TIME AND CHANCE ▲▲▲ DAVID Z ALBERT TIME AND CHANCE HARVARD UNIVERSITY PRESS Cambridge,Massachusetts London,England Copyright©2000bythePresidentandFellowsofHarvardCollege Allrightsreserved PrintedintheUnitedStatesofAmerica Second printing, 2003 LibraryofCongressCataloging-in-PublicationData Albert,DavidZ. Timeandchance/DavidZAlbert. p. cm. Includesindex. ISBN0-674-00317-9(cloth) ISBN 0-674-01132-5 (paper) 1.Timereversal. 2.Physics—Philosophy. I.Title. QC173.59.T53A432000 530.11—dc21 00-056732 FOR BEN CONTENTS Preface ix 1. Time-ReversalInvariance 1 2. Thermodynamics 22 3. StatisticalMechanics 35 4. TheReversibilityObjectionsandthePast-Hypothesis 71 5. TheScopeofThermodynamics 97 6. TheAsymmetriesofKnowledgeandIntervention 113 7. QuantumMechanics 131 Appendix:GedankenexperimentswithHeatEngines 165 Index 171 PREFACE Thisbookisintendedbothasanelementaryintroductionandasanoriginal contributiontothedevelopmentofascientificaccountofthedistinctionbe- tweenthepastandthefuture. ▲▲▲ Chapter1isarelativelystraightforwardrehearsalofwhatisperenni- allyreferredtointhephysicalliteratureas“theproblemofthedirectionof time”—butinwhatIhopeisanunprecedentedlypreciselanguageofphys- ical states, and with what I hope is an unprecedentedly careful discussion ofexactlywhatitmeansforasetofdynamicallawstodistinguish,ortofail to distinguish, between the past and the future. Chapter 2, together with themoredetailedappendixonGedankenexperimentswithheatengines,is a report on the second law of thermodynamics—which is the point at which distinctions between past and future have made their most explicit and most widely heralded and most intensively studied appearance in the laws of physics—very much along the lines of the beautiful treatment of that subject in the famous book by Enrico Fermi. Chapter 3 is an outline, more or less in the spirit of Ludwig Boltzmann, of the project of statistical mechanics—including what I hope will prove relatively novel discussions of the mathematical structure and the metaphysical status of the probabil- ity-distributions over initial conditions, and of the connection between en- tropyandinformation,andofthequestionofHaecceisstism,andofanum- ber of other matters as well. Chapter 4 is about the famous objections to that project due to J. Loschmidt and Ernst Zermello and Henri Poincaré, and also about what seems to me to be the proper remedy for those objec- tions—which is a new and fundamental and non-dynamical law of nature calledthe“past-hypothesis.”Chapter5isacritiqueofthelonghistoryofat-