Foundations of Probability and Physics

Foreword......Page 6
Contents......Page 8
Preface......Page 12
1 Inequalities among numbers......Page 16
2 The Bell inequality......Page 18
3 Implications of the Bell\'s inequalities for the singlet correlations......Page 20
4 Bell on the meaning of Bell\'s inequality......Page 21
5 Critique of Bell\'s \'vital assumption\'......Page 22
6 The role of the counterfactual argument in Bell\'s proof......Page 24
7 Proofs of Bell\'s inequality based on counting arguments......Page 25
8 The quantum probabilistic analysis......Page 27
9 The realism of ballot boxes and the corresponding statistics......Page 29
10 The realism of chameleons and the corresponding statistics......Page 31
11 Bell\'s inequalities and the chamaleon effect......Page 32
12 Physical implausibility of Bell\'s argument......Page 34
13 The role of the single probability space in CHSH\'s proof......Page 35
14 The role of the counterfactual argument in CHSH\'s proof......Page 37
15 Physical difference between the CHSH\'s and the original Bell\'s inequalities......Page 38
References......Page 42
2 The EPRB gedanken experiment......Page 44
3 The \'CHSH\' function......Page 46
4 Strongly objective interpretation......Page 47
5 Weakly objective interpretation......Page 49
6 Conclusion......Page 52
References......Page 53
1 Introduction......Page 54
3 Determination of the phase function......Page 57
4 Validity and range of applicability......Page 58
5 Evolution of a Gaussian Wave Packet......Page 60
6 Operational Issues......Page 61
References......Page 63
1 Introduction......Page 65
2 Ontic and epistemic descriptions......Page 66
3 Breaking Time-Reversal Symmetry: Extrinsic Irreversibility......Page 70
4 Breaking Time-Reversal Symmetry: Intrinsic Irreversibility......Page 75
5 Summary and Open Questions......Page 79
References......Page 82
1 Introduction......Page 86
2 Interpretations of Probability......Page 87
3 The Axioms of Probability......Page 89
4 Probability in Quantum Mechanics......Page 92
5 Conclusions......Page 97
References......Page 98
1 Introduction......Page 100
2 Outcome determination via contextual models......Page 101
3 Unitary ortho- and projective structure......Page 105
4 Representing quantum history theory......Page 106
5 Further discussion......Page 108
References......Page 109
1 Realist and empiricist interpretations of quantum mechanics......Page 110
2 EPR experiments and Bell experiments......Page 111
3 Bell\'s inequality in quantum mechanics......Page 114
4 Bell\'s inequality in stochastic and deterministic hidden-variables theories......Page 119
5 Analogy between thermodynamics and quantum mechanics......Page 122
6 Conclusions......Page 126
References......Page 129
1 Introduction......Page 130
2 The Ginibre ensembles......Page 131
References......Page 134
1 Introduction......Page 136
2 \'Hardyfication\' of Dirichlet series......Page 137
3 Factorization of n......Page 140
4 Applications......Page 142
References......Page 145
1 Introduction......Page 146
2 There is a lot to add to classical equilibrium statistics from our experience with \'Small\' systems:......Page 147
3 Relation of the topology of S(E N) to the Yang-Lee zeros of Z(T u V)......Page 149
4 The regions of positive curvature A1 of s(es ns) correspond to phase transitions of first order......Page 150
6 Macroscopic observables imply the \'EPS-probability\'......Page 151
7 On Einstein\'s objections against the EPS-probability......Page 154
8 Fractal distributions in phase space Second Law......Page 155
9 Conclusion......Page 158
Appendix......Page 159
References......Page 160
1 Introduction......Page 162
2 Formulation......Page 163
3 Wave Functions and Hilbert Space......Page 166
4 Spin......Page 168
5 Traditional Quantum Mechanics......Page 171
6 Concluding Remarks......Page 173
References......Page 175
1 Introduction......Page 176
2 Review of defining a stochastic process and white noise analysis......Page 177
3 Relations to Quantum Dynamics......Page 179
4 Addenda to foundations of the theories. Concluding remarks......Page 182
References......Page 183
1 Introduction......Page 185
2 Classical Nonergodicity and Short-Path Dynamics......Page 186
3 Universal Description of Wave Function Statistics......Page 187
4 Numerical Analyses and Discussions......Page 188
5 Conclusions......Page 190
References......Page 191
1 Introduction......Page 195
2 Quantum formalism and perturbation effects......Page 198
3. Probability transformations connecting preparation procedures......Page 202
3 Hyperbolic and hyper-trigonometric probabilistic transformations......Page 207
5 Hyperbolic quantum formalism......Page 209
6 Physical consequences......Page 213
References......Page 214
1 Introduction......Page 216
2 Analysis of the foundation of probability theory......Page 219
3 General principle of statistical stabilization of relative frequencies......Page 221
4 Probability distribution of a collective......Page 225
5 Model examples of p-adic statistics......Page 226
References......Page 232
1 Introduction......Page 234
2 De Broglie waves as an SED effect......Page 235
3 Schrodinger Equation......Page 238
4 Conclusions......Page 240
1 Introduction......Page 251
2 The Kochen-Specker theorem......Page 253
3 The Kochen-Specker inequality......Page 256
4 Independence......Page 258
5 Conclusions......Page 260
1 Introduction......Page 261
2 Quantum stochastic approach......Page 267
References......Page 270
1 What probability sets o are possible?......Page 272
2 Uniqueness of semigroups of zeros and units.......Page 275
3 Probabilities with hidden parameters......Page 279
4 Probability sets with a single unit.......Page 282
References......Page 287
1 Introduction......Page 289
2 Classical K-System......Page 290
3 Algebraic Quantum K-Systems......Page 291
4 Dynamical Entropy......Page 295
5 Some General Considerations on Abelian Models......Page 302
6 Abelian Models for Algebraic K-Systems......Page 303
7 Continuous K-Systems......Page 308
8 Mixing Properties Without Algebraic K-Property......Page 311
9 Time Evolution......Page 313
References......Page 314
1 Introduction......Page 318
3 Mathematical model......Page 319
4 Reformulated scattering problem......Page 321
5 Solution of the scattering problem......Page 323
References......Page 325
1 Quantum probabilities according to Deutsch......Page 329
2 Schrodinger\'s equation for a free particle as a consequence of position eigenstates......Page 330
3 Driven particle: Weyl equation in general space-time......Page 332
4 Realizing Deutsch\'s \'substitution\' as a time evolution......Page 333
References......Page 335
2 Linguistic Model......Page 336
3 Ensemble Model......Page 338
4 Structural Model......Page 339
5 Certain and Uncertain Structures......Page 342
6 Probability......Page 343
7 Experimental Verification......Page 345
8 Objective and Subjective Probability......Page 347
References......Page 349
1 Introduction......Page 350
2 Kolmogorov Complexity......Page 351
3 Incompressibility......Page 355
4 Reversible Complexity......Page 356
5 Complexity and Information......Page 357
7 Prefix Complexity......Page 359
8 Universal Probability......Page 361
9 Sequentially Coding Algorithms......Page 362
References......Page 364
1 Introduction......Page 365
2 Gaining experimental information......Page 366
3 Efficient representation of probabilistic information......Page 368
4 Predictions......Page 373
5 Discussion......Page 376
References......Page 378
1 Introduction......Page 379
2 Bell\'s Inequality......Page 380
3 Localized Detectors......Page 381
4 Quantum Key Distribution......Page 383
5 Gaussian Wave Functions......Page 384
6 Conclusions......Page 385
References......Page 386
1 Introduction......Page 388
References......Page 392