THE MEANING OF RELATIVITY

THE MEANING OF RELATIVITY

Albert Einstein THE MEANING OF RELATIVITY With a new Foreword by W. H. McCREA, F.R.S. CHAPMAN AND HALL SCIENCE PAPERBACKS

First published 191111 by Methuen & Co Ltd Se,;iJ'NJ edition 1937 Third edition with an a/lflllndix 1946 Fourth edition with further a/lflllndix 1950 Fifth edition 1951 Sixth edition, revised, 1956 RtfJrinted 1960 RtfJrinted with a new foreword 1967 First published as a Sdent:e Paperback 1967 by Chafnnan and Hall Ltd II New Fetter Lane, London Ec.,P 4EE RtfJrinted three times RtfJrintedl980 ISBN-13: 978-o-4Q-20560-6 e-isbn-13: 978-94-o11-60n-3 DOl: 10.10071978-94-011-60n-3 This paperback edition is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser.

This book, originally published in 1922, consisted of the text of Dr. Einstein's Stafford Little Lectures, delivered in May 1921 at Princeton University. For the third edition, Dr. Einstein added an appendix discussing certain advances in the theory of relativity since 1921. To the fourth edition, Dr. Einstein added Appendix II on his Generalized Theory of Gravitation. In the fifth edition the proof in Appendix II was revised. In the present (sixth) 'edition Appendix II has been rewritten. This edition and the Princeton University Press fifth edition, revised (1955), are identical. The text of the first edition was translated by Edwin Plimpton Adams, the first appendix by Ernst G. Straus and the second appendix by Sonja Bargmann.

CONTENTS FOREWORD IX SPACE AND TIME IN PRE-RELATIVITY PHYSICS THE THEORY OF SPECIAL RELATIVITY 23 THE GENERAL THEORY OF RELATIVITY 54 THE GENERAL THEORY OF RELATIVITY (continued) 76 APPENDIX I ON THE 'COSMOLOGIC PROBLEM' 104 APPENDIX II INDEX RELATIVISTIC THEORY OF THE NON-SYMMETRIC FIELD 127 159

A NOTE ON THE SIXTH EDITION For the present edition I have completely revised the 'Generalization of Gravitation Theory' under the title 'Relativistic Theory of the Nonsymmetric Field'. For I have succeeded-in part in collaboration with my assistant B. Kaufman-in simplifying the derivations as well as the form of the field equations. The whole theory becomes thereby more transparent, without changing its content. A. E. December I954

FOREWORD BY W. H. MCCREA, F.R.S. 'THE only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy.' So Einstein writes on page 2 of this book. Most present-day physicists would agree, and many before Einstein must have held the same opinion. Einstein, however, put the opinion into practice to better purpose than any physicist before him. And for Einstein it evidently meant what it means for most of us today: a theory is the construction of a theoretical model of the world of physics; all the mathematical discussion applies to the model; the model embodies the 'system of concepts', and it serves 'to represent the complex of our experiences' if the experience of the theoretical observer in the theoretical model can be put into satisfactory correspondence with the experience of the actual observer in the actual physical world. Classical mechanics and classical electromagnetism provide models that are good representations of two sets of actual experiences. As Einstein was the first fully to appreciate, however, it is not possible to combine these into a single self-consistent model. The construction of the simplest possible self-consistent model is the achievement of Einstein's theory of special relativity. The theory is found, in particular, to give a satisfactory representation of the electromagnetic interaction between charged particles through its use of the concept of the electromagnetic field. Special relativity as such says nothing at all about gravitational interaction. The classical concept of an instantaneous gravitational interaction ix

x FOREWORD between every pair of particles obviously cannot be admitted by the theory; evidently a field theory of gravitation is required. This is where the model-making aspect comes into its own. H. Minkowski put Einstein's special-relativity model into geometrical terms, and there can be little doubt that Einstein constructed his theory of general relativity by experimenting with the generalization of the geometrical model. In this way he constructed a field theory of gravitation by making every thing treated by the theory concerning space-time and matter a property of one single field. The successes of this theory were soon apparent. Two features of general relativity, however, were not as satisfactory as Einstein wished. First, following E. Mach, he considered that what are recognized locally as inertial properties of local matter must be 'determined by the properties of the rest of the matter in the universe. The extent to which general relativity fulfils this expectation is still undecided. However, in his efforts to discover this extent, Einstein succeeded in founding the modern study of cosmology. Secondly, although in a general way electromagnetism had pointed the way to general relativity, it was not included in the theory in that it was not a property of the single fundamental field. Another essentially independent field can be introduced, and the theory as a whole can then be made to give a largely satisfactory account of electrodynamics. But, as Einstein writes on pages 93-4, ' A theory in which the gravitational field and the electromagnetic field do not enter as logically distinct structures would be much preferable.' From the context of this and other such remarks (for example, pages 47-8) it is evident, however, that Einstein expected a lot more from such a unified theory than a mere

