Towards quantum gravity kowalski glikman

Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.

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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 13 Editor Jerzy Kowalski-Glikman Institute of Theoretical Physics University of Wrocław Pl.MaxaBorna9 50-204 Wrocław, Poland Library of Congress Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Towards quantum gravity : proceedings of the XXXV International Winter School on Theoretical Physics, held in Polancia, Poland, 2 - 11 February 1999 / Jerzy Kowalski-Glikman (ed.). - Berlin ; Heidelberg;NewYork;Barcelona;HongKong;London;Milan; Paris ; Singapore ; Tokyo : Springer, 2000 (Lecturenotesinphysics;Vol.541) ISBN 3-540-66910-8 ISSN 0075-8450 ISBN 3-540-66910-8 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustra- tions, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready by the authors/editor Cover design: design & production,Heidelberg Printed on acid-free paper SPIN: 10720709 55/3144/du-543210 Preface For almost forty years the Institute for Theoretical Physics of the University of Wroclaw has organized winter schools devoted to current problems in theoretical physics. The XXXV International Winter School on Theoretical Physics, “From Cosmology to Quantum Gravity”, was held in Polanica, a little town in south- west Poland, between 2nd and 11th February, 1999. The aim of the school was to gather together world-leading scientists working on the field of quantum gravity, along with a number of post-graduate students and young post-docs and to offer young scientists with diverse backgrounds in astrophysics and particle physics the opportunity to learn about recent developments in gravitational physics. 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. This volume contains a collection of articles based on lectures presented dur- 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 help in organizing the School and preparing its scientific programme. Dobromila Nowak worked very hard, carrying out virtually all administrative duties alone. I would also like to thank the Institute for Theoretical Physics of the Univer- sity of Wroclaw, the University of Wroclaw, the Foundation for Karpacz Winter Schools, and the Polish Committee for Scientific Research (KBN) for their fi- nancial support. Wroc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 Conservative Motivation 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 Combinatorial Descriptions 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 Minkowskian Space-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 the 3 Geon . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 4 Entropy of the 3 Geon? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 5 AdS 3 , the Spinless Nonextremal BTZ Hole, and the 2 Geon . . . . . . . . 195 6 Vacua on the Conformal Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 7 Holography and 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-Scale Physics . . . . . . . . . . . . . . . . . . . . . . 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 Planar Gravitational 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-Camelia 1 Theory Division, CERN, CH-1211, Geneva, Switzerland  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- ventional experiments could rule out the proposed phenomena? Or has there been such a remarkable improvement in experimental techniques and ideas that we are now ca- pable of testing plausible candidate quantum-gravity phenomena? These questions are analysed rather carefully for the recent proposals of tests of space-time fuzziness using modern interferometers and tests of dispersion in the quantum-gravity vacuum using observations of gamma rays from distant astrophysical sources. I also briefly discuss other proposed quantum-gravity experiments, including those exploiting the properties of the neutral-kaon system for tests of quantum-gravity-induced decoherence and those using particle-physics accelerators for tests of models with 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- vide a unified description of gravitation and quantum mechanics. Recently there 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 mechanics in a strong (classical) gravitational environment, initiated by Colella, Overhauser and Werner [10], have reached levels of sophistication [11] such that even gravitationally induced quantum phases due to local tides can be detected. In light of these developments there is now growing (although still understand- ably cautious) hope for data-driven insight into the structure of quantum gravity. 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:  Marie Curie Fellow (permanent address: Dipartimento di Fisica, Universit´a di Roma “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 ideas have improved so much that now tests of plausible quantum-gravity effects are within reach, but it could also be that theorists have had enough time in their hands to come up with scenarios speculative enough to allow testing by conventional experimental techniques. I shall argue that experiments have indeed progressed to the point were some significant quantum-gravity tests are doable. I shall also clarify in which sense the 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- gravity effects are somehow summed together. Some of the theoretical ideas that can be tested experimentally are of course quite speculative (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, which is a “theory addendum” reviewing some of the arguments [12] in support of the idea [13] that the mechanics on which quantum gravity is based might not be exactly the one of ordinary quantum mechanics, since it should accommodate a somewhat different (non-classical) concept of “measuring apparatus” and a somewhat different relationship between “system” and “measuring apparatus”.] 