Approachesto Quantum Gravi ty By Dani eleOri ti This page intentionally left blank www.com APPROACHES TO QUANTUM GRAVITY Toward a New Understanding of Space, Time and Matter The theory of quantum gravity promises a revolutionary new understanding of gravity and spacetime, valid from microscopic to cosmological distances. Research in this field involves an exciting blend of rigorous mathematics and bold speculations, foundational questions and technical issues. Containing contributions from leading researchers in this field, this book presents the fundamental issues involved in the construction of a quantum theory of gravity and building up a quantum picture of space and time. It introduces the most current approaches to this problem, and reviews their main achievements.
Each part ends in questions and answers, in which the contributors explore the merits and problems of the various approaches. This book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers. D A N I E L E O R I T I is a Researcher at the Max Planck Institute for Gravitational Physics, Potsdam, Germany, working on non-perturbative quantum gravity. He has previously worked at the Perimeter Institute for Theoretical Physics, Canada; the Institute for Theoretical Physics at Utrecht University, The Netherlands; and the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK.
He is well known for his results on spin foam models, and is among the leading researchers in the group field theory approach to quantum gravity.com APPROACHES TO QUANTUM GRAVITY Toward a New Understanding of Space, Time and Matter Edited by DANIELE ORITI Max Planck Institute for Gravitational Physics, Potsdam, Germany www.com CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.org Information on this title: www.org/9780521860451 © Cambridge University Press 2009 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2009 ISBN-13 978-0-511-51640-5 eBook (EBL) ISBN-13 978-0-521-86045-1 hardback Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.com A Sandra www.com Contents List of contributors page x Preface xv Part I Fundamental ideas and general formalisms 1 1 Unfinished revolution 3 C. Rovelli 2 The fundamental nature of space and time 13 G.
’t Hooft 3 Does locality fail at intermediate length scales? 26 R. Sorkin 4 Prolegomena to any future Quantum Gravity 44 J. Stachel 5 Spacetime symmetries in histories canonical gravity 68 N. Savvidou 6 Categorical geometry and the mathematical foundations of Quantum Gravity 84 L.
Crane 7 Emergent relativity 99 O. Dreyer 8 Asymptotic safety 111 R. Percacci 9 New directions in background independent Quantum Gravity 129 F. Markopoulou Questions and answers 150 Part II String/M-theory 167 10 Gauge/gravity duality 169 G.
Polchinski vii www.com viii Contents 11 String theory, holography and Quantum Gravity 187 T. Banks 12 String field theory 210 W. Taylor Questions and answers 229 Part III Loop quantum gravity and spin foam models 233 13 Loop quantum gravity 235 T. Thiemann 14 Covariant loop quantum gravity? 253 E.
Livine 15 The spin foam representation of loop quantum gravity 272 A. Perez 16 Three-dimensional spin foam Quantum Gravity 290 L. Freidel 17 The group field theory approach to Quantum Gravity 310 D. Oriti Questions and answers 332 Part IV Discrete Quantum Gravity 339 18 Quantum Gravity: the art of building spacetime 341 J.
Loll 19 Quantum Regge calculus 360 R. Williams 20 Consistent discretizations as a road to Quantum Gravity 378 R. Pullin 21 The causal set approach to Quantum Gravity 393 J. Henson Questions and answers 414 Part V Effective models and Quantum Gravity phenomenology 425 22 Quantum Gravity phenomenology 427 G.
Amelino-Camelia 23 Quantum Gravity and precision tests 450 C. Burgess 24 Algebraic approach to Quantum Gravity II: noncommutative spacetime 466 S.com Contents ix 25 Doubly special relativity 493 J. Kowalski-Glikman 26 From quantum reference frames to deformed special relativity 509 F. Girelli 27 Lorentz invariance violation and its role in Quantum Gravity phenomenology 528 J.
Sudarsky 28 Generic predictions of quantum theories of gravity 548 L. Smolin Questions and answers 571 Index 580 www. Ambjørn The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark and Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands G. Amelino-Camelia Dipartimento di Fisica, Universitá di Roma “La Sapienza”, P.
Moro 2, 00185 Rome, Italy T. Banks Department of Physics, University of California, Santa Cruz, CA 95064, USA and NHETC, Rutgers University, Piscataway, NJ 08854, USA C. Burgess Department of Physics & Astronomy, McMaster University, 1280 Main St. W, Hamilton, Ontario, Canada, L8S 4M1 and Perimeter Institute for Theoretical Physics, 31 Caroline St.
N, Waterloo N2L 2Y5, Ontario, Canada J. Collins Physics Department, Pennsylvania State University, University Park, PA 16802, USA L. Crane Mathematics Department, Kansas State University, 138 Cardwell Hall Manhattan, KS 66506-2602, USA x www.com List of contributors xi O. Dreyer Theoretical Physics, Blackett Laboratory, Imperial College London, London, SW7 2AZ, UK L.
Freidel Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo N2L 2Y5, Ontario, Canada R. Gambini Instituto de Física, Facultad de Ciencias, Iguá 4225, Montevideo, Uruguay F. Girelli SISSA, via Beirut 4, Trieste, 34014, Italy, and INFN, sezione di Trieste, Italy J.
