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Classical Space-Times 0 1989 Massachusetts Institute of Technology And tear our pleasures with rough strife, All rights reserved. No part of this book may be reproduced in any form by any electronic Thorough the iron grates of life. 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 For Frances, whose love passeth all understanding 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 :Po a"' O 5 3 3EE 0 X 5' k LA A-bP-bAe WWWWWWWWNN N t4rrec.r E. VI OOVIWN+ W~\UPWW-O~4 o OCO~~~N+-Im r=:E. Contents Preface General Relativity and Substantivalism: A Very I was pleased and flattered when Larry Sklar and Mike Friedman chose Holey Story to mention me in the acknowledgments to their respective books Space, Einstein's Hole Argument Time, and Space-Time and Foundations of Space-Time Theories. I return Perils of Determinism the compliment by stating that these are still the best available texts on a Space-Time Substantivalism and the Possibility of wide range of topics in the philosophy of space and time. My work may Determinism also be seen as a more substantive compliment. Sklar's and Friedman's Taking the Possibility of Determinism Seriously books were especially notable for the insights and the much-needed rigor and precision they brought to the never ending struggle between absolute The Role of the Mutability of Space-Time Structure and relational conceptions of space and time. Now the time is ripe for The Leibnizian Reaction achieving a fuller understanding of the dimensions and ramifications of the Einstein's Reaction issues framed by Sklar and Friedman. Building on their contributions, I A Catalog of Responses to Einstein's Hole Construction hope to make philosophical progress of various kinds: some of the issues Trying to Do without Space-Time Points can be settled; others can be sharpened; still others can be pushed aside as Another Relationist Approach irrelevant; and some can be shown to break down or dissolve into the An Absolutist Counterattack metaphysical ether. Regardless of the specifics of particular issues, the overarching goal here is to foster a better appreciation of how the absolute- Predication and Identity relational controversy connects to problems in mathematics, physics, Essentialism metaphysics, and the philosophy of scientific methodology. Foundation Counterpart Theory problems in physics, especially the general theory of relativity, are used Conclusion both to advance the discussion of philosophical problems and to demon- Notes strate that the absolute-relational controversy is not merely philosophical: References it cannot be confined to the back pages of philosophy journals. Although the treatment of some topics is necessarily technical, the Index 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? xii Preface Notation I am grateful to the John Simon Guggenheim Memorial Foundation and To make the symbolism familiar to the greatest number of readers, I have to the National Science Foundation (grant no. SES-8701534) for their adopted the component notation for vectors and tensors instead of the support of this project. Many colleagues unselfishly offered their advice on newer abstract index notation. Thus, ?;.fj';.::;; stands for the coordinate earlier drafts of this book; to one and all I offer in return my sincere components of a tensor of type (r,s). The Einstein summation convention appreciation, but I must especially thank Mike Friedman, A1 Janis, David on repeated indices is in effect; e.g., gijV' xjgij~j.Round and square Malament, Tim Maudlin, John Norton, Robert Rynasiewicz, and Paul - brackets around indices are used to denote, respectively, symmetrization Teller. Thanks are also due to Michael Wright, whose generous support and antisymmetrization; e.g., of the X-Club made it possible to travel to England, where I received both encouragement and helpful criticism from Harvey Brown, Jeremy Tin = i(Tj - Ti) and Tij, - i(Tj + Tj). Butterfield, Michael Redhead, Simon Saunders, and other members of the Oxbridge mob. Other colleagues could have, but didn't, offer help; here I Logic would like especially to mention Larry Sklar. However, his superb selec- tions in Chinese restaurants more than make up for this lapse. Universal quantifier Section 5.1 relies on "Remarks on Relational Theories of Motion," Canadian Journal of Philosophy 19 (1989): 83-87. Section 8.1 relies on Existential quantifier "Locality, Non-locality, and Action at a Distance: A Skeptical Review of P + Q if P then Q Some Philosophical Dogmas," in Kelvin's Baltimore Lectures and Modern Theoretical Physics, edited by P. Achinstein and R. Kargon (Cambridge: 1P not P MIT Press, 1987). Chapter 9 relies on "What Price Space-Time Substan- tivalism? The Hole Story," British Journal for the Philosophy of Science 38 Sets (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 A u B the union of A and B to the editors and publishers concerned for their permissions to reuse the A n B the intersection of A and B material here. A c B A is a subset of B x E A x is an element of A Null set Maps 4 maps x E A to 4(x) E B Inverse map of 4 Composition $ followed by 4 The dragging along induced by the map 4 of the geometric object 0 xiv Notation World Enough and Space-Time Manifolds An n-dimensional differentiable manifold (usually Cm) Real line An n-dimensional Euclidean space A local coordinate chart for M determining the local coordinates xi, i.e., Ua c M and da : M -r Rn and da(p) = (x1(p),x2(p), -. ,xn(p)) for P E M Derivatives and Connection a/axi A partial derivative with respect to the coordinate xi v2 a2/ax2+ a2/ay2 + a2/az2 sv Lie derivative with respect to V qk Connection components 1 j The ordinary derivative with respect to xi; e.g., Vilj= a vi/axj 11 j The covariant derivative with respect to xj; e.g., vil,= a vi/axj + qkvk Space-Time Models ~IJZ, Models of a theory T (M,002 . ) A model consisting of a manifold M with geometric object fields Oi Introduction Newton's Principia, published three centuries ago last year, launched the most successful scientific theory the world has known or is apt to know. But despite the undeniable success of the theory in explaining and unifying terrestrial and celestial motions, Newton's conceptions of space and time, conceptions that lay at the heart of his analysis of motion, were immediately and lastingly controversial. Huygens, who was arguably the greatest of Newton's Continental contemporaries, rejected Newton's absolute space and time, though he confined his misgivings to private correspondence and unpublished manuscripts. Leibniz, who was already involved in bitter priority disputes with the Newtonians, launched a public attack that cul- minated in the famous Leibniz-Clarke correspondence. In the eighteenth century Euler and Kant defended absolute space, though on quite different grounds, whereas Bishop Berkeley railed against it in his own inimitable fashion. In the nineteenth century Maxwell took an ambivalent stance on absolute motion, while Mach left no doubt that absolute space and time were "monstrosities" deserving no quarter. In the early twentieth century Poincark and Einstein set their authority against the absolutists, thus helping to fashion the myth that relativity theory vindicates the relational account of space, time, and motion favored by Huygens, Leibniz, and their heirs. Recent historical scholarship has markedly advanced our understanding of the roots of the absolute-relational controversy. Koyre and Cohen (1962) provided evidence that Newton had a hand in drafting Clarke's responses to Leibniz. (But see Hall 1980 for a contrary opinion.) The social and political context of the debate has been studied by Shapin (1981) and Stewart (1981). The origins of Newton's ideas on absolute space have been illuminated by McGuire (1978), who finds theological and kinematic rnoti- vations, as well as the better known dynamic arguments given in the Principia. The development of Leibniz's ideas on space and the relation of these ideas to his evolving conception of substance and his tripartite conception of reality have been explored by McGuire (1976),Winterbourne (1981), and Cover and Hartz (1986). Nevertheless, there exist a number of gaps in the literature; for instance, there is still no persuasive account of the various early reactions to Newton's "rotating bucket" experiment.
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