Probabilities in physics

1 Introduction......Page 1
2 Two Notions of Probability......Page 2
3 Typicality, Scientific Explanations, and Statistical Mechanics......Page 5
4 A Simple Example: The Kac Ring Model......Page 8
5 A Mechanical Example......Page 12
6 Probabilities and Chaotic Dynamical Systems......Page 14
7 Bohmian Mechanics and Quantum Equilibrium......Page 16
References......Page 19
2......Page 20
1 Introduction......Page 34
2 The Easy Part......Page 36
Boltzmann ’s Entropy......Page 37
The Relevance of Ergodicity and Mixing......Page 39
Boltzmann ’s Entropy Versus the Gibbs Entropy......Page 42
3 The Hard Part......Page 44
4 Typicality and Explanation......Page 47
References......Page 49
4......Page 50
1 Does Time Have a Direction?......Page 55
2 Some Time-Directed Processes......Page 56
3 The Dynamical Laws......Page 58
4 Probabilities: The Mathematical Model......Page 61
5 Physical Probabilities......Page 63
6 The Common Cause Principle......Page 66
7 Quantum Mechanics......Page 70
8 Conclusion......Page 72
References......Page 75
1 Introduction......Page 77
2 Is the Boltzmann Entropy of the Universe Finite?......Page 78
3 Relativistic Dynamics of Interacting Particle Systems......Page 86
References......Page 93
1.1 Postulates of Quantum Mechanics......Page 95
1.3 Why the “R” Operation Is Needed......Page 97
1.5 Postulated Versus Emergent Probability......Page 98
2 Reinterpretations of Quantum Mechanics Assuming It Is Exact......Page 99
2.3 Bohmian Mechanics......Page 100
2.5 Are Interpretations of Quantum Mechanics Falsifiable?......Page 101
3.1 Phenomenological Modifications: Stochastic Models......Page 102
3.2 Fundamental Modifications......Page 104
References......Page 105
1.1 Equations......Page 107
1.2 Frequently Asked Questions......Page 109
2.1 Trajectories......Page 111
2.2 Statistical Mechanics......Page 113
2.3 Statistical Bohmian Mechanics......Page 115
References......Page 122
9......Page 124
1 Introduction......Page 139
3 The Von Neumann Approach......Page 140
4 The Notion of History......Page 141
5 Probability of Histories......Page 142
6 Histories and Logic......Page 143
9 Decoherence......Page 144
10 Small Probabilities......Page 145
References......Page 146
2 Probability in Consistent Histories......Page 147
3 Probability in the Everett Interpretation......Page 149
References......Page 152
1 Introduction......Page 154
2 ‘Empirical’ Approach to Statistical Mechanics......Page 156
3 Subquantum H -Theorem......Page 158
4 An Estimate for the Relaxation Timescale......Page 159
5 Numerical Simulations......Page 160
6 Comments on ‘Typicality’......Page 163
7 The Early Universe.Suppression of Relaxation at Early Times......Page 165
8 Residual Disequilibrium Today.Experimental Tests......Page 167
9 Outlook......Page 168
References......Page 169
13......Page 171
1 Introduction......Page 182
2.1 The Set of Flat,Spacelike Hypersurfaces in Minkowski Space......Page 184
2.2 The Transport Equation......Page 185
2.3 Properties of the Transport Equation......Page 189
3 Continuous Measurement Theory and Stochastic Dynamics in the Hilbert Bundle......Page 192
3.1 Piecewise Deterministic Jump Processes: Direct Photodetection......Page 193
3.2 Generalization to the Case of Several Lindblad Operators......Page 197
References......Page 198
1 Introduction......Page 200
2 Bell-Like Inequalities for the GHZ State......Page 202
3 Analysis of the Innsbruck Experiment......Page 207
References......Page 209
1 Introduction......Page 211
2 Standard Frames for Classical and Quantum Probabilities......Page 212
3 Classical Versus Quantum Events......Page 213
4 Intrinsic Characterization of Classical and Quantum Probabilities......Page 214
5 Operational Probability Theory......Page 216
References......Page 218
1 Introduction......Page 219
2 An Example......Page 220
3 Dynamical Entropy......Page 222
4 Infinite Particle Systems......Page 223
5 Open Questions......Page 224
References......Page 225
1 Introduction......Page 226
2 Transition to Equipartition......Page 227
3 Time-Scales......Page 230
4 Concluding Remarks......Page 232
References......Page 233
2 Einstein ’s Nonconventional Conception of the Photon......Page 235
3 Einstein ’s Interpretation of Planck ’s Formula in Terms of Fluctuations......Page 237
4 A Dynamical Implementation of Einstein ’s Fluctuation Formula......Page 239
Acknowledgment......Page 242
References......Page 243
20......Page 244
1 The Over-Determination Problem......Page 249
2 Physical Probability and Propensity......Page 251
3 Statistical Stability......Page 254
4 Kolmogorov ’s Theory and the Application Problem......Page 257
References......Page 258
22......Page 260