## The physical basis of the direction of timeThe physical asymmetry of nature under time reversal is analysed in this essay. The author investigates the most important classes of phenomena that characterize a direction of time: radiation, thermodynamics, quantum phenomena, and the structure of spacetime. Their relations and the search for a cosmological common root of these "arrows of time" and of the traditional concept of causality are discussed. Particular emphasis is placed on quantum indeterminism. It is argued that a common root may be found in the properties of the time-independent wave function of the universe that arises from the quantization of general relativity. This requires that the physical concept of time is reduced to a correlation between physical states, including those characterizing clocks and observers. The description of irreversible phenomena is shown to be fundamentally "observer-related" in a way that can be formalized following Zwanzig. The book is aimed mainly at the student or scientist seeking an overview of the whole issue. Compared to the German version the book has been widely revised and extended. |

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### Contents

Introduction | 1 |

The Physical Concept of Time | 8 |

The Thermodynamical Arrow of Time | 31 |

Copyright | |

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### Common terms and phrases

absorber according approximately assumed assumption big crunch black hole Boltzmann's boundary Chap classical collapse concept of relevance considered constant coordinates correlations corresponding cosmic cosmological cosmological constant defined degrees of freedom density matrix derived described direction discussed in Sect distribution dynamics Einstein electromagnetic energy ensemble entropy Everett example expansion field theory finite formal Friedmann fundamental gravity Hamiltonian Hawking radiation homogeneous horizon hypersurface improbable indeterminism initial conditions interaction interpretation intuitive causality irrelevant irreversible leads light cone Liouville Liouville equation Mach's principle macroscopic master equation matter means measurement metric mini-superspace motion observer orbits parameter particles phase transition phenomenological photons physical potential probability quantization quantum mechanical quantum theory radiation represent result retarded Schrodinger equation Schwarzschild Second Law singularity solution spacetime statistical stofizahlansatz symmetry T-space T-symmetric theorem thermal thermodynamical arrow time-reversed tion universe vacuum value problem vanishing variables wave function wave packets Weyl tensor