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Philosophy of Physics.

Physics and Chance and Philosophy of Physics are each, albeit differently, introductory texts. Philosophy of Physics is an overview intended for newcomers, the bulk of which consists in chapters devoted to three main divisions of theoretical physics. Interestingly, Physics and Chance commences with the observation that modern physics rests on four pillars: general relativity, quantum mechanics, the theory of elementary particles, and statistical mechanics. Of these, Sklar observes, general relativity and quantum theory have been subject to intense philosophical scrutiny, while particle theory and statistical mechanics have been relatively neglected. Physics and Chance is designed to promote statistical mechanics to the rank of the elect by providing a comprehensive survey of both the relevant physics and of the philosophical puzzles that attend it. Unsurprisingly, the central chapters of Philosophy of Physics are devoted to space-time theory, quantum theory, and statistical mechanics.

Physics and Chance is the more ambitious and weighty of the two volumes. The hope is to encapsulate enough philosophy and enough physics to enable both physicists and philosophers to grapple with the foundational problems of statistical mechanics. In keeping with the aim of providing a source book for all interested parties, Sklar shies away from critical judgments in favour of the more synoptic view. He is content to limn the anatomy of a problem, note various attempts to solve it, and point out the difficulties that attend each approach. Although Sklar has his favourites among the physicists and philosophers he discusses, the book is not a partisan effort to promote one school of thought over another.

The book begins with a nice historical sketch of thermodynamics and statistical mechanics, followed by chapters on probability and statistical explanation. These last are reasonable maps of the philosophical terrain, unlikely to contain many surprises for philosophers of science. The project really gets under way in the next three chapters, which address equilibrium and non-equilibrium thermodynamics, the corresponding bits of statistical mechanics, and the attempts to 'rationalize' the former by appeal to the latter. The relevant physics is clearly and concisely presented, and it is here that one can start to see Sklar achieve his goal. What sorts of conditions might one postulate for the underlying dynamics in order to see the expected thermodynamic behaviour at the macroscopic level? Sklar has given us a place to go to find ergodicity, weak mixing, mixing, K systems and Bernoulli systems all defined and compared. The conditions and idealizations used to prove theorems are duly noted, as are the gaps between the content of the theorems and the original problems to be solved. The scope of the foundational problem begins to come into view.

That problem is easily stated: if at base, thermodynamic systems are composed of innumerable particles interacting by mechanical laws, how is one to understand the classical laws of phenomenological thermodynamics? How to understand, for example, the macroscopic equilibrium state towards which systems tend or the constant increase in entropy? Can the 'laws' of thermodynamics really be laws, or do they have some less exalted status as mere statistical generalizations?

Attempts to answer this question fall roughly into two camps. There are those who try to derive the thermodynamic laws as strict consequences of the underlying dynamics on the one hand, and those who would demote the thermodynamic principles to assertions about probable behaviour on the other. The latter inherit the problem of understanding the probability involved in 'probable', and to them we will return. The former have the seemingly more devastating difficulty of dealing with Poincare's recurrence theorem and Loschmidt's reversibility objection. According to the first, a closed system will always return arbitrarily close to its initial state, and, according to the second, any Newtonian time development from an initial state to a final one is matched by a development from the time reverse of the final state to the time reverse of the initial. If Poincare's theorem holds, then the entropy of an individual system cannot monotonically increase since it must eventually return to its starting point. And if Loschmidt's objection holds (i.e. if the underlying dynamics is invariant under time reversal, and if the entropy of any state is equal to that of its time reverse), then every evolution from a low to a high entropy state can be paired with an equally acceptable one from high to low.

Much of the history that Sklar recounts consists of physicists attempting to continue the programme of deriving the thermodynamic laws from the underlying dynamics even in the face of these objections. What seems odd is the fairly manifest futility of these attempts. One can modify the underlying dynamics by adding some 'rerandomization' posit (a tradition going back to Boltzmann's famous H-Theorem), but these surreptitious modifications simply have no justification. Or, as is more common, one can try to define something or other that does exactly obey the thermodynamic laws, even if that something or other is not determined by the state of an individual system.

This second tradition traces back to Gibbs, who suggested that thermodynamics quantities such as entropy and thermodynamic states such as equilibrium are not properly speaking properties of individual systems at all but rather of ensembles. Thus, for example, in phenomenological thermodynamics equilibrium is a stationary macroscopic state towards which systems tend. But if the underlying dynamics is ergodic, no state (except perhaps a set of measure zero) is macroscopically stationary and if Poincare's theorem holds then no non-equilibrium state can monotonically tend toward any macroscopic end state. But even if no state can be macroscopically stationary, still one can define over the entire ensemble of microstates a probability distribution which is stationary. So if one wants something stationary to fill the role of equilibrium, probability measures recommend themselves.

