The Special Theory of Relativity The Special Theory of Relativity David Bohm London and New York First published 1965 by W. This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www. This edition published 1996 by Routledge 2 Park Square, Milton Park, Abingon, Oxon, OX14 4RN Simultaneously published in the USA and Canada by Routledge 270 Madison Ave, New York NY 10016 © 1965, 1996 Sarah Bohm Foreword © 1996 B.Hiley All rights reserved.
No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication Data A catalogue record for this book has been requested ISBN 0-203-20386-0 Master e-book ISBN ISBN 0-203-26638-2 (Adobe ebook Reader Format) ISBN 0-415-14808-1 (hbk) ISBN 0-415-14809-X (pbk) Foreword The final year undergraduate lectures on theoretical physics given by David Bohm at Birkbeck College were unique and inspiring. As they were attended by experimentalists and theoreticians, the lectures were not aimed at turning out students with a high level of manipulative skill in mathematics, but at exploring the conceptual structure and physical ideas that lay behind our theories. His lectures on special relativity form the content of this book.
This is not just another text on the subject. It goes deeply into the conceptual changes needed to make the transition from the classical world to the world of relativity. In order to appreciate the full nature of these radical changes, Bohm provides a unique appendix entitled “Physics and Perception” in which he shows how many of our “self-evident” notions of space and of time are, in fact, far from obvious and are actually learnt from experience. In this appendix he discusses how we develop our notions of space and of time in childhood, freely using the work of Jean Piaget, whose experiments pioneered our understanding of how children develop concepts in the first place.
Bohm also shows how, through perception and our activity in space, we become aware of the importance of the notion of relationship and the order in these relationships. Through the synthesis of these relationships, we abstract the notion of an object as an invariant feature within this activity which ultimately we assume to be permanent. It is through the relationship between objects that we arrive at our classical notion of space. Initially, these relations are essentially topological but eventually we begin to understand the importance of measure and the need to map the relationships of these objects on to a co-ordinate grid with time playing a unique role.
His lucid account of how we arrive at our classical notions of space and absolute time is fascinating and forms the platform for the subsequent development of Einstein’s relativity. After presenting the difficulties with Newtonian mechanics and Maxwell’s electrodynamics, he shows how the Michelson-Morley experiment can be understood in terms of a substantive view of the ether provided by Lorentz and Fitzgerald. The difficulties in this approach, which assumes actual contraction of material rods as they move through the ether, are discussed before a masterful account of Einstein’s conception of space-time is presented. Bohm’s clarity on this topic was no doubt helped by the many discussions he had with Einstein in his days at Princeton.
The principle of relativity is presented in terms of the notion of relationship and the order of relationship that were developed in the appendix and he argues that a general law of physics is merely a statement that certain relationships are invariant to the way we observe them. The application of this idea to observers in relative uniform motion immediately produces the Lorentz transformation and the laws of special relativity. Interlaced with the chapters on the application of the Lorentz transformation, is a chapter on the general notion of the falsification of theories. Here he argues against the Popperian tradition that all that matters is mere experimental falsification.
Although a preliminary explanation might fit the empirical data, it may ultimately lead to confusion and ambiguity and it is this that could also lead to its downfall and eventual abandonment in favour of another theory even though it contradicts no experiment. His final chapters on time and the twin paradox exhibit the clarity that runs throughout the book and makes this a unique presentation of special relativity.HILEY Preface The general aim of this book is to present the theory of relativity as a unified whole, making clear the reasons which led to its adoption, explaining its basic meaning as far as possible in non-mathematical terms, and revealing the limited truth of some of the tacit “common sense” assumptions which make it difficult for us to appreciate its full implications. By thus showing that the concepts of this theory are interrelated to form a unified totality, which is very different from those of the older Newtonian theory, and by making clear the motivation for adopting such a different theory, we hope in some measure to supplement the view obtained in the many specialized courses included in the typical program of study, which tend to give the student a rather fragmentary impression of the logical and conceptual structure of physics as a whole. The book begins with a brief review of prerelativistic physics and some of the main experimental facts which led physicists to question the older ideas of space and time that had held sway since Newton and before.