FOREWORD amalgamation of gravitation and electromagnetism at the macroscopic level. He thought the theory should explain the existence of elementary particles and should provide a treatment of nuclear forces. Einstein spent most of the second half of his life in pursuit of this aim, but with no palpable success. This book is the nearest that Einstein ever came to writing a textbook. He must have regarded 'it as a serious effort, for he used its later editions as the vehicle of publication of his final attempts to construct a unified theory. Originally, the book consisted of the text of some lectures in Princeton in 192 I. The text gives the impression that Einstein had hopes of developing the written version of his lectures into a more systematic treatment, but that his determination wavered. For the outcome is an account of the subject that is somewhat patchy as regards both depth and degree of detail of the treatment. Consequently, anyone who seeks an excuse for not reading the book has a fairly easy task, which may explain why the existence of the book appears to be better known than its contents. Actually, in addition to being the pioneer of much of the now well-known approaches to the subject, the book contains a number of ideas that have subsequently been re-invented by other workers; neither they nor their readers noticed Einstein's priority in a work that has been through six editions. The book covers the ground I have sketched above. The first chapter is a good account of the classical treatment of space, time and mechanics and, more briefly, of electromagnetism. The second chapter is a concise introduction to the theory of special relativity. Most of this material is still to be found without much change in almost any elementary treatment of the subject. The xi

xii FOREWORD remaining two original chapters deal with the theory of general relativity. Einstein introduces his treatment with the aid of two principles: one is that it is contrary to scientific ideas to have something, the space-time of special relativity, that influences everything else but is itself influenced by nothing (page 54); the other is Einstein's' principle of equivalence' (page 56). However, these are guiding principles only, and they do not themselves lead to a particular theory. As I have said, this came from experimenting with the geometrical model, in fact by exploiting B. Riemann's generalization of classical geometry. Einstein proceeds to a fairly systematic resume of the theory, making use, for expository purposes, of the now familiar ' weak-field' approximation. He ends with a short account of his closed static universe and its possible realization of the requirements of Mach's principle. Appendix I appeared first in the edition of 1946, but it bears evidence of having been written some years earlier. It is mainly an exposition of the theory of the expanding universe as formulated by A. Friedmann who, in 1922, was the first to propose it. While it is odd that Einstein mentions no later work, except with reference to empirical evidence, his ' summary' on pages 120-6, expressing a common-sense view of cosmology in his own time, is still well worth heeding. Appendix II went through different forms in the last three editions, and Einstein's ' note' on the last of these was dated only a few months before his death. It is the final attempt, already mentioned, to formulate a unified theory. In order to develop a tensor calculus, a field of quantities known as a connexion has to be defined (in the most familiar case these quantities are the Christoffel symbols). If the quantities are defined to possess a certain symmetry,

FOREWORD xiii and a certain procedure is followed, we recover the equations of Einstein's theory of gravitation in accordance with the theory of general relativity. If the symmetry requirement is dropped, and if a suitable generalization of the previous procedure is followed, we obtain an enlarged set of equations. These are what Einstein here offers as a basis for a unified field theory. He indicates the physical requirements of such a theory only in general terms and he does not particularize as to how he expects the equations to meet the requirements. In due course other workers showed beyond much doubt that the requirements are not met. Thus the experimentation with a geometrical model, that had been so brilliantly successful in leading Einstein to the theory of general relativity, proves of no avail in leading any further. Why should scientists still want to read Einstein's book? First of all, of course, because it is Einstein's. But they will be surprised that reading Einstein can be so unexciting. The fact that it can be is perhaps the best tribute to his work. For his original writings had been found so convincing that, in lecturing about the work so soon afterwards, he had need only to explain and had no need to persuade. Indeed, it is humbling to be reminded how much of relativity theory was established during its first few years and how comparatively little further the theory was carried almost ever since. (The last few years have been seeing renewed vigour in the subject.) Apart from the appendices, this book is only an introduction to what was known when Einstein gave his lectures; the Encyklopadie article by W. Pauli [reissued as Theory of Relativity (Pergamon Press 1958)] appeared also at that time and naturally gave a more comprehensive view. But Einstein's introduction is still exceedingly serviceable, although its use is best associated with lectures on the

xiv FOREWORD subject. Finally, it need scarcely be said that anyone interested in the history of relativity theory generally, or in the development of Einstein's ideas in particular, must take full account of this book. Readers in many categories will thus be grateful to the publishers for ensuring that it remains so accessible. w. H. MCCREA