The Physical Basis of the Direction of Time

239 Pages·2007·1.895 MB·English

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

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H. Dieter Zeh
THE PHYSICAL BASIS OF
THE DIRECTION
OF TIME
5thedition
With35Figures
123
ProfessorDr.H.DieterZeh
UniversityofHeidelberg,
InstituteofTheoreticalPhysics,
Philosophenweg19,
69120Heidelberg,Germany
email:[email protected]
SeriesEditors:
AvshalomC.Elitzur RüdigerVaas
Bar-IlanUniversity, UniversityofGießen,
UnitofInterdisciplinaryStudies, CenterforPhilosophyandFoundationsofScience
52900Ramat-Gan,Israel 35394Gießen,Germany
email:[email protected] email:[email protected]
MarkP.Silverman H.DieterZeh
DepartmentofPhysics,TrinityCollege, UniversityofHeidelberg,
Hartford,CT06106,USA InstituteofTheoreticalPhysics,
email:[email protected] Philosophenweg19,
69120Heidelberg,Germany
JackTuszynski email:[email protected]
UniversityofAlberta,
DepartmentofPhysics,Edmonton,AB,
T6G2J1,Canada
email:[email protected]
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Preface
Four previous editions of this book were published in 1989, 1992, 1999, and
2001.TheywereprecededbyaGermanversion(Zeh1984)thatwasbasedon
lectures I had given at the University of Heidelberg.
Myinterestinthissubjectaroseoriginallyfromtheendeavortobetterun-
derstand all aspects of irreversibility that might be relevant for the statistical
natureandinterpretationofquantumtheory.Thequantummeasurementpro-
cess is often claimed to represent an ‘amplification’ of microscopic properties
tothemacroscopicscaleincloseanalogytotheoriginofclassicalfluctuations,
whichmayleadtothelocalonsetofaphasetransition,forexample.Thisclaim
can hardly beupheld under theassumption of universal unitary dynamics, as
is well known from the example of Schro¨dinger’s cat. However, the classical
theoryofstatisticalmechanicsoffersmanyproblemsandmisinterpretationsof
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 offered 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 fields and applications have seen considerable
progress since the last edition came out. So, while all chapters have again
been thoroughly revised for this fifth edition in order to take these develop-
ments into account, changes concentrate on Sects.2.3 (Radiation Damping),
4.3 (Decoherence), 4.6 (Interpretations of Quantum Theory), 5.3 (Expansion
oftheUniverse)andChap.6(QuantumCosmology).TherearenewSects.3.5
(on Cosmic Probabilities and History) and 4.3.3 (on Quantum Computers),
while Sect. 5.3 has been subdivided and extended. In general, I have tried
to remove ‘vague’ statements, or to make them more precise – although this
was not always possible because of the complexity or even speculative nature
of some fields. As in previous editions, the focus of the book is on questions
VI Preface
of interpretation and relations between different fields – not on technical for-
malismsandempiricallyunfoundedorpredominantlymathematicalideasand
concepts.
Many friends and colleagues helped me with their advice on various sub-
jects during the preparation of all previous editions. I cannot here repeat all
theirnames(Ihopetheyarealldulymentionedinthecorrespondingprevious
prefaces), but I wish to thank here my former collaborators Erich Joos and
Claus Kiefer for their enduring support to all editions. Special thanks this
timegotoAngelaLaheeforherencouragementtoprepareafifthedition(the
firstonefortheSpringerFrontiersCollection),andtoStephenLyleforediting
it (although he is not responsible for any errors I may have introduced with
numerous last-minute corrections).
Iintendtopostcorrectionsorrevisionstosomesectionsofthebookatmy
websitewww.time-direction.dewheneveritshouldturnouttobeappropriate.
Heidelberg, H.D. Zeh
April 2007
Contents
Introduction................................................... 1
1 The Physical Concept of Time............................. 11
2 The Time Arrow of Radiation ............................. 17
2.1 Retarded and Advanced Form of the Boundary Value Problem 20
2.2 Thermodynamical and Cosmological Properties of Absorbers.. 24
2.3 Radiation Damping...................................... 28
2.4 The Absorber Theory of Radiation ........................ 34
3 The Thermodynamical Arrow of Time..................... 39
3.1 The Derivation of Classical Master Equations ............... 43
3.1.1 µ-Space Dynamics and Boltzmann’s H-Theorem ...... 43
3.1.2 Γ-Space Dynamics and Gibbs’ Entropy .............. 48
3.2 Zwanzig’s General Formalism of Master Equations........... 57
3.3 Thermodynamics and Information ......................... 68
