The Ontology of Spacetime i Philosophy and Foundations of Physics Series Editors: Dennis Dieks and Miklos Redei In this series: Vol. 1: The Ontology of Spacetime Edited by Dennis Dieks ii The Ontology of Spacetime Edited by Dennis Dieks History and Foundations of Science, Utrecht University, Utrecht, The Netherlands Amsterdam – Boston – Heidelberg – London – New York – Oxford – Paris San Diego – San Francisco – Singapore – Sydney – Tokyo iii Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, UK First edition 2006 Copyright r 2006 Elsevier B.V. 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Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN-13: 978-0-444-52768-4 ISBN-10: 0-444-52768-0 ISSN: 1871-1774 For information on all Elsevier publications visit our website at books.elsevier.com Printed and bound in The Netherlands 060708091010987654321 iv Contents List of Contributors . ............................. vii Introduction ..................................... ix PART I: THE ONTOLOGY OF SPACETIME 1. The Implications of General Covariance for the Ontology and Ideology of Spacetime by John Earman . ................ 3 2. The Disappearance of Space and Time by Carlo Rovelli . 25 3. Spacetime Structuralism by Jonathan Bain . ............ 37 4. Minkowski Space-Time: A Glorious Non-Entity by Harvey R. Brown, Oliver Pooley . .................... 67 PART II: TIME, BECOMING AND RELATIVITY: COMPATIBILIST POSITIONS 5. The Irrelevance of the Presentist/Eternalist Debate for the Ontology of Minkowski Spacetime by Mauro Dorato . ....... 93 6. Presentism and Eternalism in Perspective by Steven F. Savitt . 111 7. Minkowski Spacetime and the Dimensions of the Present by Richard T.W. Arthur . ......................... 129 8. Becoming, Relativity and Locality by Dennis Dieks . ....... 157 9. How to Square A Non-localized Present with Special Relativity by Yuval Dolev . ............................. 177 v vi Contents 10. Philosophical Consequences of the Twins Paradox by Storrs McCall . ............................ 191 PART III: TIME, BECOMING AND RELATIVITY: INCOMPATIBILIST VOICES 11. Is There an Alternative to the Block Universe View? by Vesselin Petkov . ............................ 207 12. Special Relativity, Time, Probabilism and Ultimate Reality by Nicholas Maxwell . ............................ 229 13. Temporal Presentness and the Dynamics of Spacetime by Kent A. Peacock . ............................ 247 14. Presentism and Quantum Gravity by Bradley Monton . ...... 263 Author Index. .................................... 281 Subject Index. .................................... 285 List of Contributors R.T.W. Arthur, Department of Philosophy, McMaster University Hamilton, Canada J. Bain, Humanities and Social Sciences, Polytechnic University, Brooklyn, USA H.R. Brown, Faculty of Philosophy, University of Oxford, Oxford, UK D. Dieks, History and Foundations of Science, Utrecht University, Utrecht, The Netherlands Y. Dolev, Department of Philosophy, Bar Ilan University, Ramat-Gan, Israel M. Dorato, Department of Philosophy, University of Rome Three, Rome, Italy J. Earman, Department of History and Philosophy of Science, University of Pittsburgh, Pittsburgh, USA N. Maxwell, Department of Science and Technology Studies, University College London, London, UK S. McCall, Department of Philosophy, McGill University, Montreal, Canada B. Monton, Department of Philosophy, University of Kentucky, Lexington, USA K.A. Peacock, Department of Philosophy, University of Lethbridge, Lethbridge, Canada V. Petkov, Philosophy Department, Concordia University, Montreal, Canada O. Pooley, Oriel College, University of Oxford, Oxford, UK C. Rovelli, Centre de Physique Theorique de Luminy, Universite´ de la Me´diterrane´e, Marseille, France S.F. Savitt, Department of Philosophy, The University of British Columbia, Vancouver, Canada, V6T 1Z1. vii This page intentionally left blank viii Introduction The nature of space and time is a traditional philosophical subject. Whether space is an independently existing ‘‘substance’’ or not, and whether time is a measure of change in material processes or rather something that exists and ‘‘flows’’ even if there are no material processes going on, are questions that go back to the very beginnings of natural philosophy. But in spite of this longevity no consensus has been reached, and these issues are still exercising the minds of both scientists and philosophers. The last few decades have even seen an upsurge of interest. This is due to a number of factors. Among these figures prominently the revival of the substantivalism versus relationalism debate as a consequence of recent foundational studies of general relativity, especially the renewed attention for Einstein’s notorious ‘‘hole argument’’. Indeed, the di- ffeomorphism invariance of the equations of general relativity appears to in- dicate that prima facie different models of the theory that are related to each other by diffeomorphisms, actually represent the same physical situation. In- deed, the only difference between any two such models is in the manifold points where events take place: the contents of the events, their mutual relations, and the laws that apply are the same. If the verdict of physical sameness is accepted, the implication is that only physical objects and fields, and their coincidence relations, are relevant for the specification of the state of the universe. The identity of the spacetime points at which events take place plays no role. This suggests that it may be unnecessary at all to accept these points as independent parts of the ontological furniture of the world. Arguably, this would be a vin- dication of relationalism, since only structural properties of particles and fields, and their coincidence relations, remain as physically significant. It is possible not to go along with this conclusion, for example because one has qualms about accepting the metrical field as a physical object on the same footing as matter fields, or because of the suspicion that the spacetime points are still there, hiding in the structure of the fields in disguised form. But even so, it is clear that new light has been shed on the discussion about the ontology of spacetime. Another reason for the interest in spacetime questions is the awareness that the global temporal structures exhibited by solutions of the general relativistic field equations are very relevant to debates about the nature of time. In par- ticular, the notorious question of whether it makes sense to say that there is ix x D. Dieks ‘‘becoming’’, or that ‘‘time is flowing’’, has received a new impetus from this direction. In the 1940s, Go¨del published a number of seminal papers in which he demonstrated the existence of solutions of the Einstein equations in which closed time-like curves occur (Go¨del, 1949). He concluded from this that the doctrine according to which time is ‘‘objectively lapsing’’ is incompatible with general relativity. In the 1960s, Rietdijk and Putnam rekindled the older theme that special relativity, even more clearly than general relativity, rules out that the history of the universe can be regarded as a unique continuous succession of three-dimensional worlds (Rietdijk, 1966). At least at first sight these observa- tions seem to provide a justification for looking upon the universe as one four-dimensional, ‘‘static’’, whole; a ‘‘block universe’’ (actually a squarely pre- relativistic notion: the term seems to originate with William James (1979), in his essay ‘‘The Dilemma of Determinism’’). These relativistic considerations inject new life into the famous McTaggart A versus B series discussion, with many arguing that only the B series is a viable option. Remarkably, in connection with recent work on quantum gravity the opposite opinion can also be heard. This is because in some approaches to the quantization of general relativity, it must be assumed that there exists a global time parameter, corresponding to a priv- ileged foliation of spacetime — this would reinstate the notion that the universe’s history consists in a succession of three-dimensional worlds. This may be interpreted as being congenial to the A-like doctrine of ‘‘presentism’’. The surge of interest in questions of this kind has made the need felt for a permanent international platform