The March of Time: Evolving Conceptions of Time in the Light of Scientific Discoveries

289 Pages·2013·6.345 MB·English

by  Friedel Weinert (auth.)

Friedel Weinert
The
March of Time
Evolving Conceptions of
Time in the Light
of Scientific Discoveries
The March of Time
Friedel Weinert
The March of Time
Evolving Conceptions of Time
in the Light of Scientific Discoveries
123
FriedelWeinert
Division ofSocial Sciences and Humanities
Universityof Bradford
Bradford
UK
ISBN 978-3-642-35346-8 ISBN 978-3-642-35347-5 (eBook)
DOI 10.1007/978-3-642-35347-5
SpringerHeidelbergNewYorkDordrechtLondon
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(cid:2)Springer-VerlagBerlinHeidelberg2013
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Preface
The present volume originates from lectures and seminars, which I gave at
Victoria University in Wellington (New Zealand), at the University of Bradford
(UK) and at international conferences, organized by the International Society for
theStudyofTime(ISST).Theyareheldevery3yearsandIattendedthemeetings
inMonterey,California(2007),andCostaRica(2010).Thefollowingpagesreflect
my long-standing interest in the philosophy of time, and develop themes, which I
first explored in talks, which I gave at Sydney University, the University of
Western Ontario, and in various published papers on the notion of time.
I benefited from a British Academy Overseas Conference Award (2007) and
from two research fellowships. The first draft of this book was completed at the
Unit for History and Philosophy of Science, University of Sydney, where I was a
visitingfellowfromJunetoSeptember2009.Iwouldliketothankthemembersof
the Department for their hospitality. The final draft of the book took shape at the
Rotman InstituteofPhilosophy, Universityof WesternOntario(Canada), where I
wasaresearchfellowfromMaytoJuly2012.Iwouldliketothankthemembersof
theInstitutefortheirhospitalityandthestimulatingintellectualatmosphere,which
the Institute provides.
I was fortunate to received constructive criticism from several readers. Meir
Hemmo,fromtheUniversityofHaifa,readChap. 3.ClaudioCalosi(Universityof
Urbino) and Roman Frigg (London School of Economics) both read the whole
manuscript.ThankstotheirgenerousandexpertadviceIwasabletoimproveand
clarify the ideas discussed in this book. Finally I must express my gratitude to
Angela Lahee, my editor at Springer Verlag in Heidelberg, for her unwavering
support and her enthusiasm for a book on time.
I hope the reader will enjoy reading the book as much as I enjoyed writing it.
Friedel Weinert
v
Contents
1 Evolving Conceptions of Time in the Light
of Scientific Discoveries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Time and Cosmology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Greek Astronomy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Plato and Aristotle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 The Need for Physical Time . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Saint Augustine (354–430 AD.). . . . . . . . . . . . . . . . . . 13
2.3.2 David Hume (1711–1776) and John Locke
(1632–1704) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Kant’s Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 Time and Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5.1 Immanuel Kant (1724–1804). . . . . . . . . . . . . . . . . . . . 23
2.5.2 Gottfried W. Leibniz (1646–1716). . . . . . . . . . . . . . . . 26
2.6 The Topology of Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6.1 Linearity of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6.2 Closed Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.7 The Metric of Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.8 Some Advances in the Theory of Time in Classical Physics. . . 46
2.8.1 Galileo’s Physical Time . . . . . . . . . . . . . . . . . . . . . . . 46
2.8.2 Newton’s Mathematical Time . . . . . . . . . . . . . . . . . . . 48
2.8.3 Newton and Leibniz, Compared . . . . . . . . . . . . . . . . . 51
2.8.4 The Arrow of Time . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2.8.5 Maxwell’s Demon. . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.9 Time in Modern Physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.9.1 The Measurement of Time in the Special Theory
of Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.9.2 Invariants of Space–Time: Speed of Light . . . . . . . . . . 67
2.9.3 Further Invariants in Space–Time . . . . . . . . . . . . . . . . 69
vii
viii Contents
2.9.4 The Measurement of Time in the General
Theory of Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . 72
2.10 The Measurement of Time in Quantum Mechanics . . . . . . . . . 74
2.11 Why Measurement? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
2.12 On Permissible Inferences from Scientific Theories. . . . . . . . . 84
