Why the \'R\' Operation Is Needed......Page 107
1.5 Postulated Versus Emergent Probability......Page 108
2 Reinterpretations of Quantum Mechanics Assuming It Is Exact......Page 109
2.3 Bohmian Mechanics......Page 110
2.5 Are Interpretations of Quantum Mechanics Falsifiable?......Page 111
3.1 Phenomenological Modifications: Stochastic Models......Page 112
3.2 Fundamental Modifications......Page 114
References......Page 115
1.1 Equations......Page 117
1.2 Frequently Asked Questions......Page 119
2.1 Trajectories......Page 121
2.2 Statistical Mechanics......Page 123
2.3 Statistical Bohmian Mechanics......Page 125
References......Page 132
9 Chance of Reduction as Chance of Spontaneous Localisation......Page 134
1 Introduction......Page 149
3 The Von Neumann Approach......Page 150
4 The Notion of History......Page 151
5 Probability of Histories......Page 152
6 Histories and Logic......Page 153
9 Decoherence......Page 154
10 Small Probabilities......Page 155
References......Page 156
2 Probability in Consistent Histories......Page 157
3 Probability in the Everett Interpretation......Page 159
References......Page 162
1 Introduction......Page 164
2 \'Empirical\' Approach to Statistical Mechanics......Page 166
3 Subquantum H-Theorem......Page 168
4 An Estimate for the Relaxation Timescale......Page 169
5 Numerical Simulations......Page 170
6 Comments on \'Typicality\'......Page 173
7 The Early Universe.Suppression of Relaxation at Early Times......Page 175
8 Residual Disequilibrium Today - Experimental Tests......Page 177
9 Outlook......Page 178
References......Page 179
13 Perspectives on the Dynamical Reduction Program......Page 181
1 Introduction......Page 192
2.1 The Set of Flat,Spacelike Hypersurfaces in Minkowski Space......Page 194
2.2 The Transport Equation......Page 195
2.3 Properties of the Transport Equation......Page 199
3 Continuous Measurement Theory and Stochastic Dynamics in the Hilbert Bundle......Page 202
3.1 Piecewise Deterministic Jump Processes: Direct Photodetection......Page 203
3.2 Generalization to the Case of Several Lindblad Operators......Page 207
References......Page 208
1 Introduction......Page 210
2 Bell-Like Inequalities for the GHZ State......Page 212
3 Analysis of the Innsbruck Experiment......Page 217
References......Page 219
1 Introduction......Page 221
2 Standard Frames for Classical and Quantum Probabilities......Page 222
3 Classical Versus Quantum Events......Page 223
4 Intrinsic Characterization of Classical and Quantum Probabilities......Page 224
5 Operational Probability Theory......Page 226
References......Page 228
1 Introduction......Page 229
2 An Example......Page 230
3 Dynamical Entropy......Page 232
4 Infinite Particle Systems......Page 233
5 Open Questions......Page 234
References......Page 235
1 Introduction......Page 236
2 Transition to Equipartition......Page 237
3 Time-Scales......Page 240
4 Concluding Remarks......Page 242
References......Page 243
2 Einstein\'s Nonconventional Conception of the Photon......Page 245
3 Einstein\'s Interpretation of Planck\'s Formula in Terms of Fluctuations......Page 247
4 A Dynamical Implementation of Einstein\'s Fluctuation Formula......Page 249
Acknowledgment......Page 252
References......Page 253
20 What Interpretation for Probability in Physics?......Page 254
1 The Over-Determination Problem......Page 259
2 Physical Probability and Propensity......Page 261
3 Statistical Stability......Page 264
4 Kolmogorov\'s Theory and the Application Problem......Page 267
References......Page 268
22 Interpreting Probabilties: What\'s Interference Got to Do with It?......Page 270