Considerable emphasis is placed on some of the efforts to retain Newtonian concepts, especially those developed by Lorentz in terms of the ether theory. This procedure has the advantage, not only of helping the student to understand the history of this crucial phase of the development of physics better, but even more, of exhibiting very clearly the nature of the problems to which the older concepts gave rise. It is only against the background of these problems that one can fully appreciate the fact that Einstein’s basic contribution was less in the proposal of new formulas than in the introduction of fundamental changes in our basic notions of space, time, matter, and movement. To present such new ideas without relating them properly to previously held ideas gives the wrong impression that the theory of relativity is merely at a culminating point of earlier developments and does not properly bring out the fact that this theory is on a radically new line that contradicts Newtonian concepts in the very same step in which it extends physical law in new directions and into hitherto unexpected new domains.
Therefore, in spite of the fact that the study of the basic concepts behind the ether theory occupies valuable time for which the student may be hard pressed by the demands of a broad range of subjects, the author feels that it is worthwhile to include in these lectures a brief summary of these notions. Einstein’s basically new step was in the adoption of a relational approach to physics. Instead of supposing that the task of physics is the study of an absolute underlying substance of the universe (such as the ether) he suggested that it is only in the study of relationships between various aspects of this universe, relationships that are in principle observable. It is important to realize in this connection that the earlier Newtonian concepts involve a mixture of these two approaches, such that while space and time were regarded as absolute, nevertheless they had been found to have a great many “relativistic” properties.
In these lectures, a considerable effort is made to analyze the older concepts of space and time, along with those of “common sense” on which they are based, in order to reveal this mixture of relational and absolute points of view. After bringing out some of the usually “hidden” assumptions behind common sense and Newtonian notions of space and time, assumptions which must be dropped if we are to understand the theory of relativity, we go on to Einstein’s analysis of the concept of viii Preface simultaneity, in which he regards time as a kind of “coordinate” expressing the relationship of an event to a concrete physical proc ess in which this coordinate is measured. On the basis of the observed fact of the constancy of the actually measured velocity of light for all observers, one sees that observers moving at different speeds cannot agree on the time coordinate to be ascribed to distant events. From this conclusion, it also follows that they cannot agree on the lengths of objects or the rates of clocks.
Thus, the essential implications of the theory of relativity are seen qualitatively, without the need for any formulas. The transformations of Lorentz are then shown to be the only ones that can express in precise quantita tive form the same conclusions that were initially obtained without mathematics. In this way, it is hoped that the student will first see in general terms the significance of Einstein’s notion of space and time, as well as the problems and facts that led him to adopt these notions, after which he can then go on to the finer-grained view that is supplied by the mathematics. Some of the principal implications of the Lorentz transformation are then explained,not only with a view of exploring the meaning of this transformation, but also of leading in a natural way to a statement of the principle of relativity—that is, that the basic physical laws are the invariant relationships, the same for all observers.
The principle of relativity is illustrated in a number of examples. It is then shown that this principle leads to Einstein’s relativistic formulas, expressing the mass and momentum of a body in terms of its velocity. By means of an analysis of these formulas, one comes to Einstein’s famous relationship, E=mc2, between the energy of a body and its mass. The meaning of this relationship is developed in considerable detail, with special attention being given to the problem of “rest energy,” and its explanation in terms of to-and-fro movements in the internal structure of the body, taking place at lower levels.
In this connection, the author has found by experience that the relationship between mass and energy gives rise to many puzzles in the minds of students, largely because this relationship contradicts certain “hidden” assumptions concerning the general structure of the world, which are based on “common sense,” and its development in Newtonian mechanics. It is therefore helpful to go into our implicit common sense assumptions about mass to show that they are not inevitable and to show in what way Einstein’s notion of mass is different from these, so that it can be seen that there is no paradox involved in the equivalence of mass and energy. Throughout the book, a great deal of attention is paid quite generally to the habitual tendency to regard older modes of thought as inevitable, a tendency that has greatly impeded the develop ment of new ideas on science. This tendency is seen to be based on the tacit assumption that scientific laws constitute absolute truths.
The notion of absolute truth is analyzed in some detail in this book, and it is shown to be in poor correspondence with the actual de velopment of science. Instead, it is shown that scientific truths are better regarded as relationships holding in some limited domain, the extent of which can be delineated only with the aid of future experimental and theoretical discoveries.