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- rial presented with a completely different strategy. While my lectures in Polanica were sharply divided in a first part on theory and a second part on experiments, 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, which are given in the next two sections. Section 4 reviews the proposal of using 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-gravity induced in vacuo dispersion of electromagnetic radia- tion. In Section6Igivebrief reviews of other quantum-gravity experiments. In Section7Igiveabrief 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 gravity and their possible relation to properties of the space-time foam. Section 9 provides a theory addendum on other works which are in one way or another related to (or relevant for) the content of these [...]... been fully addressed even within the most popular quantum- gravity approaches, i.e critical superstrings and canonical/loop quantum gravity Which role should be played by the Equivalence Principle in quantum gravity? Which version/formulation of the Equivalence Principle should/could hold in quantum gravity? Additional elements for consideration in quantum- gravity models will emerge if the small discrepancy.. .Quantum- gravity phenomenology 3 notes Section 10 gives the mentioned theory addendum concerning ideas on a mechanics for quantum gravity that be not exactly of the type of ordinary quantum mechanics Finally in Section 11 I give some comments on the outlook of quantum- gravity phenomenology, and I also emphasize the fact that, whether or not they turn out to be helpful for quantum gravity, most... of the frequently discussed features of quantum gravity that I mentioned at the beginning of this section: space-time fuzziness, violations of Lorentz invariance, and violations of CPT invariance Other quantum- gravity experiments, which I shall discuss later in these notes, can probe other candidate quantumgravity phenomena, giving additional breadth to quantum- gravity phenomenology Before closing this... in canonical/loop quantum gravity it is necessary to make substantial progress in the analysis of the physical implications of these formalisms Still, in an indirect way the recent results of quantum- gravity phenomenology have already started to have an impact on theory work in these formal quantum gravity approaches The fact that it is becoming clear that (at least a few) quantum- gravity experiments... might expect based on the intuitive quantum- gravity arguments reviewed in Section 2 As mentioned, a quantum- gravity- induced deformation of the dispersion relation for photons would naturally take the form c2 p2 = E 2 [1 + F(E/EQG )], where EQG is an effective quantum- gravity energy scale and F is a modeldependent function of the dimensionless ratio E/EQG In quantum- gravity scenarios in which the Hamiltonian... GRB-based experiments, these experiments (which have the added merit of having started the recent wave of quantum- gravity proposals) also appear to provide significant quantum- gravity tests As mentioned, the effect of quantum- gravity induced decoherence certainly qualifies as a traditional quantum- gravity subject, and the level of sensitivity reached by the neutral-kaon studies is certainly significant... already reached by quantum- gravity phenomenology Another very intuitive measure of the maturity of quantum- gravity phenomenology comes from the studies of in vacuo dispersion proposed in Ref [5] (also see the more recent purely experimental analyses [25,26]) Deformed dispersion relations are a rather natural possibility for quantum gravity For example, they emerge naturally in quantum gravity scenarios... speculative ideas which have somehow surfaced in the quantum- gravity literature? Or can we test even some plausible candidate quantum- gravity phenomena? Before answering these questions it is appropriate to comment on the general expectations we have for quantum gravity It has been realized for some time now that by combining elements of gravitation with elements of quantum mechanics one is led to “interplay... optimism for the outlook of quantumgravity phenomenology which is found in these notes For each of the protons being monitored the probability of decay is extremely small, but there is a significantly large probability that at least one of the many monitored protons decay Quantum- gravity phenomenology 7 on which experiments could give insight into the nature of quantum gravity The hope that these formal... recently proposed quantum- gravity experiment concerns possible violations of CPT invariance This is a rather general prediction of quantumgravity approaches, which for example can be due to elements of nonlocality (locality is one of the hypotheses of the “CPT theorem”) and/or elements of decoherence present in the approach At least some level of non-locality is quite natural for quantum gravity as a theory . Springer, 2000 (Lecturenotesinphysics;Vol.541) ISBN 3-5 4 0-6 691 0-8 ISSN 007 5-8 450 ISBN 3-5 4 0-6 691 0-8 Springer-Verlag Berlin Heidelberg New York This work is. discuss other proposed quantum- gravity experiments, including those exploiting the properties of the neutral-kaon system for tests of quantum- gravity- induced decoherence