The structural foundations of quantum gravity

282 Pages·2006·2.428 MB·English

by  Dean Rickles, Steven French, Juha T. Saatsi

THE STRUCTURAL FOUNDATIONS
OF QUANTUM GRAVITY
This page intentionally left blank
The Structural
Foundations of
Quantum Gravity
Editedby
DEAN RICKLES,
STEVEN FRENCH,
and
JUHA SAATSI
CLARENDONPRESS·OXFORD
1
GreatClarendonStreet,Oxford
OxfordUniversityPressisadepartmentoftheUniversityofOxford.
ItfurtherstheUniversity’sobjectiveofexcellenceinresearch,scholarship,
andeducationbypublishingworldwidein
Oxford NewYork
Auckland CapeTown DaresSalaam HongKong Karachi
KualaLumpur Madrid Melbourne MexicoCity Nairobi
NewDelhi Shanghai Taipei Toronto
Withofficesin
Argentina Austria Brazil Chile CzechRepublic France Greece
Guatemala Hungary Italy Japan Poland Portugal Singapore
SouthKorea Switzerland Thailand Turkey Ukraine Vietnam
OxfordisaregisteredtrademarkofOxfordUniversityPress
intheUKandincertainothercountries
PublishedintheUnitedStates
byOxfordUniversityPressInc.,NewYork
TheSeveralContributors2006
Themoralrightsoftheauthorhavebeenasserted
DatabaserightOxfordUniversityPress(maker)
Firstpublished2006
Allrightsreserved.Nopartofthispublicationmaybereproduced,
storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,
withoutthepriorpermissioninwritingofOxfordUniversityPress,
orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriate
reprographicsrightsorganization.Enquiriesconcerningreproduction
outsidethescopeoftheaboveshouldbesenttotheRightsDepartment,
OxfordUniversityPress,attheaddressabove
Youmustnotcirculatethisbookinanyotherbindingorcover
andyoumustimposethesameconditiononanyacquirer
BritishLibraryCataloguinginPublicationData
Dataavailable
LibraryofCongressCataloginginPublicationData
Dataavailable
TypesetbyLaserwordsPrivateLimited,Chennai,India
PrintedinGreatBritain
onacid-freepaperby
BiddlesLtd,King’sLynn,Norfolk
ISBN0–19–926969–6 978–0–19–926969–3
1 3 5 7 9 10 8 6 4 2
Preface
The papers in this collection are concerned with certain foundational aspects of
quantum gravity. We have chosen to group them together under the banner of
‘structuralism’.Thewaysinwhichthevariouspapersfallunderthisbanner,andthe
extenttowhichtheydoso,aresomewhatdiverse.Cao,forexampleviewsquantum
gravity as lending support to a structural realist conception of ontology. Stachel
likewiseadvocates asimilarview,thoughthe two authors’viewsare very dissimilar
intheirdetails.DoratoandPauri’scontribution,anattempttomotivateaposition
theycall‘structuralspacetimerealism’,bearsmanysimilaritiestoStachel’sposition,
thoughtheysteerclearoftherelationalistlabelthatStachelishappytowear.Pooley,
on the other hand, cautions against the pulling of structural realist views from the
formalism(specificallyfromdiffeomorphisminvariance).Insteadhearguesthatthere
is a perfectly reasonable and preferable non-structural interpretation that can be
given;namely,‘sophisticatedsubstantivalism’.Interestingly,bothStachelandPooley
see the developments of quantum gravity (or diffeomorphism-invariant physics in
general)asworkingagainsttheviewknownas‘haecceitism’—namelytheviewthat
therecanbepossibilitiesthatdiffernon-qualitatively(solelyinvirtueofwhichobjects
play which role in the qualitative structure). Stachel interprets this as motivating a
relationalistpositionaccordingtowhichobjects,insofarastheyexistatall,aresimply
conceivedasderivingtheirexistencefromtheirplaceinanetworkofrelations.Such
apositiongivesastructuralcharacterizationofobjects.But,aswementioned,Pooley
interpretsmattersdifferently,arguingthatasubstantivalistpositioncanbedefended
withinananti-haecceitisticmetaphysicstoo.Ricklesarguesthattheontologicalissue
attherootofthesubstantivalism/relationalismdebatecannotbesettledbyquantum
gravity (or diffeomorphism-invariant physics) since an underdetermination takes
hold in these contexts. However, he shows how a structuralist conception of the
observables of these theories can help to avoid a serious problem in the context of
the problems of time and change they face. The chapters by Smolin and Baez in
very different ways argue that a metaphysics of relations is suggested by quantum
gravity.Ourcontentionisthatthiskindofrelationalismiseasilyandbestconstrued
as a variety of structuralism. There is a common core to the views expressed in
these papers, which can be characterized as the stance that relational structures are
of equal or more fundamental ontological status than objects. The present volume
seekstoextendwhathasbeenafruitfuldialoguebetweenphysicistsandphilosophers
working on quantum gravity. Our goal is fairly modest: to suggest a possible,
andfitting,interpretativeandontologicalperspectivefromwhichtoviewquantum
gravityphysics.
