1、This page intentionally left blankTIME, CHANCE AND REDUCTIONPhilosophical Aspects of Statistical MechanicsStatistical mechanics attempts to explain the behaviour of macroscopic physical systemsin terms of the mechanical properties of their constituents. Although it is one of thefundamentaltheoriesof
2、physics,ithasreceivedlittleattentionfromphilosophersofscience.Nevertheless, it raises philosophical questions of fundamental importance on the nature oftime, chance and reduction. Most philosophical issues in this domain relate to the questionof the reduction of thermodynamics to statistical mechani
3、cs.This book addresses issues inherent in this reduction: the time-asymmetry of thermo-dynamics and its absence in statistical mechanics; the role and essential nature of chanceand probability in this reduction when thermodynamics is non-probabilistic; and how, if atall, the reduction is possible. C
4、ontaining contributions on current research by experts in thefield, this is an invaluable survey of the philosophy of statistical mechanics for academicresearchers and graduate students interested in the foundations of physics.Gerhard Ernst is a Professor of History of Philosophy and Moral Philosoph
5、y atUniversitat Stuttgart. His main research interests are in moral philosophy, epistemologyand philosophy of science.Andreas Huttemann is a Professor of Philosophy at Westfalische Wilhelms-Universitat Munster. His research interests include philosophy of science and early modernphilosophy.TIME, CHA
6、NCE AND REDUCTIONPhilosophical Aspects of Statistical MechanicsEdited byGERHARD ERNSTUniversitat StuttgartANDREAS HUTTEMANNWestf alische Wilhelms-Universitat MunsterCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore,So Paulo, Delhi, Dubai, TokyoCambridge Universit
7、y PressThe Edinburgh Building, Cambridge CB2 8RU, UKFirst published in print formatISBN-13 978-0-521-88401-3ISBN-13 978-0-511-77010-4 Cambridge University Press 20102010Information on this title: www.cambridge.org/9780521884013This publication is in copyright. Subject to statutory exception and to t
8、he provision of relevant collective licensing agreements, no reproduction of any partmay take place without the written permission of Cambridge University Press.Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites refe
9、rred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.Published in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orgeBook (NetLibrary)HardbackContentsList of contributors page vi1 Introduc
10、tion 1Gerhard Ernst and Andreas HuttemannPart I: The arrows of time 112 Does a low-entropy constraint prevent us from influencingthe past? 13Mathias Frisch3 The past hypothesis meets gravity 34Craig Callender4 Quantum gravity and the arrow of time 59Claus KieferPart II: Probability and chance 695 Th
11、e natural-range conception of probability 71Jacob Rosenthal6 Probability in Boltzmannian statistical mechanics 92Roman Frigg7 Humean metaphysics versus a metaphysics of powers 119Michael EsfeldPart III: Reduction 1378 The crystallization of Clausiuss phenomenologicalthermodynamics 139C. Ulises Mouli
12、nes9 Reduction and renormalization 159Robert W. Batterman10 Irreversibility in stochastic dynamics 180Jos UffinkIndex 208vContributorsRobert W. Batterman Department of Philosophy, Talbot College,University of Western Ontario, London ON, N6A 3K7, CanadaCraig Callender Philosophy Department, Universit
13、y of California SanDiego, 9500 Gilman Drive, La Jolla CA 920930119, USAGerhard Ernst Institut fur Philosophie, Universitat Stuttgart, Seidenstrae36, D-70174 Stuttgart, GermanyMichael Esfeld Universite de Lausanne, Section de Philosophie, CH-1015Lausanne, SwitzerlandRoman Frigg Department of Philosop
14、hy, Logic and Scientific Method, LondonSchool of Economics and Political Science, Houghton Street, London WC2A2AE, UKMathias Frisch Skinner Building, University of Maryland, College Park MD20742, USAAndreas Huttemann Philosophisches Seminar, WestfalischeWilhems-Universitat Munster, Domplatz 23, D-48
15、143 Munster, GermanyClaus Kiefer Institut fur Theoretische Physik, Universitat zu Koln, ZulpicherStrae 77, D-50937 Koln, GermanyC. Ulises Moulines Seminar fur Philosophie, Logik undWissenschaftstheorie, Ludwig-Maximilians-Universitat Munchen, Ludwigstrae31, D-80539 Munchen, GermanyJacob Rosenthal In
