Direction of Time

Direction of Time......Page 3
 Preface......Page 5
 Introduction to Time, Its Arrow and the Present Book......Page 6
  Time and Physics......Page 7
  Time, Philosophy, and Psychology......Page 11
  Time, Mathematics and Information Theory......Page 15
  References......Page 18
 Contents......Page 25
 Contributors......Page 27
 List of Participants......Page 29
   1.1.1 Nothing Changes/Everything Changes......Page 31
   1.1.2 Objective Time, Subjective Time......Page 32
   1.1.3 Time\'s Arrow, Time\'s Cycle......Page 33
   1.1.4 Causality and the Two Forms of Time......Page 34
   1.2.1 Reversibility of Motion: Galileo......Page 35
   1.2.2 Reversibility and Irreversibility in the Earth\'s History: Burnet, Hutton, and Lyell......Page 36
   1.2.4 Irreversibility of Biological Evolution: Darwin......Page 37
   2.1.2 Boltzmann, Loschmidt and Zermelo: Time\'s Arrow or Time\'s Cycle?......Page 38
   2.1.3 Order, Disorder, and Information......Page 39
   2.2.2 Irreversibility of Quantum Measurement......Page 40
   2.2.3 Ontic and Epistemic Uncertainties......Page 41
   2.2.4 A Unified Statistical Description of the Quantum World......Page 42
 References......Page 43
Chapter 2: A Simple Model for Decoherence......Page 45
 References......Page 49
Chapter 3: On the Different Aspects of Time in the Fundamental Theories of Physics......Page 50
 1 Classical Physics-Time Without Importance......Page 51
 2 Special Relativity-His Own Time for Everybody......Page 52
 4 Quantum Theory-The Disappearance of Time......Page 53
 5 The Real Structure of Time-The Facts Are Created on the Border Between Classical Physics and Quantum......Page 54
 6 Cosmology-Time Becomes Universal and Receives a Beginning......Page 55
 7 Possible Conclusions......Page 57
 References......Page 58
Chapter 4: Quantum Events and Irreversibility......Page 59
 1 Our Intuitive Outlook on Time......Page 63
  1.1 Physics......Page 64
  1.2 The Eternal Universe......Page 67
  2.1 The Present Moment......Page 68
  2.2 Asymmetry of Time and Free Will......Page 70
 3 Conclusion......Page 75
 References......Page 76
Chapter 6: The Direction of Time in Quantum Mechanics......Page 77
 1 Decoherence and Irreversibility......Page 78
  1.1 The Theory of Irreversible Processes......Page 79
  1.2 The Case of Decoherence......Page 80
  1.3 The General Behavior of Decoherence......Page 81
  1.4 The Direction of Time......Page 82
  1.5 The Logical Direction of Time......Page 83
 References......Page 84
Chapter 7: Two Arrows of Time in Nonlocal Particle Dynamics......Page 85
 References......Page 90
 1 The (Deterministic) Time We Know......Page 91
 2 The (Random) Time We Would Like to Know......Page 98
 References......Page 100
 1 Introduction......Page 102
 2 Time in Different Cultures......Page 103
 3 Time Metaphors......Page 106
 References......Page 111
Chapter 10: The Direction of Time Ensured by Cosmology......Page 112
 1 The Cosmic Arrow of Time......Page 114
 2 The Effects of the Cosmic Time Arrow......Page 116
 References......Page 118
 1 From CPT Invariance Violation and Cosmic Asymmetry to the Fundamental Concept of Entropy......Page 120
  1.1 Arrows of Time and Their Relations......Page 121
  1.2 The Fundamental Principle of Entropy in Thermodynamics Theory......Page 122
  1.3 Irreversibility of Complex Systems......Page 124
  2.1 The Meanings of Symmetry......Page 127
  2.2 Examples of Symmetry Breaking......Page 128
 3 Spontaneous Symmetry Breakdown, Gauge Fields and Particle Physics......Page 132
 4 Some Mathematical Aspects of Bifurcations, Singularities and Universality......Page 137
 5 Brief Remarks on Conservative and Dissipative Systems......Page 138
 6 Some Qualitative and Geometrical Properties of Psychological Time......Page 139
  Further Reading......Page 142
Chapter 12: Is Time Directed?......Page 144
 1 Ontology of Time......Page 146
 3 Statistical Thermodynamics, Part 1......Page 147
 4 Questions......Page 149
 6 Classical Definition......Page 150
 7 Predicted Relative Frequency......Page 151
 8 Axiomatic......Page 152
 9 Property of What?......Page 153
 10 Statistical Thermodynamics, Part Two......Page 154
 12 Predictions......Page 155
 13 Direction of Time?......Page 156
 14 Quantum Mechanics......Page 157
 15 Necessitiy of Classical Concepts......Page 158
