The Meaning of Quantum Gravity Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application

Editor: ALWYN VAN DER MERWE University of Denver, U.S.A.

Editorial Advisory Board: AS 1M BARUT, University of Colorado, U.s.A. HERMANN BONDI, University of Cambridge, u.K. BRIAN D. JOSEPHSON, University of Cambridge, u.K. CLIVE KILMIS TER, University of London, u.K. GUNTER LUDWIG, Philipps-Universitiit, Marburg, F.R.G. NATHAN ROSEN, Israellnstitu'te of Technology, Israel MENDEL SACHS, State University of New York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, Zentralinstitutfiir Astrophysik der Akademie der Wissenschaften, D.D.R. The Meaning of Quantum Gravity

by H. -H. von Borzeszkowski and H.-J. Treder Einstein-Laboratorium [iir Theoretische Physik der Akademie der Wissenschaften der D.D.R., Potsdam-Babelsberg, D.D.R.

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Dordrecht / Boston / Lancaster / Tokyo Library of Congress Cataloging in Publication Data

Borzeszkowski, H.-H. von (Horst-Heino von) The meaning of quantum gravity.

(Fundamental theories of physics) Bibliography: p. Includes index. 1. Quantum gravity. I. Treder, Hans Jiirgen. II. Title. III. Series. QC178.B635 1987 530.1 87-27501 ISBN-13: 978-94-010-8229-7 e-ISBN-13: 978-94-009-3893-9 DOl: 10.1007/978-94-009-3893-9

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All Rights Reserved © 1988 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover I st edition 1988 No part of the material protected by "this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner Table of Contents

Preface vii

Chapter 1 / Quantum Theory and Gravitation 1

Chapter 2 / Quantum Mechanics and Classical Gravitation 9 2.1. Diffraction of Particles by a Grating 10 2.2. Diffraction of Particles by a Gravitational Grating 12 2.3. Gravitational Atomic Model 15 2.4. Equivalence Principle and Heisenberg's Fourth Relation 17 2.5. Quantum Mechanics and the Weak Principle of Equivalence 22

Chapter 3 / Measurement in Quantum Gravity 24 3.1. The Bohr-Rosenfeld Principles of Measurement in Quantum Field Theory 25 (a) The Landau-Peierls Arguments 25 (b) The Bohr-Rosenfeld Arguments 28 3.2. Measurement in Quantum Gravity 35 3.3. Ehrenfest's Theorems 38

Chapter 4 / Mathematical Descriptions of Quantum Gravity 43 4.1. Heisenberg-Euler-Kockel Approximation 43 4.2. On Gauge Fixing in Quantum Gravity 49

Chapter 5 / Quantum Postulates and the Strong Principle of Equivalence 56 5.1. Gravitons and the Linear Approximation of General Relativity Theory 56 5.2. Gravitons and the Nonlinear High-Frequency Approximation of General Relativity Theory 61 5.3. Compton Effect 66 5.4. Lamb Shift 68 5.5. Black-body Radiation 71 5.6. A Historical Remark: Black-body Radiation and Compton Effect 75

Chapter 6 / Planckions 79 6.1. Heavy Gravitons 79

v VI Table of Contents

6.2. Planckions as Biggest Elementary Particles and as Smallest Test Bodies 95 6.3. Foam and Block Spaces 100

Appendix A / Massive Shell Models and Shock Waves in Gravita- tional Theories with Higher Derivatives 103

Appendix B / On the Physical Meaning of Planck's 'Natural Units' 114

References 124

Index 129 Preface

In discussing the question of whether General Relativity Theory really needs to be quantized, a simply negative answer cannot be accepted, of course. Such an answer is not satisfying because, first, Einstein's gravitational equations connect gravity and non-gravitational matter and because, second, it can be taken for granted that non-gravitational matter has an atomic or quantum structure such that its energy-momentum tensor standing on the right-hand side of Einstein's equations is formed out of quantum operators. These two facts make it impossible to read the left-hand side of Einstein's equations as an ordinary classical function. This does not necessarily mean, however, that we must draw the conclusion that General Relativity Theory, similar to electrodynamics, could or should be quantized in a rigorous manner and that this quantization has similar consequences to quantum electrodynamics. In other words, when for reasons of consistency quantization is tried, then one has to ask whether and where the quantization procedure has a physical meaning, i.e., whether there exist measurable effects of quantum gravity. IQ accordance with these questions, we are mainly dealing with the discus• sion of the principles of quantized General Relativity Theory and with the estimation of quantum effects including the question of their measurability. This analysis proves that it is impossible to distinguish between classical and quantum General Relativity Theory for the extreme case of Planck's orders of magnitude. In other words, there does not exist a physically meaningful rigorous quantization conception for Einstein's theory. Because the quantized Einstein theory for free gravitational fields contains all universal constants known today, namely h, c, and G, it satisfies the Einstein-Heisenberg demands on a unitary theory. A unitary theory should, therefore, basically imply General Relativity. If this is accepted then, as a consequence of the quantum gravity analysis presented here, one has to conclude that a super-GUT (i.e., a GUT including gravity) should not differentiate between quantum and classical physics.

August, 1987 H.-H. VON BORZESZKOWSKI H.-J. TREDER vii