Towards Quantum Gravity: Proceeding of the XXXV International Winter School on Theoretical Physics Held in Polanica, Poland, 2–11 February 1999

384 Pages·2000·2.041 MB·English

by  Giovanni Amelino-Camelia (auth.), Jerzy Kowalski-Glikman (eds.)

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Jerzy Kowalski-Glikman (Ed.)
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
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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)
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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