Towards Quantum Gravity: Proceeding of the XXXV International Winter School on Theoretical Physics Held in Polanica, Poland, 2–11 February 1999 PDF
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Towards Quantum Gravity Proceedings of the XXXV International Winter School on Theoretical Physics Held in Polanica, Poland, 2-11 February 1999 1 3 Editor JerzyKowalski-Glikman InstituteofTheoreticalPhysics UniversityofWrocław Pl.MaxaBorna9 50-204Wrocław,Poland LibraryofCongressCataloging-in-PublicationDataappliedfor DieDeutscheBibliothek-CIP-Einheitsaufnahme Towardsquantumgravity:proceedingsoftheXXXVInternational WinterSchoolonTheoreticalPhysics,heldinPolancia,Poland,2 -11February1999/JerzyKowalski-Glikman(ed.).-Berlin; Heidelberg;NewYork;Barcelona;HongKong;London;Milan; Paris;Singapore;Tokyo:Springer,2000 (Lecturenotesinphysics;Vol.541) ISBN3-540-66910-8 ISSN0075-8450 ISBN3-540-66910-8Springer-VerlagBerlinHeidelbergNewYork Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthe materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustra- tions, recitation, broadcasting, reproduction on microfilm or in any other way, and storageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonly undertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrent version,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.Violations areliableforprosecutionundertheGermanCopyrightLaw. ©Springer-VerlagBerlinHeidelberg2000 PrintedinGermany Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. Typesetting:Camera-readybytheauthors/editor Coverdesign:design&production,Heidelberg Printedonacid-freepaper SPIN:10720709 55/3144/du-543210 Preface For almost forty years the Institute for Theoretical Physics of the University of Wroc(cid:23)lawhasorganizedwinterschoolsdevotedtocurrentproblemsintheoretical physics.TheXXXV InternationalWinterSchoolon TheoreticalPhysics,“From Cosmology to Quantum Gravity”, was held in Polanica, a little town in south- westPoland,between2ndand11thFebruary,1999.Theaimoftheschoolwasto gathertogetherworld-leadingscientistsworkingonthefieldofquantumgravity, alongwithanumberofpost-graduatestudentsandyoungpost-docsandtooffer young scientists with diverse backgrounds in astrophysics and particle physics theopportunitytolearnaboutrecentdevelopmentsingravitationalphysics.The lectures covered macroscopic phenomena like relativistic binary star systems, gravitational waves, and black holes; and the quantum aspects, e.g., quantum space-time and the string theory approach. Thisvolumecontainsacollectionofarticlesbasedonlecturespresenteddur- ing the School. They cover a wide spectrum of topics in classical relativity, quantum gravity, black hole physics and string theory. Unfortunately, some of the lecturers were not able to prepare their contributions, and for this reason I decided to entitle this volume “Towards Quantum Gravity”, the title which better reflects its contents. I would like to thank all the lecturers for the excellent lectures they gave and for the unique atmosphere they created during the School. Thanks are due to Professor Jan Willem van Holten and Professor Jerzy Lukierski for their helpinorganizingthe Schoolandpreparingitsscientificprogramme.Dobromila Nowak workedvery hard, carryingout virtually all administrative duties alone. I would also like to thank the Institute for Theoretical Physics of the Univer- sityofWroc(cid:23)law,the UniversityofWrocl(cid:23)aw,theFoundationforKarpaczWinter Schools, and the Polish Committee for Scientific Research (KBN) for their fi- nancial support. Wroc(cid:23)law, November, 1999 Jerzy Kowalski - Glikman Contents Are We at the Dawn of Quantum-Gravity Phenomenology? Giovanni Amelino-Camelia.......................................... 1 1 Introduction.................................................... 1 2 First the Conclusions: What Has This Phenomenology Achieved? ..... 3 3 Addendum to Conclusions: Any Hints to Theorists from Experiments? ............................................. 6 4 Interferometry and Fuzzy Space-Time ............................. 8 5 Gamma-Ray Bursts and In-vacuo Dispersion ....................... 15 6 Other Quantum-Gravity Experiments ............................. 20 7 Classical-Space-Time-Induced Quantum Phases in Matter Interferometry......................................... 24 8 Estimates of Space-Time Fuzziness from Measurability Bounds ....... 25 9 Relations with Other Quantum Gravity Approaches................. 36 10 Quantum Gravity, No Strings Attached............................ 39 11 ConservativeMotivation and Other Closing Remarks ................ 44 Classical and Quantum Physics of Isolated Horizons: A Brief Overview Abhay Ashtekar.................................................... 50 1 Motivation ..................................................... 50 2 Key Issues ..................................................... 52 3 Summary ...................................................... 55 4 Discussion ..................................................... 65 Old and New Processes of Vorton Formation Brandon Carter ................................................... 71 Anti-de Sitter Supersymmetry Bernard de Wit, Ivan Herger ....................................... 79 1 Introduction.................................................... 79 2 Supersymmetry and Anti-de Sitter Space .......................... 80 3 Anti-de Sitter Supersymmetry and Masslike Terms .................. 83 4 The Quadratic Casimir Operator.................................. 85 5 Unitary Representations of the Anti-de Sitter Algebra ............... 87 6 The Oscillator Construction ...................................... 92 7 The Superalgebra OSp(1|4) ...................................... 