Acknowledgements
The following collection of papers began life as a workshop on structural aspects
of quantum gravity held at the biennial PSA meeting in Milwaukee, 2002. The
workshop was organized by Steven French and his two doctoral students Dean
RicklesandJuhaSaatsi.Theparticipantstherewere:JohnBaez,DeanRickles,Juha
Saatsi,LeeSmolin,andJohnStachel.Thepresentvolumeseekstoextendthebasic
themeofthatworkshopwithcontributionsfromtheaforementionedspeakers(Juha
Saatsi excepted) and other physicists and philosophers of physics. We thank the
Philosophy of Science Association for providing us with the forum that sparked
offthis book. Theeditors wouldalso like to thank the Department ofPhilosophy,
UniversityofLeedsforitssupportinprovidingtravelfundstoattendPSA2002,at
whichtheoriginalsymposiumontheStructural FoundationsofQuantumGravity
was presented. In addition, Dean Rickles would like to thank the International
CollaborationonComplexInterventionsandtheDepartmentofPhilosophyatthe
UniversityofCalgaryforsupportduringthefinalstagesofthisbook.
The production team at Oxford University Press were excellent throughout: the
refereesappointedbythepressbolsteredourenthusiasmforthisprojectandhunted
out some blunders; the copy-editor Edwin Pritchard did a superb job resulting in
numerous improvements to the original manuscript; Jenni Craig did a fine job in
helpingtopushthebookthroughtocompletion.
Finally, Steven would like to acknowledge, as always, the support of Dean and
Morgan. Dean wishes to acknowledge Kirsty, Sophie, and Gaia for their patience
andmuchneededgrounding.
DeanRickles,StevenFrench,JuhaSaatsi
Contents
NotesonContributors xi
1. QuantumGravityMeetsStructuralism:InterweavingRelations
intheFoundationsofPhysics 1
DeanRicklesandStevenFrench
1.1 QuantumGravity:Background,Concepts,andMethods 1
1.1.1 TheHoleArgumentandSpacetimeOntology 2
1.1.2 GaugingtheHoleArgument 4
1.1.3 EnterQuantumGravity 7
1.1.4 CategorizingtheManifoldMethods 14
1.1.5 What’sWrongwithBackground-DependentMethods? 16
1.1.6 What’sRightaboutBackground-IndependentMethods? 18
1.1.7 BackgroundIndependenceandStructuralism 20
1.2 StructuralismandStructuralRealism 25
1.2.1 MotivatingStructuralism 25
1.2.2 WhatisStructuralism? 25
1.2.3 …andWhereDoesitComefrom? 26
1.2.4 StructuralRealism 30
2. StructuralRealismandQuantumGravity 40
TianYuCao
2.1 StructuralRealism 41
2.2 PhysicalRealityofSpacetimeandQuantumFields 43
2.3 QuantumGravity 47
3. Structure,Individuality,andQuantumGravity 53
JohnStachel
3.1 WhatisStructuralRealism? 53
3.2 StructureandIndividuality 55
3.3 EffectiveFieldTheoryandAsymptoticQuantization 60
3.4 StringTheory 63
3.5 QuantumGeneralRelativity:SomePreliminaryProblems 65
3.5.1 StatesorProcesses:WhichisPrimary? 65
3.5.2 FormalismandMeasurability 68
3.6 CanonicalQuantization(LoopQuantumGravity) 71
