This page intentionally left blank UNDERSTANDING SPACE-TIME This book presents the history of space-time physics, from Newton to Einstein, as a philosophical development reflecting our increasing understanding of the connections between ideas of space and time and our physical knowledge. It suggests that philosophy’s greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time, and motion and the roles they play in our assumptions about physical objects and physical measurements. This way of thinking leads to new interpretations of the work of Newton and Einstein and the connections between them. It also offers new ways of looking at old questions about a-priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. robert disalle is Associate Professor in the Department of Philosophy, University of Western Ontario. His publications include a contribution to The Cambridge Companion to Newton (2002). UNDERSTANDING SPACE-TIME The Philosophical Development of Physics from Newton to Einstein ROBERT DISALLE University of Western Ontario cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru,UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521857901 © Robert DiSalle 2006 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 2006 isbn-13 978-0-511-16834-5 eBook (EBL) isbn-10 0-511-16834-9 eBook (EBL) isbn-13 978-0-521-85790-1 hardback isbn-10 0-521-85790-2 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. For my parents, Richard DiSalle and Joan Malinowski DiSalle ...L’amor del bene, scemo del suo dover, quiritta si ristora Contents List of figures page ix Preface x 1 Introduction 1 2 Absolute motion and the emergence of classical mechanics 13 2.1 Newton and the history of the philosophy of science 13 2.2 The revisionist view 15 2.3 The scientific and philosophical context of Newton’s theory 17 2.4 The definition of absolute time 20 2.5 Absolute space and motion 25 2.6 Newton’s De Gravitatione et aequipondio fluidorum 36 2.7 The Newtonian program 39 2.8 “To exhibit the system of the world” 47 2.9 Newton’s accomplishment 52 3 Empiricism and a priorism from Kant to Poincare55´ 3.1 A new approach to the metaphysics of nature 56 3.2 Kant’s turn from Leibniz to Newton 60 3.3 Kant, Leibniz, and the conceptual foundations of science 64 3.4 Kant on absolute space 66 3.5 Helmholtz and the empiricist critique of Kant 72 3.6 The conventionalist critique of Helmholtz’s empiricism 79 3.7 The limits of Poincare’s´ conventionalism 86 3.8 The nineteenth-century achievement 94 4 The origins and significance of relativity theory 98 4.1 The philosophical background to special relativity 99 4.2 Einstein’s analysis of simultaneity 103 4.3 From special relativity to the “postulate of the absolute world” 112 4.4 The philosophical motivations for general relativity 120 4.5 The construction of curved space-time 131 4.6 General relativity and “world-structure” 137 4.7 The philosophical significance of general relativity 149 vii viii Contents 5 Conclusion 153 5.1 Space and time in the history of physics 153 5.2 On physical theory and interpretation 158 References 163 Index 171 Figures 1 Newtonian absolute time page 21 2 The definition of equal time intervals 24 3 Absolute motion in absolute space 26 4 Galilean relativity 29 5 The causal structure of Minkowski space-time 113 6 Newton’s Corollary VI 128 7 Free-fall as an indicator of space-time curvature 130 8 Coordinates in homaloidal and non-homaloidal spaces 145 ix Preface This book concerns the philosophy of space and time, and its connection with the evolution of modern physics. As these are already the subjects of many excellent books and papers – the literature of the “absolute versus relational” debate – the production of yet another book may seem to require some excuse. I don’t claim to defend a novel position in that controversy, or to defend one of the standard positions in a novel way. Still less do I pretend to offer a comprehensive survey of such positions and how they stand up in light of the latest developments in physics. My excuse is, rather, that I hope to address an entirely different set of philosophical problems. The problems I have in mind certainly have deep connections with the problems of absolute and relative space, time, and motion, and the roles that they play, or might play, in the history and future of physics. But they can’t be glossed by the standard questions on space-time metaphysics: is motion absolute or relative? Are space and time substantival or relational? Rather, they are problems concerning how any knowledge of space, time, and motion – or spatio-temporal relations – is possible in the first place. How do we come to identify aspects of our physical knowledge as knowledge of space and time? How do we come to understand features of our experience as indicating spatio-temporal relations? How do the laws of physics reveal something to us about the nature of space and time? I see two compelling reasons to focus on these questions. On the one hand, I believe it will give us a more illuminating picture of the connection between the metaphysics of space and time and the development of philos- ophy in general. Historically, there have been two significant attempts to integrate the physics and the philosophy of space and time with a general theory of knowledge: Kant’s critical philosophy, in its attempt to compre- hend Euclid and Newton within a theory of the synthetic a priori; and logical positivism, in its attempt to comprehend Einstein within a conven- tionalist view. These attempts are widely recognized as failures, and I don’t intend to try to rehabilitate them. But I believe that there is some insight to x Preface xi be gained from a better understanding of why they failed; more important, I hope to show that the task in which they failed – to explain the peculiar character of theories of space and time, and the peculiar role that they have played as presuppositions for the empirical theories of physics – is no less important for us than it was for them, and, moreover, is more nearly within our grasp. On the other hand, I believe that focusing on these questions will give us a clearer picture of the history of physics. For, as I hope to show in the following chapters, the moments when such questions have become most urgent are precisely the most revolutionary moments in the history of space-time physics. The great conceptual transformations brought about by Newton, Einstein, and their fellows simply could not have happened as they did without profound reflection on these very questions. And our sense that these transformations were crucial steps forward – that, apart from increasingly useful theories, they actually yielded deeper understand- ing of the nature and structure of space-time – has everything to do with the success of their philosophical work. This is not an entirely novel idea. Something like it was at the heart of the positivists’ interpretation of relativity theory: Einstein introduced spe- cial and general relativity by some “philosophical analysis” of the concepts of space and time. But this interpretation was based on a rather simplistic picture of relativity, as well as simplistic notions of what a “philosophical analysis” could be. Given the inadequacies of the positivists’ attempt to put relativity into philosophical perspective, it has since appeared easier to see the relevance of philosophy to physics in simpler terms: as a source of philo- sophical motivations for physicists, and even of theoretical hypotheses, but not as a method of scientific analysis. For such motivations and hypotheses, it would seem, are inescapably subjective, and their objective worth can only be judged by the empirical success of the theories that they produce. Einstein thought that anyone who followed the philosophical steps that he had taken, whatever their scientific background, would be convinced of the basic principles of special and general relativity. By the later twentieth century, however, philosophers came to think of those steps as somewhat arbitrary, and as not very clearly related to the theories that Einstein actu- ally produced. They had a heuristic value for Einstein, and may have again for a future theory of space-time. To believe again that such philosophical arguments could be crucial – not only to the motivation for a theory, but also to its real significance in our scientific understanding of the world – we need a more philosophically subtle and historically realistic account of those arguments, and the peculiar roles that philosophy and physics have played in them. xii Preface That is what this book aims to provide. It is not distinguished by any technical arguments or results; it benefits, in that regard, from the tradition of important works on absolute and relational space-time, such as Sklar (1977), Friedman (1983), and Earman (1989), that have done so much to make space-time geometry a familiar part of philosophical discourse.