The Physical Basis of The Direction of Time

238 Pages·1999·6.464 MB·English

by  Professor Dr. H. Dieter Zeh (auth.)

The Physical Basis of
The Direction of Time
Springer-Verlag Berlin Heidelberg GmbH
H. Dieter Zeh
The Physical Basis of
The Direction of Time
Third Edition
With 34 Figures
Springer
Professor Dr. H. Dieter Zeh
Institut fur Theoretische Physik
Universitat Heidelberg
Philosophenweg 19
0-69120 Heidelberg, Germany
ISBN 978-3-540-64865-9
Library of Congress Cataloging-in-Publication Data. Zeh, H. D. (Heinz Dieter), 1932-. The physical basis
of the direction of time I H. Dieter Zeh. - 3rd ed. p. cm. Includes bibliographical references and index.
1. Space and time. 2. Time. 3. Physics-Philosophy. 4. Thermodynamics.
ISBN 978-3-540-64865-9 ISBN 978-3-662-03805-5 (eBook)
DOI 10.1007/978-3-662-03805-5
I. Title. QCI73.59.S65Z38 1999 530.11-dc21 99-14727
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Preface to the Third Edition
This third edition of the Direction of Time offers far more reVISIons and
additions than the second one of 1992. During the seven years that have
elapsed since the latter appeared, several fields of research related to the
arrow of time have shown remarkable progress. For example, in quantum
theory decoherence has proved to be its most ubiquitous manifestation, while
articles on various interpretations of quantum theory (many of them with
inbuilt time-asymmetric dynamical aspects) can and do now regularly appear
in reputed physics journals. Therefore, Chap. 4 has been widely rewritten,
while the second part of Chap. 3 was affected by these changes in order to
prepare for the discussion of measurements and dynamical maps within the
framework of classical ensemble theory.
However, all parts of the book have been revised, and some of them
completely rewritten, while its overall structure could essentially be main
tained. Some of its new aspects may be listed here: The Introduction now
attempts to distinguish rigorously between those time asymmetries which still
preserve dynamical determinism and the various 'irreversibilities' (arrows of
time proper), which are the subject of this book. In Chap. 2, the concept of
forks of causality is contrasted to that of forks of indeterminism (to be used
in Chaps. 3 and 4), while the treatment of the radiation reaction of a moving
charge (Sect.2.3) had to be updated. In Chap. 3, Sects. 3.2-3.4 have been
given a new structure, while a discussion of semigroups and their physical
meaning has been added to Sect. 3.4. In Chap. 4, only Sects. 4.1 and 4.5 (the
former Sect. 4.3) are not entirely new. In particular, there is now an extended
separate Sect. 4.3 on decoherence. Sections 4.4 (on quantum dynamical maps)
and 4.6 (on the time arrow in various interpretations of quantum theory) have
been added. In Chap. 5, the thermodynamics of acceleration is now presented
as a separate Sect. 5.2, while Sect. 5.3 on the expansion of the universe con
tains a discussion of the consistency of cosmic two-time boundary conditions.
The dynamical interpretation of general relativity with its intrinsic concept of
time is discussed in Sect. 5.4. Chapter 6 is now on all aspects of quantum cos
mology, including the former Sect. 5.2.2 (now Sect. 6.1) on phase transitions
of the vacuum. In Sect. 6.2 on quantum gravity, emphasis is on timelessness,
which appears as a consequence of reparametrization invariance upon quanti
zation. There is a new Sect. 6.2.2 on the emergence of classical time along the
lines of the Tomonaga-Schwinger equation, while Sect. 6.2.3 describes some
speculations on the impact of quantum cosmology on the concept of black
VI Preface to the Third Edition
holes and their thermodynamical aspects. A numerical toy model has been
appended after the Epilog in order to illustrate some typical arguments of
statistical mechanics.