 16 Process of Measurement......Page 159
 17 Objectivity......Page 161
 References......Page 162
  1.1 Time and Temporality-Being and Becoming......Page 163
  1.2 The Metaphysics of Time......Page 164
  1.3 Zeno\'s Paradoxes......Page 165
  2.1 Newtonian Space-Time and Time Reversal (Reversal of Motion)......Page 167
  2.2 Arrows of Time......Page 168
  3.1 Special Relativity......Page 169
  3.2 General Relativity......Page 170
 4 Thermodynamics......Page 172
  4.1 The Second Theorem-A Law?......Page 173
  4.2 Maxwell\'s Demon, Entropy and Information......Page 174
  5.1 The Measurement Problem......Page 175
  5.2 Interpretations of QM......Page 177
 6 Conclusion......Page 178
 References......Page 179
 1 Time in Classical and Relativistic Dynamics......Page 182
 2 Time in Quantum Dynamics......Page 184
 3 Time in Thermodynamics......Page 185
 4 Time in Evolutionary Dynamics......Page 186
 5 Time in Computation and Information Dynamics......Page 187
 References......Page 189
Chapter 15: The Philosophical Significance of the Relativistic Conception of Time......Page 190
 1 Introduction......Page 196
  2.1 Near-Death Experiences......Page 197
  2.2 Drug-Induced States......Page 198
  2.3 Mental Psychoses......Page 200
  2.4 Mystical States......Page 203
 3 An Outline of the Algebraic Geometrical Model of Time Dimension......Page 206
 4 Conclusion......Page 209
 References......Page 211
Chapter 17: Where to Put It? The Direction of Time Between Axioms and Supplementary Conditions......Page 212
 1 How to Understand Boltzmann\'s Legacy......Page 214
 2 Hilbert Versus Gödel on General Relativity and Cosmology......Page 217
 References......Page 221
 1 How Old is an Electron?......Page 223
 2 Time as a One-Dimensional Connected Continuum......Page 227
 3 A Non-archimedean Model of Time......Page 229
 4 Time in Classical Physics......Page 230
 5 Reversibility and Homogeneity......Page 236
 7 Time Reversal: Axiomatic Approach......Page 237
 8 Examples......Page 238
 9 Time Reflections in von Neumann Algebras......Page 240
 10 Time Reversibility and Time Reversal Invariance......Page 242
 11 Evolutions......Page 243
 12 Time Reversal in the Schrödinger Representation......Page 244
 14 Antilinear Anti-automorphisms......Page 246
 16 Automorphisms with Anti-invariant States......Page 247
 17 Motivations for the Definition of Time Reversal......Page 248
 18 Time Reflections in Local Algebras......Page 250
 19 The Adjoint and the Time Reversed of a Markov Semigroup......Page 251
 20 Field Algebras......Page 253
 22 rho0-Anti-invariant Gaussian States......Page 254
 References......Page 255
  1.1 The Arrows of Time......Page 257
  1.2 The Aim of This Paper......Page 258
  2.2 Shannon Information and Entropy......Page 259
   2.2.1 Shannon Versus Boltzmann Entropy......Page 260
   2.2.2 A Mathematical Definition of Shannon Entropy......Page 262
  2.3 Information Content......Page 264
  2.4 Algorithmic Information Content......Page 265
  3.1 The Idea of Computable Information Content......Page 266
 4 Information and Dynamics......Page 268
  4.1 Physical Systems......Page 269
  4.3 Gradient-Like Systems......Page 270
  5.1 Szilard......Page 271
  5.4 Bennet......Page 272
 6 Conclusions......Page 273
 References......Page 274
 2 Opposite Arrows......Page 276
  3.1 Solving the Two-Time Boundary Value Problem......Page 278
  3.3 Closed Timelike Curves......Page 282
 4 Causality......Page 283
 References......Page 285
 1 Introduction......Page 287
 2 Retarded and Advanced Fields......Page 288
 3 Cat Maps......Page 289
 4 (Anti-)Causality......Page 290
 5 Cosmology and Gravitation......Page 292
 References......Page 294
 1 Introduction......Page 296
 2 The Thermodynamic Arrow: Causality and Entropy Increase......Page 297
  2.1 Symmetric Behavior of Entropy in the Two-Time Boundary Condition Context......Page 298
  2.2 Symmetric Behavior of Causality in the Two-Time Boundary Condition Context......Page 300
  2.4 Prediction and Retrodiction......Page 301
 3 A Computer......Page 302
 4 Arrow-Like Features in Computer States......Page 303
 5 Conclusions......Page 305
 References......Page 306
 1 Introduction......Page 308
 2 Wet Carpets and Detective Stories......Page 310
 3 Phase Space Volume......Page 311
 4 Quantum Measurement......Page 312
 References......Page 313
Index......Page 314