Quantum concepts in space and time

QUANTUM CONCEPTS IN SPACE AND TIME......Page 1
Title Page......Page 3
Copyright Page......Page 4
Preface......Page 6
Contents......Page 8
Contributors......Page 10
1.1. The Einstein–Podolsky–Rosen–Bohm thought experiment with photons......Page 12
1.2. Bell\'s theorem......Page 14
1.3. Experiments—generalities......Page 17
1.4. Orsay experiments......Page 18
1.4.1. Experiment with one-channel polarizers (Aspect et al. 1981)......Page 20
1.4.2. Experiment with two-channel polarizers (Aspect et al. 1982b)......Page 21
1.4.3. Experiment with time-varying polarizers (Aspect et al. 1982a)......Page 23
References......Page 25
2.1. Introduction......Page 27
2.2. Linearity versus nonlhiearity......Page 28
2.3. Two-slit diffraction......Page 31
2.4. Two-slit complementarity experiments......Page 35
References......Page 37
3.1. Introduction......Page 39
3.2. Where to look for macroscopic superpositions......Page 40
3.3. Macroscopic quantum tunnelling and coherence......Page 45
3.4. The watched-pot effect: experimental feasibility......Page 47
3.5. Conclusion......Page 50
References......Page 51
4.1. Introduction......Page 52
4.2. Non-local phenomena of the first type......Page 55
4.3. Dynamical considerations......Page 57
4.3.1. Example: Scattering by electric flux lines......Page 60
4.3.2. Non-local phenomena of the second type......Page 62
4.3.3. Semi-classical considerations......Page 64
4.4. Conclusion......Page 66
References......Page 67
5.1. Introduction......Page 68
5.2. Gravitationally coupled electromagnetic fields and quantum interference......Page 69
5.3. Thermoelectric–gravitational effects......Page 72
5.4. Quantum gravimeters......Page 73
References......Page 75
6.1. Introduction......Page 76
6.2. Decay in quantum mechanics......Page 77
6.3. Continuous observation......Page 80
6.4. The decay process......Page 82
6.5. The observing apparatus......Page 84
6.6. Continuous projection postulates......Page 86
6.7. The paradox score......Page 89
6.8. Reasons to be exponential......Page 90
6.9. The ensemble interpretation......Page 91
References......Page 93
7.1. State vector reduction in quantum theory......Page 95
7.3. Properties of a dynamical reduction theory......Page 96
7.4. Equivalent statements of the Reduction and Fundamental properties......Page 98
7.6. Experimental tests of the Constant Mean hypothesis......Page 99
7.7. Superluminal communication......Page 101
7.8. The gambler\'s ruin game......Page 104
7.9. The diffusion equation......Page 105
7.10. Reduction time......Page 107
7.11. Stochastic differential equations......Page 108
7.12. Stratonovich and Itô modelling......Page 110
7.13. Nonlinear Schrödinger equation......Page 111
7.14. The Schrödinger difference equation......Page 112
7.15. Brownian motion analogy......Page 113
7.17. Damped Schrödinger equation......Page 115
7.18. Concluding remarks......Page 117
References......Page 118
8.1. The problem of the superposition principle......Page 120
8.2. The possible role of gravity......Page 122
8.3. The imprecision in space–time structure......Page 124
8.4. Wave propagation......Page 130
8.5. Microscopic and macroscopic behaviour......Page 132
8.6. Possible experiments......Page 136
8.7. Conclusion......Page 137
References......Page 139
9.1. Quantum theory and objective reality......Page 140
9.2. Singularities and the Second Law......Page 145
9.3. Gravitational entropy and reduction......Page 152
References......Page 156
10.1. Introduction......Page 158
10.2. Review of the theory of Brownian motion......Page 163
10.3. Nelson\'s derivation of quantum mechanics as a Brownian motion process......Page 166
10.4. Testability of Nelson\'s assumptions......Page 168
10.5. Stochastic mechanics in a background gravitational field......Page 170
10.6. A non-local hidden variable theory......Page 174
References......Page 183
11.1. Introduction......Page 185
11.2. Configuration entropy......Page 186
11.3. The problem of the undetermined potential......Page 188
11.4. Nonlinearities in the Schrödinger equation......Page 189
11.5. Fluctuations......Page 190
References......Page 191
12.1. Prospective......Page 193
12.2. Some features of the quantum-mechanical world-view......Page 194
12.3. Bell\'s theorem and local hidden variables theories......Page 197
12.4. Aspects of non-locality......Page 202
12.5. Nonlinearity and the actualization of potentialities......Page 207
12.6. Conclusions......Page 210
Appendix: the Everett interpretation......Page 212
References......Page 214
Frank J. Tipler......Page 215
References......Page 225
David Deutsch......Page 226
14.2. Experiment 2: quantum parallelism......Page 227
14.3. Experiment 3: the quantum observer......Page 231
14.5. Discussion......Page 234
References......Page 236
15.1. Introduction......Page 237
15.2. Probabilities and two-sided diagrams......Page 238
15.3. Transition probabilities on scri......Page 241
References......Page 245
16.1. Introduction......Page 247
16.3. Gauge-invariant dynamics......Page 248
16.4. Two different concepts of motion......Page 250
16.5. General relativity as a generalization of gauge-invariant dynamics......Page 251
16.6. Quantum mechanics and general relativity......Page 253
16.7. The Hamiltonian constraints of general relativity......Page 254
References......Page 257
17.1. Introduction......Page 258
17.2. Quantum set theory......Page 259
17.3. Quantum gravity......Page 260
17.4. Quantum dynamics......Page 261
17.6. Third relativity......Page 263
Acknowledgement......Page 265
Y. Aharonov and M. Schwartz......Page 266
References......Page 270
19.1. Introduction......Page 271
19.2. Program Universe 2......Page 272
19.3. Labels and quantum number conservation......Page 275
19.4. Reconstruction of relativistic quantum mechanics......Page 277
19.5. Understanding the mass scale and mass unit......Page 280
19.6. Sununary......Page 281
References......Page 283
Don N. Page......Page 285
Acknowledgements......Page 295
References......Page 296
P. Hajicek......Page 297
References......Page 302
Robert M. Wald......Page 304
References......Page 312
23.1. Introduction......Page 313
23.2.1. Preliminaries......Page 316
23.2.2. An enlarged phase space for GR......Page 319
23.2.3. Choice of polarization/representation......Page 321
23.3. Discussion......Page 325
References......Page 327
24.1. Introduction......Page 329
24.3. Classical thermal properties......Page 330
24.4. (Scalar) quantum theory......Page 331
24.4. Four dimensions......Page 332
24.5. Normalization and renormalization......Page 333
References......Page 335
25.2. Representation of \'in–in\' expectation values......Page 336
25.3. Alternative representation......Page 338
25.4. Equation for small disturbances. Mode functions......Page 339
25.5. Retarded and advanced Green\'s functions......Page 340
25.6. Variational law and superdeterminants......Page 341
25.7 Feynman propagator analogue......Page 342
25.8. The effective action and the effective field equations......Page 343
25.9. Reality, causality, and the role of the measure......Page 344
25.10. The role of the heat kernel......Page 345
References......Page 347
Tsou Sheung Tsun......Page 348
References......Page 351
27.1. Introduction......Page 352
27.2. Hamiltonian formulation, quantum states and operators......Page 353
27.3. The quantum constraints......Page 355
27.4. The quantum amplitude......Page 357
27.5. Divergences in the quantum amplitude in the presence of boundaries......Page 360
References......Page 361
Index......Page 362