3 Flux and Stasis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.1 Parmenidean Stasis and Heraclitean Flux . . . . . . . . . . . . . . . . 89
3.2 Idealism About Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.2.1 Saint Augustine (A.D 354–430). . . . . . . . . . . . . . . . . . 91
3.2.2 Immanuel Kant (1724–1804). . . . . . . . . . . . . . . . . . . . 93
3.2.3 John McTaggart (1866–1925) . . . . . . . . . . . . . . . . . . . 97
3.3 Realism About Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
3.3.1 Isaac Barrow (1630–1677) . . . . . . . . . . . . . . . . . . . . . 99
3.3.2 Isaac Newton (1642–1727). . . . . . . . . . . . . . . . . . . . . 101
3.3.3 Newtonian and Neo-Newtonian (Galilean)
Space–Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.4 Relationism About Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.4.1 Relationism According to Leibniz . . . . . . . . . . . . . . . . 112
3.4.2 The Geometry of Situations . . . . . . . . . . . . . . . . . . . . 114
3.4.3 The Order of Succession. . . . . . . . . . . . . . . . . . . . . . . 116
3.4.4 Leibnizian Space–Time . . . . . . . . . . . . . . . . . . . . . . . 118
3.4.5 Possible Orders of Succession and Coexistence. . . . . . . 120
3.5 The Theory of Relativity and the Block Universe . . . . . . . . . . 122
3.5.1 The Time Machine . . . . . . . . . . . . . . . . . . . . . . . . . . 123
3.5.2 Einstein and the Block Universe . . . . . . . . . . . . . . . . . 124
3.5.3 The Block Universe. . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.6 Minkowski Spacetime and the Block Universe . . . . . . . . . . . . 130
3.6.1 Minkowski Space–Time. . . . . . . . . . . . . . . . . . . . . . . 130
3.6.2 The Philosophy of Being . . . . . . . . . . . . . . . . . . . . . . 136
3.7 An Alternative Representation of Minkowski Space–Time . . . . 141
3.7.1 Alfred Arthus Robb’s Account . . . . . . . . . . . . . . . . . . 142
3.7.2 Constantin Carathéodory’s Account. . . . . . . . . . . . . . . 143
3.8 Space–Time and Invariance. . . . . . . . . . . . . . . . . . . . . . . . . . 145
3.8.1 Invariant Relationships c and ds . . . . . . . . . . . . . . . . . 145
3.8.2 Thermodynamic Clocks . . . . . . . . . . . . . . . . . . . . . . . 150
3.8.3 Philosophy of Becoming. . . . . . . . . . . . . . . . . . . . . . . 154
3.9 The General Theory of Relativity . . . . . . . . . . . . . . . . . . . . . 155
3.9.1 Gödel’s Argument for the Unreality of Time . . . . . . . . 160
3.9.2 Thermodynamic and Cosmological Arrows. . . . . . . . . . 162
3.10 Substantivalism and Relationism About Space–Time . . . . . . . . 165
Contents ix
4 Symmetry and Asymmetry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
4.1 Fundamental Equations and Human Experience. . . . . . . . . . . . 169
4.2 Entropy and Order. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
4.3 Reversibility and Irreversibility . . . . . . . . . . . . . . . . . . . . . . . 182
4.4 The Role of Boundary Conditions . . . . . . . . . . . . . . . . . . . . . 186
4.4.1 The Asymmetry of Boundary Conditions . . . . . . . . . . . 189
4.4.2 The Sectional Nature of Time. . . . . . . . . . . . . . . . . . . 193
4.4.3 De Facto and De Jure Irreversibility . . . . . . . . . . . . . . 195
4.4.4 The Law of Conditional Independence. . . . . . . . . . . . . 198
4.4.5 The Switch-Over Problem. . . . . . . . . . . . . . . . . . . . . . 200
4.4.6 The Symmetry of Boundary Conditions . . . . . . . . . . . . 201
4.5 The Emergence of Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
4.6 Time in Basic Quantum Mechanics . . . . . . . . . . . . . . . . . . . . 211
4.6.1 Spin Echo Experiment . . . . . . . . . . . . . . . . . . . . . . . . 219
4.6.2 Quantum Mechanics and Branching Events . . . . . . . . . 221
4.6.3 Consistent Histories and Decoherence . . . . . . . . . . . . . 225
4.6.4 Environmental Decoherence . . . . . . . . . . . . . . . . . . . . 231
4.6.5 Cosmological Decoherence. . . . . . . . . . . . . . . . . . . . . 235
4.7 Time Travel Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
4.7.1 Is it Possible to Travel into the Future? . . . . . . . . . . . . 241
4.7.2 Is it Possible to Travel into the Past?. . . . . . . . . . . . . . 245
4.7.3 Two Coherent Solutions to Time Travelling
into the Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
Bibliography. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Chapter 1
Evolving Conceptions of Time in the Light
of Scientific Discoveries
Theconceptoftimeisperhapsoneofthemostintegratinginhumanknowledge.Itappears
inmanyfields,includingphilosophy,biologyand,mostprominently,inphysics,whereit
plays a central role. It has interested Man of all Ages, and the finest minds from Saint-
Augustine to Kant and Einstein have paid attention to its meaning, and the mystique
shroudingitsmostnotoriousproperty:thatofflowingonlyforward,itsirreversibility.
