The Physical Basis of The Direction of Time (The Frontiers ...

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Index 229 forward determinism, 66, 79–81 free will, 8, 15, 66 Friedmann cosmology, 153–155, 166, 167, 169, 170, 181, 186, 189, 191, 195 multipole expansion of, 154, 167 FRW metric, 153, 161 Γ -space, 44, 48, 52, 57, 59 Gödel’s theorem, 72 graceful exit problem, 168 Green’s function, retarded, 20, 25, 64, 120 H-functional, 46, 51 H-theorem, 46 Hamiltonian constraint, 111, 165, 166, 179, 180 Hawking radiation, 138, 144, 145, 148, 152 heat capacity, negative, 5, 135 heat death, 39, 41 historical nature, 7, 23, 40, 66 history apparent, 104, 113, 193 consistent, 128, 160 decoherent, 124 horizon problem, 157 human knowledge, 85, 201 hyperbolic equation, 20, 23, 24, 138, 182, 183, 188, 191 ideal gas, monatomic, 47, 136 indeterminism apparent, 202 local, 56 macroscopic, 56, 72, 73 symmetric, 81 inflation, 144, 157–159, 167 information capacity, see entropy capacity information loss paradox, 147, 195 ink drop analogy, 53, 55 invariant rate of radiation, 30, 32 irreversibility, 4, 19, 40, 42, 43, 46, 56, 79, 80, 85, 125, 130, 145, 188, 201 logical, 76 Itô process, 118 Jacobi principle, 12, 164, 165 K-system, 55 Kaltgeburt, 41, 137 Kerr–Newman solution, 143, 145 Klein’s lemma, 88 Kramers–Moyal expansion, 66 Kretzschmann invariance, 13 Kruskal (Szekeres) metric, 140, 141, 143, 144, 149, 169, 170 LAD equation, 32–34, 65, 66, 78 Langevin equation, 66, 124, 129, 180, 204 law-like, 4, 28, 42, 81, 119 arrow of time, 132, 133 laws of Nature, 1, 2, 4, 6, 17, 19 Leibniz relativity, 13, 165 light cone structure, 2, 14, 15, 20, 22, 29, 30, 32, 34, 35, 140, 141, 150, 152, 157, 162, 197 Liouville equation, 20, 51, 52, 60, 61, 66, 86, 94, 101 operator, 52, 63, 85 theorem, 51 locality, 59–61, 67, 97, 101, 103 locality of observer, 61, 101, 128, 132, 144, 149, 177, 193, 202 Lyapunov exponent, 106 Mach’s principle, 13, 16, 163, 165 Markovian dynamics, 62–65, 89 master arrow, 6, 9, 27, 156, 158, 177 master equation, 42–68, 78, 80, 83, 88–93, 99, 101, 104, 105, 107, 116, 119, 120, 124, 128, 129, 134, 192, 203, 204 Maxwell demon, 8, 73, 77, 85, 130 distribution, 47, 50, 69, 101 memory, 5, 7, 13, 74, 76, 77, 83, 107, 174, 202 mini-superspace, 168, 183, 191 mirror, accelerated, 152, 153 mixture, improper, see ensemble, apparent momentum constraints, 165, 169, 180, 188 µ-space, 43–48, 50, 57, 62
230 Index negentropy, 68, 75, 130, 137 neutron star, 137 no-hair conjecture, cosmological, 157 no-hair theorem, 143, 196 nonlocality, 16, 18, 34, 80, 86, 96, 97, 105, 115, 128, 143, 148, 152, 176, 191, 202 observer-relatedness, 54, 68, 202 occupation number representation, 49, 78, 93, 203 Olbers’ paradox, 26, 27 opposite arrows of time, 57, 196 overdetermination, 18, 56, 66, 83 partition function, 50, 93 path integral, 99, 105, 106 Pauli equation, 54, 88, 90–92 Penrose mechanism, 145 perpetuum mobile of second kind, 73, 75, 130 phase space cell, 44, 53, 159 phase transition of vacuum, 154, 157, 158, 175, 176 Poincaré time, 42, 43, 55, 57, 63, 203, 204 positivity, 116 postselection, 126 pre-master equation, 63, 89 prediction, 83, 126, 146 preparation, 8, 40, 48, 122 present, subjective, 11, 13, 14, 200 probability conservation, 51, 87 interpretation, 5, 8, 82, 85, 92, 95, 100, 113, 128, 134, 180 psycho-physical parallelism, 130, 132, 200, 202 quantization rules, 85–94 quantum Brownian motion, 104 computer, 108 jump, 20, 92, 113–114, 123, 124 measurement, 8, 100, 126 ideal, 99 non-demolition, 99 Zeno effect, 62, 106, 107 quasi-classical, 16, 102, 103, 106, 107, 111, 112, 117, 128, 131, 132, 160, 173, 174, 178, 180, 182, 187–189, 195–197 quasi-stochastic, 102, 187 qubit, 108 radiation reaction, 31–33, 36–38, 122, 150 recoherence, 103, 134, 159, 160, 192, 196 recurrence objection, 15, 42 redundancy, 66, 108, 176, 181 relaxation time, 62–65, 103, 203, 204 relevance concept, see Zwanzig projection reparametrization invariance, 163–165, 168, 187 reset, 74–77, 80, 126 retardation, 7, 16–38, 60, 65, 121, 126, 155, 202 retrodiction, 40 reversibility