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FOUNDATIONS OF SPACE AND TIME ReflectionsonQuantumGravity Afteralmostacentury,thefieldofquantumgravityremainsasdifficultandinspiring asever.Today,itfindsitselfafielddivided,withtwomajorcontendersdominating: stringtheory,theleadingexemplificationofthecovariantquantizationprogram;and loop quantum gravity, the canonical scheme based on Dirac’s constrained Hamil- tonianquantization.However,therearenowanumberofotherinnovativeschemes providingpromisingnewavenues. Encapsulating the latest debates on this topic, this book details the different approaches to understanding the very nature of space and time. It brings together leading researchers in each of these approaches to quantum gravity to explore thesecompetingpossibilitiesinanopenway.Itscomprehensivecoverageexplores all the current approaches to solving the problem of quantum gravity, addressing the strengths and weaknesses of each approach, to give researchers and graduate studentsanup-to-dateviewofthefield. JEFF MURUGAN is a Senior Lecturer in the Department of Mathematics and Applied Mathematics and a member of the Astrophysics, Cosmology & Gravity Center, University of CapeTown. He is interested in all aspects of gravity and is currently working on string theory and connections between gauge theories and gravity. AMANDA WELTMANisaSeniorLecturerintheDepartmentofMathematicsand Applied Mathematics and a member of the Astrophysics, Cosmology & Gravity Center, University of Cape Town. She works in the exciting bridging areas of string cosmology, studying physical ways to test string theory within the context ofcosmology. GEORGE F. R. ELLISisEmeritusProfessorofAppliedMathematicsandHonorary Research Associate in the Mathematics Department, University of Cape Town. He works on general relativity theory, cosmology, complex systems, and the way physicsunderliesthefunctioningofthehumanbrain. Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:07 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:07 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 FOUNDATIONS OF SPACE AND TIME Reflections on Quantum Gravity Editedby JEFF MURUGAN, AMANDA WELTMAN & GEORGE F. R. ELLIS Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:07 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 CAMBRIDGEUNIVERSITYPRESS Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,SãoPaulo,Delhi,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9780521114400 ©CambridgeUniversityPress2012 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithoutthewritten permissionofCambridgeUniversityPress. Firstpublished2012 PrintedintheUnitedKingdomattheUniversityPress,Cambridge AcataloguerecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloguinginPublicationdata Foundationsofspaceandtime:reflectionsonquantumgravity/[editedby]JeffMurugan, AmandaWeltman&GeorgeF.R.Ellis. p. cm. Includesbibliographicalreferencesandindex. ISBN978-0-521-11440-0(hardback) 1. Spaceandtime. 2. Quantumgravity. I. Murugan,Jeff. II. Weltman,Amanda. III. Ellis,GeorgeF.R.(GeorgeFrancisRayner) IV. Title. QC173.59.S65F68 2011 (cid:2) 531.14–dc22 2011000387 ISBN978-0-521-11440-0Hardback CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredtoin thispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis, orwillremain,accurateorappropriate. Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:07 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 Contents Listofcontributors pagexi 1 Theproblemwithquantumgravity 1 jeffmurugan,amandaweltman&georgef.r.ellis 2 Adialogueonthenatureofgravity 8 t.padmanabhan 2.1 Whatisitallabout? 8 2.2 LocalRindlerobserversandentropyflow 12 2.3 Thermodynamicreinterpretationofthefieldequations 17 2.4 Fieldequationsfromanewvariationalprinciple 25 2.5 Comparisonwiththeconventionalperspectiveandfurther comments 35 2.6 Summaryandoutlook 43 References 47 3 Effectivetheoriesandmodificationsofgravity 50 c.p.burgess 3.1 Introduction 50 3.2 Modifyinggravityovershortdistances 52 3.3 Modifyinggravityoverlongdistances 61 3.4 Conclusions 66 References 67 4 Thesmall-scalestructureofspacetime 69 stevencarlip 4.1 Introduction 69 4.2 Spontaneousdimensionalreduction? 70 4.3 Strongcouplingandsmall-scalestructure 77 v Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:20 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 vi Contents 4.4 Spacetimefoam? 80 4.5 Whatnext? 