JoséAngelSánchezAsiain,Forword,inJ.J.Halliwelletal.(1994),xiii.
1.1 Introduction
Our earliest ancestors must have had a dim awareness of time, since their very
existence was heavily dependent on the cycle of seasons. They will have been
aware of the rhythm of day and night and no doubt of lunar cycles. Their pre-
occupation with daily survival and the hunt for food and shelter may not have
granted them much time for thoughts of a more abstract nature but one may
speculate that in quiet moments by the fireside on starry nights they may have
succumbed to reflections about the nature of time. No written records of these
musings exist but cave drawings and large stone structures, like Stonehenge,
testify to the curiosity of our earliest ancestors about the universe. The Greeks,
however, left numerous written documents about their preoccupation with the
cosmos and the nature of time. They demonstrate that time is one of the most
fundamental notions, which is dominant in both human existence and human
endeavours to understand the surrounding world. Many thinkers have grappled
withthenotionoftimeandtheircollectiveeffortshaveproducedsomeinfluential
modelsoftime(Chap.2).Althoughthesephilosophicalmodelsestablishimportant
insights into the notion of time, and are therefore of considerable value as
guidelines of investigation, they cannot be divorced from scientific discoveries
about time (Chaps. 3, 4) so that our evolving conceptions of time have to be
considered in the light of scientific discoveries. New discoveries in cosmology
F.Weinert,TheMarchofTime,DOI:10.1007/978-3-642-35347-5_1, 1
(cid:2)Springer-VerlagBerlinHeidelberg2013
2 1 EvolvingConceptionsofTimeintheLightofScientificDiscoveries
abouttheevolutionoftheuniversehaveledtoradicalnewviewsaboutthenotion
of time. When these ideas are considered and our views of the history of time
reckoning are extended to the present day, three striking features, which will
structure the contents of this book, stand out.
1. Most considerations of time, up to the 21st century establish a link between
time and cosmology (Chap. 2). Cosmology is the study of the large-scale
structure of the universe, to which the Greeks made significant contributions.
The particular cosmological feature, which struck early observers, was the
periodicregularityofplanetarymotions.Asweshallsee,thisfeatureisclearly
present in the views of Plato and Aristotle, as well as Ptolemy. In Greek
cosmologytheuniverseisaclosedsystem.The‘fixedstars’constitutetheouter
boundaryofthecosmosbeyondwhichthedeitiesreside.TheEarthismodeled
as a stationary sphere near the center of the universe, and all the planets and
stars perform circular motions around the ‘central’ Earth. Their preoccupation
with the eternal regularity of celestial motions predestined the Greeks to con-
sider the passage of time and its measurement. Modern cosmology has moved
to different preoccupations, especially to the question of the origin of the
universe and its overall history and its eventual demise. Modern cosmology is
more concerned with the question of the arrow of time at least insofar as this
concerns the observable expansion of the cosmos and the question of its
eventualfate––willtheuniverseexpandforeverorwillitsexpansiongrindtoa
halt and then enter a phase of recontraction? All these processes depend on
certain regularities, which are required for the measurement of the arrow and
the passage oftime.Talkofthe direction or anisotropy of time may thus refer
eithertoanexperienceofaone-directional,forwardmovementofeventsinour
galactic vicinity, which will be characterized as the passage of time; or to the
globalmovementofthe whole universe, pointing like anarrow froman initial
beginning in the Big Bang to its eventual end, either in a contraction of the
universe (Big Crunch) or the complete disappearance of all energy gradients
(HeatDeath).Time, ofcourse,cannot bemeasureddirectly; regular events are
needed to measure time. But the anisotropy of time could conceivably be
experienced in the absence of such regularities. Imagine a universe, in which
only random sounds can be heard or in which occasional light flashes appear
fromdifferentdirections.Ifyouarethe unfortunateinhabitantofsuchalonely
universe, you will be at a loss to establish a regular pattern between the
intervalsofthesoundsorflashes.Youcouldnottellhowlongtheintervalslast
between the flashes and the sounds. Nevertheless, you could count the sounds
and flashes you experience, say up to 100, which would give you a basic
‘before-after’ relationship between the series of observed sounds and flashes.
Hence you could determine the passing of time by the irregular events you
perceive although you would not be able to measure the passage of time. The
measurement of the passage of time requires some regularity, often of a peri-
odickind.Suchaperiodicregularityrequiresregularintervalsbetweenevents,
astheGreeksobservedintheorbitsoftheplanets.However,regularityisnota