While it seems manifest in our experience that time flows - from the past, to the present moment and into the future, there are a number of philosophical and physical objections to this. In the quest to make sense of this conundrum philosophers and physicists confront fascinating and irresistible questions such as: Can effects precede causes? Can one travel in time? Can the expan- sion of the universe or the process of measurement in quantum mechanics provide a direction of time? In this book eleven eminent scholars, standing at the boundary between physics and philosophy, attempt to answer these questions in an entertain- ing yet rigorous way. For example, William Unruh's chapter is one of the first non-technical essays by this important cosmologist. Philip Stamp and Anthony Leggett discuss macroscopic quantum phenomena, a subject which has not been discussed much outside the specialist literature. John Earman's chapter on time travel is likely to become one of the landmarks in the literature. The book will be enjoyed by anyone of a speculative turn of mind fasci- nated by the puzzle of time. Time's Arrows Today Time's Arrows Today Recent physical and philosophical work on the direction of time Edited by Steven F Savitt University of British Columbia CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao 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/9780521461115 © Cambridge University Press 1995 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1995 Reprinted 1998 A catalogue record for this publication is available from the British Library ISBN-13 978-0-521-46111-5 hardback ISBN-10 0-521-46111-1 hardback ISBN-13 978-0-521-59945-0 paperback ISBN-10 0-521-59945-8 paperback Transferred to digital printing 2005 Contents Preface ix Notes on the contributors x Introduction 1 PART l Cosmology and time's arrow 1 Time, gravity, and quantum mechanics 23 WILLIAM UNRUH, Physics: UBC 2 Cosmology, time's arrow, and that old double standard 66 HUW PRICE, Philosophy: Sydney PART 2 Quantum theory and time's arrow 3 Time's arrow and the quantum measurement problem 97 ANTHONY LEGGETT, Physics: Urbana-Champaign 4 Time, decoherence, and 'reversible' measurements 107 PHILIP STAMP, Physics: UBC 5 Time flow, non-locality, and measurement in quantum 155 mechanics STORRS McCALL, Philosophy: McGill 6 Stochastically branching spacetime topology 173 ROY DOUGLAS, Mathematics: UBC PART 3 Thermodynamics and time's arrow 7 The elusive object of desire: in pursuit of the kinetic 191 equations and the Second Law LAWRENCE SKLAR, Philosophy: Michigan 8 Time in experience and in theoretical description of the 217 world LAWRENCE SKLAR, Philosophy: Michigan VU Contents 9 When and why does entropy increase? 230 MARTIN BARRETT & ELLIOTT SOBER, Philosophy: Wisconsin PART 4 Time travel and time's arrow 10 Closed causal chains 259 PAUL HORWICH, Philosophy: MIT 11 Recent work on time travel 268 JOHN E ARM AN, History and Philosophy of Science: Pittsburgh References 311 Index 325 Vlll Preface Most of the contributors to this volume are philosophers of science, but three are physicists (Leggett, Stamp, and Unruh) and one is a mathematician (Douglas). Their chapters are intended to be original contributions towards answers to, rather than comprehensive discussions of, some of the oddly exasperating and fascinating questions known collectively as the problem of the direction of time, but the chapters were written with an eye towards communicating their results to the scientifically literate non-specialist. Most of the work in this volume was presented at the Time's Arrows Today' Conference held on the campus of the University of British Columbia in June, 1992. The exceptions are the papers by Douglas and Earman and Sklar's The elusive object of desire: in pursuit of the kinetic equations and the Second Law'. I am grateful to the Social Sciences and Humanities Research Council of Canada and to the Dean of the Faculty of Arts and the President of the Univer- sity of British Columbia for their generous support of that conference. In addition I wish to express my gratitude to Philip Stamp, whose advice and assistance have been invaluable, to Roy Douglas, who has long provided for me a model of rigorous thinking, and to William Unruh, without whose help my discussion of Penrose's thought experiment in the Introduction would have been much easier to write. Steven F. Savitt Vancouver, British Columbia
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