95 VIII Contents 8 Conclusions .................................................... 98 References ........................................................ 99 Combinatorial Dynamics and Time in Quantum Gravity Stuart Kauffman, Lee Smolin........................................ 101 1 Introduction.................................................... 101 2 CombinatorialDescriptions of Quantum Spacetime.................. 104 3 The Problem of the Classical Limit and its Relationship to Critical Phenomena........................................... 108 4 Is There Quantum Directed Percolation?........................... 111 5 Discrete Superspace and its Structure ............................. 112 6 Some Simple Models ............................................ 114 7 The Classical Limit of the Frozen Models .......................... 115 8 Dynamics Including the Parameters ............................... 116 9 A New Approach to the Problem of Time .......................... 117 Non-commutative Extensions of Classical Theories in Physics Richard Kerner.................................................... 130 1 Deformations of Space-Time and Phase Space Geometries............ 130 2 Why the Coordinates Should not Commute at Planck’s Scale......... 133 3 Non-commutative Differential Geometry ........................... 134 4 Non-commutative Analog of Kaluza-Klein and Gauge Theories ....... 137 5 MinkowskianSpace-Time as a Commutative Limit .................. 142 6 Quantum Spaces and Quantum Groups............................ 149 7 Conclusion ..................................................... 155 References ........................................................ 155 Conceptual Issues in Quantum Cosmology Claus Kiefer ...................................................... 158 1 Introduction.................................................... 158 2 Lessons from Quantum Theory ................................... 159 3 Quantum Cosmology ............................................ 167 4 Emergence of a Classical World................................... 176 5 Acknowledgements .............................................. 184 References ........................................................ 185 Single-Exterior Black Holes Jorma Louko ...................................................... 188 1 Introduction.................................................... 188 2 Kruskal Manifold and the 3 Geon............................... 189 3 Vacua on Kruskal and on tRhPe 3 Geon ........................... 192 4 Entropy of the 3 Geon? ...R.P................................... 194 5 AdS , the SpinlResPs Nonextremal BTZ Hole, and the 2 Geon........ 195 3 RP 6 Vacua on the Conformal Boundaries............................... 198 7 Holographyand String Theory.................................... 200 8 Concluding Remarks ............................................ 201 References ........................................................ 201 Contents IX Dirac-Bergmann Observables for Tetrad Gravity Luca Lusanna ..................................................... 203 Meaning of Noncommutative Geometry and the Planck-Scale Quantum Group Shahn Majid ...................................................... 227 1 Introduction.................................................... 227 2 The Meaning of Noncommutative Geometry........................ 231 3 Fourier Theory ................................................. 242 4 Bicrossproduct Model of Planck-ScalePhysics ...................... 251 5 Deformed Quantum Enveloping Algebras .......................... 260 6 Noncommutative Differential Geometry and Riemannian Manifolds ....................................... 268 References ........................................................ 274 Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance Carlo Rovelli, Marcus Gaul ......................................... 277 1 Introduction.................................................... 277 2 Basic Formalism of Loop Quantum Gravity ........................ 281 3 Quantization of the Area......................................... 300 4 The Physical Contents of Quantum Gravity and the Meaning of Diffeomorphism Invariance ..................... 303 5 Dynamics, True Observables and Spin Foams....................... 311 6 Open Problems and Future Perspectives ........................... 322 Black Holes in String Theory Kostas Skenderis................................................... 325 1 Introduction.................................................... 325 2 String Theory and Dualities ...................................... 329 3 Brane Solutions................................................. 335 4 Black Holes in String Theory ..................................... 341 Gravitational waves and massless particle fields Jan Willem van Holten ............................................. 365 1 PlanarGravitational Waves ...................................... 365 2 Einstein-Scalar Waves ........................................... 368 3 Einstein-Dirac Waves............................................ 370 4 Einstein-Maxwell Waves ......................................... 