3.7 TheCausalSet(Causet)Approach 75
3.8 WhatStructurestoQuantize? 77
viii Contents
4. Points,Particles,andStructuralRealism 83
OliverPooley
4.1 WhatisStructuralRealism? 84
4.2 Underdetermination 86
4.3 WhatisOnticStructuralRealism? 91
4.4 Objects 94
4.5 SophisticatedSubstantivalism 99
4.6 Stachel’sGeneralizedHoleArgumentforSets 104
4.7 StachelonIdenticalParticles 109
4.8 IdenticalParticlesandIdentityoverTime 114
4.9 TwoMoralsforQuantumGravity 116
5. HolismandStructuralisminClassicalandQuantum
GeneralRelativity 121
MauroDoratoandMassimoPauri
5.1 Introduction:TwoStrandsofPhilosophyofPhysics
thatOughttobeBroughttogether 121
5.2 Many‘Realisms’orOne? 123
5.2.1 What,Exactly,isaPhysicalStructure? 124
5.3 ACaseStudy:TheHolisticandStructuralNature
ofGeneral-RelativisticSpacetimeinaClassofModelsofGR 126
5.3.1 TheHoleArgumentanditsConsequences 126
5.3.2 TheDynamicalIndividuationofPoint-Events 130
5.4 DevelopingHintsfortheQuantumGravityProgramme 140
5.5 StructuralSpacetimeRealism 144
5.5.1 TheNatureofPoint-EventsandOvercoming
theSubstantivalism/RelationismDebate 145
6. TimeandStructureinCanonicalGravity 152
DeanRickles
6.1 Introduction 152
6.2 Constraints,Gauge,andHoles 153
6.2.1 HamiltonianSystems:ConstraintsandGauge 154
6.2.2 ConstraintsandGaugeinGeneralRelativity 157
6.2.3 InterpretingGaugeTheories 159
6.3 WhatistheProblemofTime? 163
6.4 ASnapshotofthePhilosophicalDebate 166
6.4.1 TimeSeriesfromAtoD 167
6.4.2 MaudlinversusEarman 171
6.5 CatalogueofResponses 175
6.5.1 TimefullStratagems 176
6.5.2 TimelessStratagems 179
6.6 EnterStructuralism 188
6.7 Conclusion 191
Contents ix
7. TheCaseforBackgroundIndependence 196
LeeSmolin
7.1 Introduction 196
7.2 ABriefHistoryofRelationalTime 200
7.3 WhatPhysicistsMeanWhenWeTalkaboutRelational
SpaceandTime 203
7.4 GeneralRelativityasaPartlyRelationalTheory 204
7.4.1 TheProblemofTimeandRelatedIssues 207
7.5 RelationalismandtheSearchfortheQuantumTheoryofGravity 209
7.5.1 TheCausalSetTheory 210
7.5.2 LoopQuantumGravity 212
7.5.3 CausalDynamicalTriangulationModels 216
7.5.4 Background-IndependentApproachestoString
andMTheory 217
7.6 RelationalismandReductionism 219
7.6.1 TheChallengeoftheStringTheoryLandscape 223
7.7 ARelationalApproachtotheProblemsofUnification
andDeterminationoftheStandardModelParameters 226
7.8 RelationalismandNaturalSelection 227
7.9 WhatabouttheCosmologicalConstantProblem? 229
7.10TheIssueofExtendingQuantumTheorytoCosmology 230
7.10.1 RelationalApproachestoQuantumCosmology 230
7.10.2 RelationalApproachestoGoingbeyondQuantumTheory 232
7.11Conclusions 233
8. QuantumQuandaries:ACategory-TheoreticPerspective 240
JohnBaez
8.1 Introduction 240
8.2 LessonsfromTopologicalQuantumFieldTheory 244
8.3 The∗-CategoryofHilbertSpaces 249
8.4 TheMonoidalCategoryofHilbertSpaces 254
8.5 Conclusions 261
Index 267
This page intentionally left blank