16、stitut fur Philosophie der Universitat Bonn, Am Hof 1,D-53113 Bonn, GermanyJos Uffink Institute for History and Foundations of Science, UtrechtUniversity, P.O. Box 80.000, NL-3508 TA, Utrecht, The Netherlandsvi1Introductiongerhard ernst and andreas huttemann1.1 Statistical mechanics and philosophySt
17、atistical mechanics attempts to explain the behaviour of macroscopic physicalsystems(inparticulartheirthermalbehaviour)intermsofthemechanicalpropertiesoftheirconstituents.Inordertoachievethisaimitreliesessentiallyonprobabilisticassumptions. Even though in general we do not know much about the detail
18、edbehaviour of each degree of freedom (each particle), statistical physics allows usto make very precise predictions about the behaviour of systems such as gases,crystals, metals, plasmas, magnets as wholes.The introduction of probabilistic concepts into physics by Maxwell, Boltzmannand others was a
19、 significant step in various respects. First, it led to a completelynew branch of theoretical physics. Second, as Jan von Plato pointed out, the verymeaning of probabilistic concepts changed under the new applications. To givean example: whereas before the development of statistical physics variatio
20、n couldbe conceived as the deviation from an ideal value this was no longer a tenableinterpretation in the context of statistical physics. Genuine variation had to beaccepted (von Plato, 2003: 621).Furthermore, the introduction of probabilistic concepts triggered philosophicalspeculations, in partic
21、ular with respect to the question whether the atomic worlddoes indeed follow strict deterministic laws (cf. von Plato, 1994;Stoltzner, 1999).Forinstance,in1873MaxwellgavealectureentitledDoestheProgressofPhysicalScience tend to give any advantage to the opinion of Necessity (or Determinism)over that
22、of the Contingency of Events and the Freedom of the Will? He wonderedwhether the promotion of natural knowledge may tend to remove the prejudicein favour of determinism which seems to arise from assuming that the physicalscience of the future is a mere magnified image of that of the past (quoted inv
23、on Plato, 1994: 87). Other physicists in the field voiced similar views. FranzExner, an Austrian physicist, argued in his lectures on the physical foundations12 Gerhard Ernst and Andreas Huttemannof natural science that the concepts of causation and laws of nature have to berevised in the light of t
24、he need to introduce probabilistic concepts into physics.With respect to determinism he claims that deterministic laws obtain only in themacro-world and that there is no reason to assume that determinism is true at thelevel of atoms. It may very well be the case, he argues, that the most fundamental
25、laws of physics are probabilistic. (The lectures were written in and before the firstworld war; Exner, 1922: lectures 8695.) These views which arose in the contextof philosophical reflections on the nature of the new statistical mechanics maywell have contributed to the willingness with which some p
26、roponents of the newlyemerging quantum mechanics gave up determinism.Bethatasitmay,philosophicalreflectiononstatisticalmechanicscamealmosttoanendwiththeadventofothernewfundamentalphysicaltheories,suchasquantummechanics and the theory of general relativity. For sixty years philosophers ofphysicsfocus
27、edalmostexclusivelyontheinterpretationofquantummechanicsandthe philosophical implications of the theory of general relativity. It was only withthe publication of Lawrence Sklars Physics and Chance (1993) that the discussionof philosophical and foundational problems of statistical mechanics became mo
28、repopular again among philosophers of physics. Sklar (1993: 6) surmised that theneglect of statistical mechanics was partly due to the fact that the field itself isin a certain disarray. Compared to the situation in quantum mechanics and thetheories of relativity there are not only different philoso
29、phical interpretations ofphysicaltheoriesbutalsowidelydivergingapproachesandschoolswithinstatisticalmechanics itself. It was Sklars aim to provide a survey and make some of theseapproaches accessible and thus to stimulate further philosophical investigations. Itseems that by and large he succeeded.
