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.
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accelerated according approximation assumed black hole Boltzmann’s boundary conditions causality characterize classical collapse concept configuration space coordinates correlations corresponding cosmic cosmology decay decoherence defined degrees of freedom density matrix derived described deterministic Einstein energy ensemble entropy entanglement entropy example field theory finite formal Friedmann fundamental global Hamiltonian Hilbert space horizon initial condition interaction interpretation irreversible Kiefer lead light cones macroscopic master equation matter means measurement metric molecules motion Newton’s nonlocal objects observed parameter phase space phenomenological photons Phys physical entropy probability quantization quantum field quantum field theory quantum gravity quantum mechanical quantum theory quasi-classical radiation relevant represent retarded reversal Schrödinger equation Schwarzschild Sect singularity solution spacetime spatial statistical subsystems superposition symmetry tensor thermal thermodynamical arrow three-geometries time-dependent tion trajectories universe variables wave function wave packets Weyl tensor Wheeler–DeWitt equation world lines Zwanzig projection µ-space
Page 6 - ... position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations — then so much the worse for Maxwell's equations. If it is found to be contradicted by observation — well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
Page 6 - A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, it will never be overthrown (for the special attention of those who are skeptics on principle).
Page 6 - The law that entropy always increases — the second law of thermodynamics — holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equation — then so much the worse for Maxwell's equation.
Page 19 - If one accepts the latter point of view, experience requires one to regard the representation by means of the retarded potentials as the only possible one, provided one is inclined to assume that the fact of the irreversibility of radiation processes has to be present in the laws of Nature. Ritz considers the restriction to the form of the retarded potentials as one of the roots of the Second Law, while Einstein believes that the irreversibility is exclusively based on reasons of probability.
Page 19 - Betrachtung wesentlich zu beschränken, betrachtet Ritz diese Beschränkung als eine prinzipiell nicht erlaubte. Stellt man sich auf diesen Standpunkt, so nötigt die Erfahrung dazu, die Darstellung mit Hilfe der retardierten Potentiale als die einzig mögliche zu betrachten, falls man der Ansicht zuneigt, daß die Tatsache der Nichtumkehrbarkeit der Strahlungsvorgänge bereits in den Grundgesetzen ihren Ausdruck zu finden habe.
Page 11 - ... aware of time when we do not distinguish any change (the mind appearing to abide in a single indivisible and undifferentiated state), whereas if we perceive and distinguish changes, then we say that time has elapsed, it is clear that time cannot be disconnected from motion and change. Plainly, then, time is neither identical with movement nor capable of being separated from it.