372 Are We at the Dawn of Quantum-Gravity Phenomenology? Giovanni Amelino-Camelia1 Theory Division, CERN, CH-1211, Geneva, Switzerland(cid:1)(cid:1) Abstract. A handful of recent papers has been devoted to proposals of experiments capable of testing some candidate quantum-gravity phenomena. These lecture notes emphasize those aspects that are most relevant to the questions that inevitably come to mind when one is exposed for the first time to these research developments: How come theory and experiments are finally meeting in spite of all the gloomy forecasts that pervade traditional quantum-gravity reviews? Is this a case of theorists having put forward more and more speculative ideas until a point was reached at which con- ventionalexperimentscouldruleouttheproposedphenomena?Orhastherebeensuch a remarkable improvement in experimental techniques and ideas that we are now ca- pableoftestingplausiblecandidatequantum-gravityphenomena?Thesequestionsare analysedrathercarefullyfortherecentproposalsoftestsofspace-timefuzzinessusing modern interferometers and tests of dispersion in the quantum-gravityvacuum using observations of gamma rays from distant astrophysical sources. I also briefly discuss otherproposedquantum-gravityexperiments,includingthoseexploitingtheproperties oftheneutral-kaonsystemfortestsofquantum-gravity-induceddecoherenceandthose using particle-physics accelerators for tests of modelswith large extra dimensions. 1 Introduction Traditionally the lack of experimental input [1] has been the most important obstacle in the search for “quantum gravity”, the new theory that should pro- videaunifieddescriptionofgravitationandquantummechanics.Recentlythere has been a small, but nonetheless encouraging, number of proposals [2–9] of experiments probing the nature of the interplay between gravitation and quan- tum mechanics. At the same time the “COW-type” experiments on quantum mechanicsinastrong(classical)gravitationalenvironment,initiatedby Colella, OverhauserandWerner [10], have reachedlevelsofsophistication[11] suchthat evengravitationallyinduced quantumphasesduetolocaltidescanbedetected. In light of these developments there is now growing (although still understand- ablycautious)hopefordata-driveninsightintothestructureofquantumgravity. The primary objective of these lecture notes is the one of giving the reader an intuitive idea of how far quantum-gravity phenomenology has come. This is somewhat tricky. Traditionally experimental tests of quantum gravity were believed to be not better than a dream. The fact that now (some) theory and (some) experiments finally “meet” could have two very different explanations: (cid:1)(cid:1) MarieCurieFellow(permanentaddress:DipartimentodiFisica,Universit´adiRoma “La Sapienza”, Piazzale Moro 2, Roma,Italy J. Kowalski-Glikman (Ed.): Proceedings 1999, LNP 541, pp. 1−49, 2000. Springer-Verlag Berlin Heidelberg 2000 2 Giovanni Amelino-Camelia it could be that experimental techniques and ideashave improved so much that nowtestsofplausiblequantum-gravityeffectsarewithinreach,butitcouldalso bethattheoristshavehadenoughtimeintheirhandstocomeupwithscenarios speculative enough to allow testing by conventional experimental techniques. I shall argue that experiments have indeed progressed to the point were some significantquantum-gravitytestsaredoable.Ishallalsoclarifyinwhichsensethe traditional pessimism concerning quantum-gravity experiments was built upon the analysis of a very limited set of experimental ideas, with the significant omission of the possibility (which we now find to be within our capabilities) of experiments set up in such a way that very many of the very small quantum- gravityeffectsaresomehowsummedtogether.Someofthetheoreticalideasthat canbetestedexperimentallyareofcoursequitespeculative(decoherence,space- time foam, large extra dimensions, ...) but this is not so disappointing because it seems reasonable to expect that the new theory should host a large number of new conceptual/structural elements in order to be capable of reconciling the (apparent) incompatibility between gravitation and quantum mechanics. [An example of motivation for very new structures is discussed here in Section 10, whichisa“theoryaddendum”reviewingsomeofthearguments[12]insupportof theidea[13]thatthemechanicsonwhichquantumgravityisbasedmightnotbe exactly the one of ordinary quantum mechanics, since it should accommodate a somewhat different (non-classical) concept of “measuring apparatus” and a somewhatdifferent relationshipbetween “system”and “measuringapparatus”.] The bulk of these notes gives brief reviews of the quantum-gravity experi- ments that can be done. The reader will be asked to forgive the fact that this review is not very balanced. The two proposals in which this author has been involved [5,7] are in fact discussed in greater detail, while for the experiments proposed in Refs. [2–4,8,9] I just give a very brief discussion with emphasis on the most important conceptual ingredients. The students who attended the School might be surprised to find the mate- rialpresentedwithacompletelydifferentstrategy.WhilemylecturesinPolanica weresharplydividedinafirstpartontheoryandasecondpartonexperiments, here some of the theoretical intuition is presented while discussing the experi- ments. It appears to me that this strategy might be better suited for a written presentation. I also thought it might be useful to start with the conclusions, whicharegiveninthenexttwosections.Section4reviewstheproposalofusing modern interferometers to set bounds on space-time fuzziness. In Section 5 I review the proposal of using data on GRBs (gamma-ray bursts) to investigate possible quantum-gravityinduced in vacuo dispersion of electromagnetic radia- tion. In Section 6 I give brief reviews of other quantum-gravity experiments. In Section 7 I give a brief discussion of the mentioned “COW-type” experiments testing quantum mechanics in a strong classical gravity environment. Section 8 provides a “theory addendum” on various scenarios for bounds on the measur- ability of distances in quantum gravityand their possible relation to properties of the space-time foam. Section 9 provides a theory addendum on other works which arein one wayor anotherrelated to (orrelevant for) the content of these
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