81 References 82 5 Ultravioletdivergencesinsupersymmetrictheories 85 kellogstelle 5.1 Introduction 85 5.2 Algebraicrenormalizationandectoplasm 93 References 103 6 Cosmologicalquantumbilliards 106 axelkleinschmidt&hermannnicolai 6.1 Introduction 106 6.2 Minisuperspacequantization 109 6.3 AutomorphyandtheE Weylgroup 113 10 6.4 Classicalandquantumchaos 116 6.5 Supersymmetry 118 6.6 Outlook 119 References 122 7 ProgressinRNSstringtheoryandpurespinors 125 dimitrypolyakov 7.1 Introduction 125 7.2 BRSTchargesofhigher-orderBRSTcohomologies 135 7.3 PropertiesofQ :cohomologies 136 n 7.4 NewBRSTchargesanddeformedpurespinors 137 7.5 Conclusions 138 References 139 8 Recenttrendsinsuperstringphenomenology 140 massimobianchi 8.1 Foreword 140 8.2 Stringtheory:anotherprimer 141 8.3 Phenomenologicalscenarios 149 8.4 Intersectingvsmagnetizedbranes 153 8.5 UnorientedD-braneinstantons 156 8.6 Outlook 159 References 159 9 Emergentspacetime 164 robertdemellokoch&jeffmurugan 9.1 Introduction 164 9.2 Simplicityofthe 1-BPSsector 166 2 Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:20 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 Contents vii 9.3 Dictionary 167 9.4 Organizingthedegreesoffreedomofamatrixmodel 168 9.5 Gravitons 171 9.6 Strings 172 9.7 Giantgravitons 173 9.8 Newgeometries 175 9.9 Outlook 178 References 180 10 Loopquantumgravity 185 hannosahlmann 10.1 Introduction 185 10.2 Kinematicalsetup 187 10.3 TheHamiltonconstraint 197 10.4 Applications 203 10.5 Outlook 207 References 208 11 Loopquantumgravityandcosmology 211 martinbojowald 11.1 Introduction 211 11.2 Effectivedynamics 214 11.3 Discretedynamics 225 11.4 Consistentdynamics 242 11.5 Consistenteffectivediscretedynamics 247 11.6 Outlook:futuredynamics 251 References 252 12 Themicroscopicdynamicsofquantumspaceasagroupfieldtheory 257 danieleoriti 12.1 Introduction 257 12.2 Dynamicsof2Dquantumspaceasagroupfieldtheory 279 12.3 Towardsagroupfieldtheoryformulationof4Dquantum gravity 293 12.4 Aselectionofresearchdirectionsandrecentresults 302 12.5 Someimportantopenissues 314 12.6 Conclusions 317 References 318 13 Causaldynamicaltriangulationsandthequestforquantumgravity 321 j.ambjørn,j.jurkiewicz&r.loll 13.1 Quantumgravity–takingaconservativestance 321 Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:20 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 viii Contents 13.2 WhatCDTquantumgravityisabout 323 13.3 WhatCDTquantumgravityisnotabout 325 13.4 CDTkeyachievementsI–demonstratingtheneedfor causality 326 13.5 CDTkeyachievementsII–theemergenceof spacetimeasweknowit 330 13.6 CDTkeyachievementsIII–awindowonPlanckiandynamics 332 13.7 Openissuesandoutlook 334 References 335 14 Propertimeisstochastictimein2Dquantumgravity 338 j.ambjørn,r.loll,y.watabiki,w.westra&s.zohren 14.1 Introduction 338 14.2 TheCDTformalism 339 14.3 GeneralizedCDT 343 14.4 Thematrixmodelrepresentation 347 14.5 CDTstringfieldtheory 347 14.6 Thematrixmodel,onceagain 352 14.7 Stochasticquantization 355 14.8 TheextendedHamiltonian 358 References 360 15 Logicistothequantumasgeometryistogravity 363 rafaelsorkin 15.1 Quantumgravityandquantalreality 363 15.2 Historiesandevents(thekinematicinput) 364 15.3 Preclusionandthequantalmeasure(thedynamicalinput) 366 15.4 The3-slitparadoxanditscognates 368 15.5 Freeingthecoevent 371 15.6 Themultiplicativescheme:anexampleofanhomomorphic coevents 374 15.7 Preclusiveseparabilityandthe“measurementproblem” 377 15.8 Openquestionsandfurtherwork 380 15.9 Appendix:Formaldeductionofthe3-slitcontradiction 382 References 383 16 Causalsets:discretenesswithoutsymmetrybreaking 385 joehenson 16.1 Introduction:seeingatomswiththenakedeye 385 16.2 Causalsets 387 16.3 Towardsquantumgravity 395 Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:20 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013 Contents ix 16.4 Consequencesofspacetimediscreteness 401 16.5 Conclusion:backtotheroughground 405 References 407 17 TheBigBang,quantumgravityandblack-holeinformationloss 410 rogerpenrose 17.1 Generalremarks 410 17.2 Theprinciplesofequivalenceandquantumsuperposition 411 17.3 Cosmologyandthe2ndlaw 412 17.4 Twistortheoryandtheregularizationofinfinities 415 References 417 18 Conversationsinstringtheory 419 amandaweltman,jeffmurugan&georgef.r.ellis References 433 Index 435 Downloaded from Cambridge Books Online by IP 132.166.47.205 on Wed Oct 30 09:50:20 WET 2013. http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511920998 Cambridge Books Online © Cambridge University Press, 2013