I also hope that most of the disadvantages that resulted from the fact
that I had (very unfortunately) translated many parts of the first edition
from the German lecture notes (Zeh 1984) which preceded it have now been
overcome. Two new books on the arrow of time (Price 1996 and Schulman
1997) have recently appeared. They are both excellently written, and they
discuss many important aspects of 'irreversible' physics in a consistent and
illuminating manner - often nicely complementing each other as well as this
book. However, I differ from their views in two respects: I regard gravity
(not least its quantized form) as basic for the arrow of time, as I try to
explain in Chaps. 5 and 6, and I do not think that the problem of quantum
measurements can be solved by means of an appropriate final condition in a
satisfactory way (see Footnote 3 of Chap. 4).
I wish to thank Julian Barbour, Erich Joos, Claus Kiefer, Joachim
Kupsch, York Ramachers, Huw Price, Fritz Rohrlich, Paul Sheldon and Max
Tegmark for their comments on early versions of (parts of) the manuscript.
Heidelberg, April 1999 H.D. Zeh
Preface to the Second Edition
Modern text processing offered the possibility of taking into account recent
results and developments in order to present this new printing as a revised
edition. I have used this opportunity to change many formulations throughout
the book, rewrite several passages, and to add further comments where it
appeared appropriate. This is also reflected by the grown list of references.
Most changes and additions (including four new figures) will be found in
Chap. 6, where research has been most active recently, and (somewhat less)
in Chap. 5 and Sect. 4.2. A conference on 'Physical Origins of the Asymmetry
of Time' (see Halliwell, Perez-Mercador and Zurek 1994) held at Mazagon
(Spain) just before this book goes to the press revealed, however, that there
is little consensus yet among working scientists about the interpretation of
time in quantum gravity (Chap. 6).
I wish to thank all those colleagues who helped me with their critical re
marks to improve the book (as I hope), in particular Paul Busch, Heinz-Dieter
Conradi, Erich Joos, Claus Kiefer, Joachim Kupsch, Don Page, Huw Price,
Larry Schulman, Robert Wald, John Wheeler and Wojciech Zurek. My thanks
go also to Ion Stamatescu, whose regular seminars at the Forschungsstatte der
Evangelischen Studiengemeinschajt (FESt) at Heidelberg provided a platform
for discussions and continuing contact with my former collaborators.
Heidelberg, November 1991 H. D. Zeh
Preface to the First Edition
This book arose from a series of lectures which I gave at the University of
Heidelberg during the summer terms of 1979, 1982 and 1986. They led in
1984 to the publication in German of Die Physik der Zeitrichtung, which
appeared as Vol. 200 of the Springer Lecture Notes in Physics. The present
English version is not merely a translation of these notes, but has been widely
revised and extended. The number of changes and additions roughly increases
with chapter number. Chaps. 5 and 6 have been completely rewritten (except
for Sect. 5.1, which is a revised version of the former § 5.2). The new title is
intended to express the somewhat more ambitious program of this book as
compared to its German predecessor.
My interest in this subject stemmed originally from an attempt to place
the quantum mechanical measurement process in its proper relation to other
irreversible phenomena. It soon became evident that statistical thermody
namics is too limited for the search for the common roots of the obviously
related arrows of time. It is precisely the interconnectedness of many areas of
physics, and not least their relation to some fundamental concepts (or per
haps prejudices) of epistemology, which sustained my fascination with the
subject of this book over many years. Thus it was not my intention to de
scribe technicalities or mathematical problems, but to point out the essential
physical ideas (which are often overlooked). In none of its chapters does the
book predominantly address the specialist of the various fields; in fact it is
aimed mainly at the student or scientist who is interested in an overview of
the whole problem, and who wants to consider his specific field of research in
its relation to others. I also hope that the book may be of some interest to
the philosopher who is familiar with the concepts of theoretical physics.
My first lecture on this subject as a whole was stimulated by Paul
Davies' (1977) book entitled The Physics of Time Asymmetry. However, I
felt that some of its subjects (for example the thermodynamical arrow of
time - Chap. 3 of this book) might deserve a technically more detailed dis
cussion, that the formal relations between the different arrows should be
elaborated upon, and in particular that the peculiar role and importance
of the quantum measurement process should be further analyzed (Chap. 4).