Henson Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands G. Horowitz Physics Department, University of California, Santa Barbara, CA 93106, USA J. Jurkiewicz Institute of Physics, Jagellonian University, Reymonta 4, PL 30-059 Krakow, Poland J. Kowalski-Glikman Institute for Theoretical Physics, University of Wroclaw 50-204 Wroclaw, pl.
Livine Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex 07, France R. Loll Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands S. Majid School of Mathematical Sciences, Queen Mary, University of London 327 Mile End Rd, London E1 4NS, UK and Perimeter Institute for Theoretical Physics, 31 Caroline St., Waterloo ON N2L 2Y5, Canada F. Markopoulou Perimeter Institute for Theoretical Physics, 31 Caroline St., Waterloo ON N2L 2Y5, Canada www.com xii List of contributors D.
Oriti Max Planck Institute for Gravitational Physics, Am Mühlenberg 1, D 14476 Golm, Germany R. Percacci SISSA, via Beirut 4, Trieste, 34014, Italy, and INFN, sezione di Trieste, Italy A. Perez Centre de Physique Théorique, Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille I, Aix-Marseille II, et du Sud Toulon-Var, laboratoire afilié à la FRUMAM (FR 2291), Campus de Luminy, 13288 Marseille, France J. Polchinski Department of Physics, University of California, Santa Barbara CA 93106, USA J.
Pullin Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 USA C. Rovelli Centre de Physique Théorique, Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille I, Aix-Marseille II, et du Sud Toulon-Var, laboratoire afilié à la FRUMAM (FR 2291), Campus de Luminy, 13288 Marseille, France N. Savvidou Theoretical Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK L. Smolin Perimeter Institute for Theoretical Physics, Waterloo N2J 2W9, Ontario, Canada and Department of Physics, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada R.
Sorkin Perimeter Institute for Theoretical Physics, Waterloo N2J 2W9, Ontario, Canada J. Stachel CAS Physics, Boston University, 745 Commonwealth Avenue, MA 02215, USA D. Sudarsky Instituto de Ciencias Nucleares, Universidad Autónoma de México, A.com List of contributors xiii W. Taylor Massachusetts Institute of Technology, Lab for Nuclear Science and Center for Theoretical Physics, 77 Massachusetts Ave., Cambridge, MA 02139-4307, USA T.
Thiemann Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, D-14476 Golm, Germany and Perimeter Institute for Theoretical Physics, 31 Caroline St. North, Waterloo N2L 2Y5, Ontario, Canada G. ’t Hooft Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, NL-3584 CE Utrecht, The Netherlands R. Williams Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK www.com Preface Quantum Gravity is a dream, a theoretical need and a scientific goal.
It is a theory which still does not exist in complete form, but that many people claim to have had glimpses of, and it is an area of research which, at present, comprises the collective efforts of hundreds of theoretical and mathematical physicists. This yet-to-be-found theory promises to be a more comprehensive and com- plete description of the gravitational interaction, a description that goes beyond Einstein’s General Relativity in being possibly valid at all scales of distances and energy; at the same time it promises to provide a new and deeper understanding of the nature of space, time and matter. As such, research in Quantum Gravity is a curious and exciting blend of rig- orous mathematics and bold speculations, concrete models and general schemata, foundational questions and technical issues, together with, since recently, tentative phenomenological scenarios. In the past three decades we have witnessed an amazing growth of the field of Quantum Gravity, of the number of people actively working in it, and consequently of the results achieved.
This is due to the fact that some approaches to the prob- lem started succeeding in solving outstanding technical challenges, in suggesting ways around conceptual issues, and in providing new physical insights and scenar- ios. A clear example is the explosion of research in string theory, one of the main candidates to a quantum theory of gravity, and much more. Another is the develop- ment of Loop Quantum Gravity, an approach that attracted much attention recently, due to its successes in dealing with many long standing problems of the canonical approach to Quantum Gravity. New techniques have been then imported to the field from other areas of theoretical physics, e.
Lattice Gauge Theory, and influenced in several ways the birth or growth of even more directions in Quantum Gravity research, including for example discrete approaches. At the same time, Quantum Gravity has been a very fertile ground and a powerful motivation for developing xv www.com xvi Preface new mathematics as well as alternative ways of thinking about spacetime and mat- ter, which in turn have triggered the exploration of other promising avenues toward a Quantum Gravity theory. I think it is fair to say that we are still far from having constructed a satis- factory theory of Quantum Gravity, and that any single approach currently being considered is too incomplete or poorly understood, whatever its strengths and suc- cesses may be, to claim to have achieved its goal, or to have proven to be the only reasonable way to proceed. On the other hand every single one of the various approaches being pursued has achieved important results and insights regarding the Quantum Gravity problem.
Moreover, technical or conceptual issues that are unsolved in one approach have been successfully tackled in another, and often the successes of one approach have clearly come from looking at how similar difficulties had been solved in another. It is even possible that, in order to achieve our common goal, formulate a com- plete theory of Quantum Gravity and unravel the fundamental nature of space and time, we will have to regard (at least some of) these approaches as different aspects of the same theory, or to develop a more complete and more general approach that combines the virtues of several of them. However strong faith one may have in any of these approaches, and however justified this may be in light of recent results, it should be expected, purely on historical grounds, that none of the approaches currently pursued will be understood in the future in the same way as we do now, even if it proves to be the right way to proceed.