30、The last decade has seen the field flourishing.There have been major philosophical monographs like David Alberts Time andChance (2000) as well as a lot of other work to a significant extent by thecontributors of this volume.1There is even a recent volume entitled ContemporaryDebates in Philosophy of
31、 Science (by Christopher Hitchcock, 2004), in whichphilosophical issues pertaining to statistical mechanics figure more prominentlythan those of quantum mechanics or the theories of relativity.The main philosophical and foundational questions that are currently discussedconcern the relation of stati
32、stical mechanics and thermodynamics. Thermody-namics started as a theory of heat engines. It gradually developed into a rathergeneral theory that describes matter in all its phases and their thermal and magneticbehaviourinparticular.Thermodynamicsmakesvirtuallynoassumptionsaboutthemicro-structure of
33、 the systems it describes. But of course the systems described bythermodynamics do have a micro-structure. Statistical mechanics was developed in1For a very helpful state of the art article see Uffink (2007).Introduction 3the hope to explain the thermodynamic macro-laws in terms of the behaviour of
34、thesystems constituents. Surprisingly, this reductive enterprise turned out to be ratherdifficult. Most foundational/philosophical issues are related in one way or anotherto the question of the reduction of thermodynamics to statistical mechanics. Inparticular, there are three focal issues:(1) One l
35、aw in thermodynamics exhibits a pertinent time-asymmetry (according to thesecondlawofthermodynamics,theentropyinaclosedsystemneverdecreasesintime),whereasthefundamentallawsofstatisticalmechanicsfailtoexhibitsuchanasymmetry.So, where does the time-asymmetry come in? And how is the thermodynamic time-
36、asymmetry related to other arrows of time in physics?(2) Statistical mechanics is a probabilistic theory, while thermodynamics is not. So, howis the concept of probability to be interpreted in order to be coherent and to makethermodynamic behaviour intelligible?(3) Thermodynamics allegedly is reduci
37、ble to statistical mechanics. But how exactly, ifat all, does the reduction work? And what concept of reduction is here employedanyway?Part one of this collection of essays is concerned mainly with the first topic (seeSection 1.2), part two with the second (see Section 1.3), and part three with thet
38、hird (see Section 1.4).1.2 The arrows of timeTime seems to have a direction. However, it is not so clear what this claim exactlyamounts to and whether a direction of time could be distinguished from processesin time having a direction. Even though the fundamental dynamical laws in physicsdo not have
39、 a temporal direction both in physics as well as in ordinary life we comeacross various temporally directed phenomena (arrows of time). There are severalsuch arrows in physics (see the chapter by Kiefer): We only observe certain sorts ofradiation, entropy never decreases and our universe expands. Si
40、milarly, causationseems to have a temporal direction. Furthermore, we seem to know more about thepast than about the future. And counterfactual dependence seems to be temporallydirected as well: If A had not occurred then C would not have occurred eitherseems to be in general a good candidate for a
41、true proposition only if what isdescribed by A precedes what is described by C (see Horwich, 1987). The chaptersby Mathias Frisch, Craig Callender and Claus Kiefer are all concerned with thearrows of time.The contribution by Mathias Frisch deals with the question of how various of thetemporal asymme
42、tries are related to one another. There is a long tradition accord-ing to which the causal asymmetry is closely related to the temporal asymmetry4 Gerhard Ernst and Andreas Huttemannembodied in the second law of thermodynamics. This view has recently beendefendedbyDavidAlbertandbyBarryLoewer,whoargu
43、ethatthecausalasymme-try can be grounded in those facts that explain the second law of thermodynamics.Both accounts centrally involve the claim that it follows from Boltzmannsaccount of the thermodynamic asymmetry (the so-called past hypothesis, whichpostulates a low-entropy constraint on the early
44、universe) that possible macro-evolutions are much more restricted toward the past than toward the future. Thestatisticalmechanicalaccount,asLoewerputsit,resultsinatime-asymmetrictree-structure for possible macro-evolutions. Frisch argues that statistical mechanicsallows not only for branchings but a
45、lso for the reconvergence and merging ofpossiblemacro-histories.AsaconsequencehemaintainsthatAlbertsandLoewersaccounts do not work in their present form because they fail to explain how ourstrict concepts of causal influence and causal control emerge.Craig Callenders chapter argues that it is essent
46、ial for answering the problem ofthedirectionoftimetotakegravityintoaccount.Moreparticularly,hedealswiththequestion whether the low-entropy constraint is plausible given what we know aboutgravity. The past hypothesis, which is invoked to explain why entropy increases (orrather:neverdecreases)seemstob
47、e prima facie patentlyfalse.Accordingtocurrentcosmologicaltheoriestheearlyuniverseisanalmosthomogeneousisotropicstateofapproximatelyuniformtemperature,i.e.averyhighentropystate,notalow-entropystate as postulated by the past hypothesis. The standard response to this objectionis that we forgot to incl
48、ude gravity. Gravity, it is said, saves the past hypothesis. Sonow the essential question is whether the gravitational behaviour of the stars etc.can plausibly be interpreted as the movement to an equilibrium state. Callenderargues that the inclusion of gravity into the Boltzmannian account of the d
49、irectionof time is highly non-trivial. After sketching some serious problems with gravity,he develops a sketch of how one can obtain a never decreasing Boltzmann entropyin self-gravitating systems described by certain types of gravitational kineticequations.Claus Kiefer approaches the different arrows of time from the perspective of aphysicist. His aim is to explain how the various physical arrows can in principle beunderstood on the basis of a fundamental theory of quantum gravity. After a briefdiscussion of the time-direct