3.3.1 Thermodynamics Based on Information .............. 68
3.3.2 Information Based on Thermodynamics .............. 73
3.4 Semigroups and the Emergence of Order ................... 77
3.5 Cosmic Probabilities and History .......................... 82
4 The Quantum Mechanical Arrow of Time.................. 85
4.1 The Formal Analogy..................................... 86
4.1.1 Application of Quantization Rules ................... 86
4.1.2 Master Equations and Quantum Indeterminism ....... 89
4.2 Ensembles Versus Entanglement........................... 94
4.3 Decoherence ............................................101
4.3.1 Trajectories.......................................103
4.3.2 Molecular Configurations as Robust States ...........106
4.3.3 Quantum Computers ..............................108
4.3.4 Charge Superselection .............................109
VIII Contents
4.3.5 Quasi-Classical Fields and Gravity...................111
4.3.6 Quantum Jumps ..................................113
4.4 Quantum Dynamical Maps ...............................115
4.5 Exponential Decay and ‘Causality’ in Scattering.............119
4.6 The Time Arrow in Various Interpretations
of Quantum Theory .....................................124
5 The Time Arrow of Spacetime Geometry ..................135
5.1 Thermodynamics of Black Holes...........................139
5.2 Thermodynamics of Acceleration ..........................148
5.3 Expansion of the Universe ................................153
5.3.1 Instability of Homogeneity..........................155
5.3.2 Inflation and Causal Regions........................157
5.3.3 Big Crunch and a Reversal of the Arrow .............158
5.4 Geometrodynamics and Intrinsic Time .....................161
6 The Time Arrow in Quantum Cosmology..................171
6.1 Phase Transitions of the Vacuum ..........................175
6.2 Quantum Gravity and the Quantization of Time ............177
6.2.1 Quantization of the Friedmann Universe..............181
6.2.2 The Emergence of Classical Time....................187
6.2.3 Black Holes in Quantum Cosmology .................193
Epilog .........................................................199
Appendix: A Simple Numerical Toy Model ....................203
References.....................................................209
Index..........................................................227
Introduction
TheasymmetryofNatureundera‘reversaloftime’(thatis,areversalofmo-
tion and change) appears only too obvious, as it deeply affects our own form
of existence. If physics is to justify the hypothesis that its laws control ev-
erything that happens in Nature, it should be able to explain (or consistently
describe) this fundamental asymmetry which defines what may be called a
direction in time or even – as will have to be discussed – a direction of time.
Surprisingly, the very laws of Nature are in pronounced contrast to this fun-
damentalasymmetry:theyareessentiallysymmetricundertimereversal.Itis
this discrepancy that defines the enigma of the direction of time, while there
isnolackofasymmetricdynamicalformalismsorpicturesthatgobeyondthe
fundamental empirical laws.
It has indeed proven appropriate to divide the formal dynamical descrip-
tion of Nature into laws and initial conditions. Wigner (1972), in his Nobel
Prize lecture, called this conceptual distinction Newton’s greatest discovery,
since it demonstrates that the laws by themselves are far from determining
Nature. The formulation of these two pieces of the dynamical description re-
quires that appropriate kinematical concepts (formal states or configurations
z, say), which allow the unique mapping (or ‘representation’) of all possible
states of physical systems, have already been defined on empirical grounds.
For example consider the mechanics of N mass points. Each state z is
then equivalent to N points in three-dimensional space, which may be rep-
resented in turn by their 3N coordinates with respect to a certain frame of
reference. States of physical fields are instead described by certain functions
onthree-dimensionalspace.IfthelawsofNaturecontainkinematicalelements
(constraintsonkinematicalconceptsthatwouldotherwisebetoogeneral,such
as divB = 0 in electrodynamics), one should distinguish them from the dy-
namical laws proper. This is only in formal contrast to relativistic spacetime
symmetry (see Sect.5.4).
The laws of Nature, thus refined to their purely dynamical content, de-
scribe the time dependence of physical states, z(t), in a general form – usu-
ally by means of differential equations. They are called deterministic if they