objection, 41, 42 Rindler coordinates, 31, 149–151 Rindler particles, 151, 152 Rindler vacuum, see Rindler particles Ritz’s retarded electrodynamics, 18–20, 24, 28, 34, 42, 119, 138 robust, 51, 55, 56, 71, 74, 77, 82, 83, 89, 106–108, 111, 124, 132, 133, 174, 175, 185 Schmidt canonical representation, 97, 99, 133, 152 Schott term, 33 Schwarzschild solution, 139–143, 145, 150, 169, 194–196 Second Law, 5–7, 19, 25, 39, 41, 56, 60, 67, 73, 75, 77, 136, 143, 146, 155, 159 Unified, 146 self-acceleration, 33 self-organization, see evolution, biological semigroup, 66, 77, 79–81, 104 singularity, naked, 142 Sommerfeld radiation condition, 23, 60 spin wave, 57 statistical operator, see density operator
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the frontiers collection
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H. Dieter Zeh THE PHYSICAL BASIS OF
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Preface Four previous editions of t
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Contents Introduction .............
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Introduction The asymmetry of Natur
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Introduction 3 tion of time (thus a
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Introduction 5 1. Radiation. In mos
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Introduction 7 language is loaded w
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Introduction 9 between temporal and
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12 1 The Physical Concept of Time i
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14 1 The Physical Concept of Time r
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16 1 The Physical Concept of Time a
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18 2 The Time Arrow of Radiation Th
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20 2 The Time Arrow of Radiation by
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22 2 The Time Arrow of Radiation t
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24 2 The Time Arrow of Radiation or
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26 2 The Time Arrow of Radiation wa
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28 2 The Time Arrow of Radiation th
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30 2 The Time Arrow of Radiation m
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32 2 The Time Arrow of Radiation v
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34 2 The Time Arrow of Radiation wh
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36 2 The Time Arrow of Radiation th
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38 2 The Time Arrow of Radiation 'i
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40 3 The Thermodynamical Arrow of T
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86 4 The Quantum Mechanical Arrow o
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100 4 The Quantum Mechanical Arrow
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136 5 The Time Arrow of Spacetime G
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172 6 The Time Arrow in Quantum Cos
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Page 208 and 209: Epilog 201 The role of time is very
Page 210 and 211: Appendix: A Simple Numerical Toy Mo
Page 212 and 213: Notebook: A Toy Model Appendix: A S
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Page 216 and 217: References References marked with (
Page 218 and 219: References 211 Bläsi, B., and Hard
Page 220 and 221: References 213 Davies, P.C.W., and
Page 222 and 223: References 215 Gerlach, U.H. (1988)
Page 224 and 225: References 217 Horwich, P. (1987):
Page 226 and 227: References 219 Levine, H., Moniz, E
Page 228 and 229: References 221 Pearle, Ph. (1976):
Page 230 and 231: References 223 Smoluchowski, M. Rit
Page 232 and 233: References 225 Zeh, H.D. (1971): On
Page 234 and 235: Index absorber, 18, 24-28, 36-38, 5
Page 238 and 239: Index 231 stochastic process, see d
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