The physical basis of the direction of time

Four previous editions of this book were published in 1989, 1992, 1999, and 2001. They were preceded by a German version (Zeh 1984) that was based on lectures I had given at the University of Heidelberg. My interest in this subject arose originally from the endeavor to better - derstand all aspects of irreversibility that might be relevant for the statistical natureandinterpretationofquantumtheory. Thequantummeasurementp- cess is often claimed to represent an 'ampli?cation' of microscopic properties to the macroscopic scale in close analogy to the origin of classical ?uctuations, whichmayleadtothelocalonsetofaphasetransition,forexample. Thisclaim can hardly be upheld under the assumption of universal unitary dynamics, as is well known from the example of Schr¨ odinger's cat. However, the classical theoryofstatisticalmechanicso?ersmanyproblemsandmisinterpretationsof its own, which are in turn related to the oft-debated retardation of radiation, irreversible black holes with their thermodynamical aspects, and - last but not least - the expansion of the Universe. So the subject o?ered a great and exciting 'interdisciplinary' challenge. My interest was also stimulated by Paul Davies' (1977) book that I used successfully for my early lectures. Quantum gravity, that for consistency has to be taken into account in cosmology, even requires a complete revision of the concept of time, which leads to entirely novel and fundamental questions of interpretation (Sect. 6. 2). Many of these interesting ?elds and applications have seen considerable progress since the last edition came out.

Author Notes

H. Dieter Zeh studied physics in Brunswick and Heidelberg, where he began work on theoretical nuclear physics. After a year of research at the California Institute of Technology, he moved to the University of California in San Diego to work on the synthesis of the heavy elements, before returning to the University of Heidelberg, where he later became professor of theoretical physics. His studies of collective motion in nuclei led him to address the quantum-to-classical transition in general, and in particular the quantum measurement problem, which is in turn related to many aspects of irreversibility (arrows of time). During this work, Zeh recognized and formulated the universal and unavoidable role of uncontrollable quantum entanglement, thus becoming a founder of the area now known as decoherence.

Introduction	p. 1
1 The Physical Concept of Time	p. 11
2 The Time Arrow of Radiation	p. 17
2.1 Retarded and Advanced Form of the Boundary Value Problem	p. 20
2.2 Thermodynamical and Cosmological Properties of Absorbers	p. 24
2.3 Radiation Damping	p. 28
2.4 The Absorber Theory of Radiation	p. 34
3 The Thermodynamical Arrow of Time	p. 39
3.1 The Derivation of Classical Master Equations	p. 43
3.1.1 ¿-Space Dynamics and Boltzmann's H-Theorem	p. 43
3.1.2 ¿-Space Dynamics and Gibbs' Entropy	p. 48
3.2 Zwanzig's General Formalism of Master Equations	p. 57
3.3 Thermodynamics and Information	p. 68
3.3.1 Thermodynamics Based on Information	p. 68
3.3.2 Information Based on Thermodynamics	p. 73
3.4 Semigroups and the Emergence of Order	p. 77
3.5 Cosmic Probabilities and History	p. 82
4 The Quantum Mechanical Arrow of Time	p. 85
4.1 The Formal Analogy	p. 86
4.1.1 Application of Quantization Rules	p. 86
4.1.2 Master Equations and Quantum Indeterminism	p. 89
4.2 Ensembles Versus Entanglement	p. 94
4.3 Decoherence	p. 101
4.3.1 Trajectories	p. 103
4.3.2 Molecular Configurations as Robust States	p. 106
4.3.3 Quantum Computers	p. 108
4.3.4 Charge Superselection	p. 109
4.3.5 Quasi-Classical Fields and Gravity	p. 111
4.3.6 Quantum Jumps	p. 113
4.4 Quantum Dynamical Maps	p. 115
4.5 Exponential Decay and `Causality' in Scattering	p. 119
4.6 The Time Arrow in Various Interpretations of Quantum Theory	p. 124
5 The Time Arrow of Spacetime Geometry	p. 135
5.1 Thermodynamics of Black Holes	p. 139
5.2 Thermodynamics of Acceleration	p. 148
5.3 Expansion of the Universe	p. 153
5.3.1 Instability of Homogeneity	p. 155
5.3.2 Inflation and Causal Regions	p. 157
5.3.3 Big Crunch and a Reversal of the Arrow	p. 158
5.4 Geometrodynamics and Intrinsic Time	p. 161
6 The Time Arrow in Quantum Cosmology	p. 171
6.1 Phase Transitions of the Vacuum	p. 175
6.2 Quantum Gravity and the Quantization of Time	p. 177
6.2.1 Quantization of the Friedmann Universe	p. 181
6.2.2 The Emergence of Classical Time	p. 187
6.2.3 Black Holes in Quantum Cosmology	p. 193
Epilog	p. 199
Appendix: A Simple Numerical Toy Model	p. 203
References	p. 209
Index	p. 227

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents