World Enough and Space-Time Absolute versus Relational Theories of Space and Time John Barman A Bradford Book The MIT Press Cambridge, Massachusetts London, England © 1989 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times New Roman by Asco Trade Typesetting Ltd., Hong Kong and printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Earman, John. World enough and space-time. "Bradford book." Includes index. 1. Space and time. 2. Absolute, The. 3. Relationism. 4. Science-Methodology-Philosophy. 5. Science-Philosophy. I. Title. QC173.59.S65E17 1989 530.1'1 88-36404 ISBN 0-262-05040-4 And tear our pleasures with rough strife, Thorough the iron grates of life. For Frances, whose love passeth all understanding Contents Preface xi Notation Xlll In troduction 1 The Origins of the Absolute-Relational Controversy 6 1 Newton on Absolute Space and Time 7 2 Senses of Absoluteness 11 3 Relationism 12 4 Leibniz and the Ideality of Space 1 5 5 Other Relationisms 16 6 The Vacuum 18 7 Conclusion 20 Appendix: Newton's Scholium on Absolute Space and Time 20 2 Classical Space-Times 27 1 Machian Space-Time 27 2 Leibnizian Space-Time 30 3 Maxwellian Space-Time 31 4 Neo-Newtonian or Galilean Space-Time 33 5 Full Newtonian Space-Time 33 6 Aristotelian Space-Time 34 7 Other Classical Space-Times 35 8 Review and Quiz 36 Appendix: Absolute Objects 38 3 Choosing a Classical Space-Time 41 1 Arguments from the Meaning of 'Motion' 41 2 Arguments from Epistemology 42 3 Arguments from ScientificTheorizing 43 4 Symmetry Principles 45 5 Absolute Space 48 6 Symmetries, the Structure of Space-Time, and Substantivalism 55 viii Contents 7 Conclusion 57 Appendix: Comments on Symmetry, Invariance, and Dynamics 57 4 Rotation 61 1 Newton's Argument from Rotation 61 2 The Huygens-Leibniz Correspondence 66 3 Huygens's Response 67 4 Leibniz's Response 71 5 Berkeley's Response 73 6 Kant's Response 76 7 Maxwell's Response 78 8 Mach's Response 81 9 Poincare's Response 84 10 Instrumentalism 87 1 1 Conclusion 89 5 Relational Theories of Motion: A Twentieth-Century Perspective 91 1 Relational Theories of Motion in a Classical Setting 91 2 The Relational Theories of Barbour and Bertotti 92 3 Einstein on Rotation 96 4 Rotation and Relativity 97 5 Relativistic Rigid Motion 98 6 Relativity, Relationism, and Rotation 101 7 Einstein's Critique Revisited 102 8 Mach's Principle 105 9 Conclusion 108 Appendix: Rigid Motion in Relativistic Space-Times 108 6 Substantivalism: Newton versus Leibniz 111 Space and Space-Time as Substances 111 2 Leibniz's Argument 116 Contents ix 3 The Structure of Leibniz's Argument 118 4 Leibniz's Weapons 118 5 The Reach and Implications of Leibniz's Argument 120 6 Limitations (?) on Leibniz's Argument 121 7 Responses to Leibniz's Argument 122 8 The Absolutist Counterattack 125 9 Sklar's Maneuver 126 10 Another Relationist Maneuver 128 11 Leibniz on Force 130 12 Possibilia and Relationism 134 13 Conclusion 136 7 Kant, Incongruent Counterparts, and Absolute Space 137 Kant's Argument against Relationism 137 2 A Relationist Account of the Distinction between Right and Left 143 3 Parity Nonconservation 147 4 Incongruent Counterparts and the Intuitive Nature of Space 150 5 Conclusion 152 8 Modern Treatments of Substantivalism and Relationism 154 1 Field's View 154 2 Relativity and Fields 155 3 Fields and Manifold Substantivalism 158 4 The FirsLHCileConstruction 159 5 Friedmancon Relationism: Model-Submodel versus Model EmbeddiIJ.g 163 6 Mundy on Relational Theories of Euclidean Space and Minkowski Space-Time 166 7 What the Antisubstarttivalist Must Do 170 8 Conclusion 173 x Contents 9 General Relativity and Substantivalism: A Very Holey Story 175 Einstein's Hole Argument 175 2 Perils of Determinism 177 3 Space-Time Substantivalism and the Possibility of Determinism 179 4 Taking the Possibility of Determinism Seriously 180 5 The Role of the Mutability of Space-Time Structure 183 6 The Leibnizian Reaction 185 7 Einstein's Reaction 186 8 A Catalog of Responses to Einstein's Hole Construction 1 89 9 Trying to Do without Space-Time Points 191 10 Another Relationist Approach 194 11 An Absolutist Counterattack 195 12 Predication and Identity 196 13 Essentialism 199 14 Counterpart Theory 202 15 Conclusion 207 Notes 209 References 220 Index 229 Preface I was pleased and flattered when Larry Sklar and Mike Friedman chose to mention me in the acknowledgments to their respective books Space, Time, and Space-Time and Foundations of Space-Time Theories. I return the compliment by stating that these are still the best available texts on a wide range of topics in the philosophy of space and time. My work may also be seen as a more substantive compliment. Sklar's and Friedman's books were especially notable for the insights and the much-needed rigor and precision they brought to the never ending struggle between absolute and relational conceptions of space and time. Now the time is ripe for achieving a fuller understanding of the dimensions and ramificationsof the issues framed by Sklar and Friedman. Building on their contributions, I hope to make philosophical progress of various kinds: some of the issues can be settled; others can be sharpened; still others can be pushed aside as irrelevant; and some can be shown to break down or dissolve into the metaphysical ether. Regardless of the specifics of particular issues, the overarching goal here is to foster a better appreciation of how the absolute­ relational controversy connects to problems in mathematics, physics, metaphysics, and the philosophy of scientific methodology. Foundation problems in physics, especially the general theory of relativity, are used both to advance the discussion of philosophical problems and to demon­ strate that the absolute-relational controversy is not merely philosophical: it cannot be confined to the back pages of philosophy journals. Although the treatment of some topics is necessarily technical, the organization and level of presentation of this work make it appropriate for use in an upper-level undergraduate or beginning graduate course in the philosophy of science. The bibliography, while making no pretense at completeness, is extensive enough to guide the reader into both the classic and the more up-to-date literature. I have made no attempt to disguise my own predilections and prejudices, but at important junctions I have tried to indicate the alternative paths and the arguments pro and con for each. To some extent this may be a mistake, for philosophy might be better served if we chose simply to ignore various positions. I harbor no illusion that the considerations I marshal here achieve anything approaching closure. Indeed, I hope that this work will be judged by one of the most reliable yardsticks of fruitful philosophiz­ ing, namely, How many discussions does it engender? How many disserta­ tion topics does it spin off? Xll Preface I am grateful to the John Simon Guggenheim Memorial Foundation and to the National Science Foundation (grant no. SES-8701534) fo r their support of this project. Many colleagues unselfishly offered their advice on earlier drafts of this book; to one and all I offer in return my sincere appreciation, but I must especially thank Mike Friedman, Al Janis, David Malament, Tim Maudlin, John Norton, Robert Rynasiewicz, and Paul Teller. Thanks are also due to Michael Wright, whose generous support of the �-Club made it possible to travel to England, where I received both encouragement and helpful criticism from Harvey Brown, Jeremy Butterfield, Michael Redhead, Simon Saunders, and other members of the Oxbridge mob. Other colleagues could have, but didn't, offerhelp; here I would like especially to mention Larry Sklar. However, his superb selec­ tions in Chinese restaurants more than make up for this lapse. Section 5.1 relies on "Remarks on Relational Theories of Motion," Canadian Journal of Philosophy 19 (1989): 83-87. Section 8.1 relies on "Locality, Non-locality, and Action at a Distance: A Skeptical Review of Some Philosophical Dogmas," in Kelvin's Baltimore Lectures and Modern Theoretical Physics, edited by P. Achinstein and R. Kargon (Cambridge: MIT Press, 1987). Chapter 9 relies on "What Price Space-Time Subs tan­ tivalism? The Hole Story," British Journal fo r the Philosophy of Science 38 (1987): 515-525; and "Why Space Is Not a Substance (at Least Not to First Degree)," Pacific Philosophical Quarterly 67 (1986): 225-244. I am grateful to the editors and publishers concerned for their permissions to reuse the material here. Notation To make the symbolism familiar to the greatest number of readers, I have adopted the component notation for vectors and tensors instead of the newer abstract index notation. Thus, �:j�2.::j� stands for the coordinate components of a tensor of type (r, s). The Einstein summation convention j j on repeated indices is in effect; e.g., gijV == LjgijV . Round and square brackets around indices are used to denote, respectively, symmetrization and antisymmetrization; e.g., 1[iJl == t(1;j - �i) and 1(ij) == tCf;j + T;J Logic (x) Universal quantifier (3x) Existential quantifier P --+ Q if P then Q I P not P Sets u A u B the union of A and B n A n B the intersection of A and B c A c B A is a subset of B E X E A x is an element of A o Null set Maps tPmaps x E A to tP(x) E B Inverse map of tP Composition t/I followed by tP The dragging along induced by the map tP of the geometric object 0 xiv Notation Manifolds M An n-dimensional differentiable manifold (usually CO) !R Real line IEn An n-dimensional Euclidean space A local coordinate chart for M determining the local coordinates Xi, i.e., Va c M and ifJa: M --.