Moreover, our knowledge about the arrow of time that appears in general rel
ativity and cosmology (Chap. 5) has grown enormously since the appearance
of Davies' book, partly due to his own contributions. In addition, attempts
to understand the problem of the quantization of the spacetime metric, and
x Preface to the First Edition
therefore of time itself, have gained considerable momentum during recent
years, and may even turn out to give the whole issue a completely new per
spective (Chap. 6). I thus hope that this book is appearing at an appropriate
time.
Chapter 1 briefly summarizes my understanding of the physical concept
of time. Chap. 2 on the radiation arrow will hardly contain anything that
is not generally accepted, except perhaps for the remark that the Wheeler
Feynman absorber condition has to be supplemented by an asymmetric condi
tion in order to characterize absorbers. Chap. 3 on thermodynamics empha
sizes the fundamental observer-relatedness of the macroscopic description,
which may appear to be in conflict with the objective nature of the ther
modynamical concepts. Chap. 4 on the quantum mechanical arrow may be
greeted controversially, since I have tried - for good reasons - to present
a consistent description that avoids the 'non-concepts' of complementarity
and dualism used in a fundamental way by the Copenhagen interpretation.
Chap. 5 describes the important cosmological aspects of arrows of time and
the relations between the concepts of spacetime geometry and thermodynam
ics that have been discovered during the last two decades as a consequence
of combining general relativity and quantum field theory. Finally, Chap. 6
about the quantization of time combines concepts and results from Chaps. 1,
4 and 5.
I am very much indebted to Dr. Erich Joos for his assistance during
preparation of the original German version, and to Dr. Claus Kiefer, for cor
responding help with the present book. They were both unbelievably patient
in correcting several preliminary versions and suggesting improvements. I also
wish to thank Dr. M. Stockier for his very careful reading of the manuscript.
Ms. Sonja Bartsch and Ms. Beate Witzler helped me very much by typing
an early version for the Macintosh, and Mr. Carl Ulbricht by eliminating
some of the most disturbing Germanisms from it. I am particularly glad to
acknowledge the assistance of Dr. Angela Lahee in editing the (almost) final
version. Mr. K. Mattes performed the translation into TEX.
Heidelberg, February 1989 H. D. Zeh
Contents
Introduction. . . . . . . . . 1
1. The Physical Concept of Time 9
2. The Time Arrow of Radiation 15
2.1 Retarded and Advanced Form
of the Boundary Value Problem . . . . . . 18
2.2 Thermodynamical and Cosmological Properties
of Absorbers . . . . . . . . . 22
2.3 Radiation Damping . . . . . . 26
2.4 The Absorber Theory of Radiation 32
3. The Thermodynamical Arrow of Time 37
3.1 The Derivation of Classical Master Equations 40
3.1.1 f.l-Space Dynamics and Boltzmann's H-Theorem 41
3.1.2 r-Space Dynamics and Gibbs' Entropy 45
3.2 Zwanzig's General Formalism of Master Equations 55
3.3 Thermodynamics and Information. . . . . 66
3.3.1 Thermodynamics Based on Information 66
3.3.2 Information Based on Thermodynamics 71
3.4 Semigroups and the Emergence of Order 75
4. The Quantum Mechanical Arrow of Time . . 83
4.1 The Formal Analogy . . . . . . . . 84
4.1.1 Application of Quantization Rules 84
4.1.2 Master Equations and Quantum Indeterminism 87
4.2 Ensembles or Entanglement 92
4.3 Decoherence . . . . . . 99
4.3.1 Trajectories . . . . 100
4.3.2 Molecular Configurations as Robust States 102
4.3.3 Charge Superselection 104
4.3.4 Fields and Gravity 106
4.3.5 Quantum Jumps . . 108