Sklar signs on rather easily to the idea that one ought to seek such a stationary distribution. He recounts in some detail the conditions under which such a stationary distribution will be unique, and tackles problem about how to define the relevant quantities from the distribution (i.e. should one look at average behaviour, or the behaviour of averages). He similarly follows through the various attempts to find something or other that increases monotonically, something that can stand in for entropy. But the question that keeps recurring, as a result of the clarity of his overall presentation, is what the point of these exercises could be. If something can be guaranteed to increase then that something can't be a function of the physical state of the box of gas before me. Since phenomenological thermodynamics originally was about such individual boxes, about their pressures and volumes and temperatures, 'saving' it by making it be about probability distributions over ensembles seems a Pyrrhic victory. It is remarkable, and not a little depressing, to see the amount of effort and ingenuity that has gone into finding something of which the phenomenological laws can be strictly true, while insuring that the something cannot possibly be the phenomena.

Sklar sees this tension, and discusses it most thoroughly in a chapter on the reduction of thermodynamics. He sees the difficulties of a situation in which one has a choice between 'reducing' thermodynamics so that its laws become at best assertions about the probable behaviour of individual systems versus reducing it so its laws become exceptionless laws of some abstract entity. He nicely points out the difficulties attending the idea that thermodynamics reduces to statistical mechanics at all. Dynamics alone do not guarantee that the macroscopic world will display normal thermodynamic behaviour, as the reversibility objection demonstrates. So thermodynamics 'reduces' to statistical mechanics only given some probability distribution over initial states, and then only 'reduces' as being likely to be true. The key question therefore becomes the status of the probability distribution over initial states.

Focus on the initial state naturally leads to questions of cosmology, both to explain the low entropy of the initial state of the universe and to explain the canonical probability distribution over initial microstates. Sklar includes a chapter on cosmological questions, particularly on the problem of irreversibility. This complements the last chapter, which deals with the general problem of time's arrow. For even if one could find some plausible constraint to apply to the initial state of the universe, a constraint which implies, say, increasing entropy, why not apply the same constraint to the final state of the universe, thereby predicting anti-thermodynamic behaviour? Just framing this problem raises a host of objections concerning the relation of terms such as 'initial' and 'final' to the very thermodynamic facts at issue.

Throughout Physics and Chance, Sklar provides clear and comprehensive accounts of both the relevant physics and of the conceptual problems embedded in interpreting the physics. He has digested and condensed a tremendous amount of material, and admirably fulfilled the task he set himself: conveying the problematic forcefully enough to engage the attention of philosophers and physicists. Physics and Chance should take its place alongside Space, Time, and Spacetime as a rigorous and authoritative guide to philosophical problems in a field of physics. Ironically, the great strength of the book as a stimulant of thought also leaves one slightly frustrated. Sklar has no axe to grind, and although he produces many telling objections to the positions he recounts, he does not offer a clearly defined positive view. But the thicket of confusions and problems he chronicles are in need of an ax, and a keen axman, to clear them. I hope we can look forward to more partisan views from Sklar in the future.

After perusing Physics and Chance, one turns to Philosophy of Physics with a deep appreciation of the difficulties that must have attended writing it. In Physics and Chance Sklar devotes 420 pages to laying out the general problematic surrounding statistical mechanics; in Space, Time, and Spacetime he required the same amount of space to discuss relativity. But in Philosophy of Physics he proposes to introduce the basic concepts and problems of relativity, statistical physics, and quantum theory in a mere 230 pages. The results are rather uneven.

The section on spacetime theory is the most successful, reflecting a long experience introducing the topic to students. The presentation is compressed, but would be comprehensible to the attentive reader. Topics include the classical debates about the ontological status of space, the transition from classical to relativistic physics, general relativity, the conventionality of geometry, and causal theories of spatio-temporal structure. There is even a discussion of the so-called 'hole' argument against taking spacetime to be a substance, although when reduced to a single paragraph the point of the argument is likely to be lost on a neophyte. Indeed, this chapter functions not so much as a freestanding survey of the field but as a skeleton upon which one could hang articles when teaching an introductory course. This is not to disparage Sklar's achievement: such a skeleton is just what one needs when articles (as is typical) are impossible to understand on their own. This sort of rapid overview could well provide cogency to a course that would otherwise appear disjointed.

The section on statistical physics is a highly condensed sampling from Physics and Chance. It is the sort of precis thaty can be well appreciated by someone already familiar with the field, but may be too dense for most students. Again, one might well use it as a supplement to a more leisurely exposition given in a classroom.

The chapter on quantum theory is far the least successful, although this is mostly a reflection of the state of the field. There is, for example, a long discussion of the various 'no hidden variables' proofs, up to and including Bell's theorem as a version of such a proof, but no mention of the existence of a deterministic 'hidden variables' theory (Bohm's theory) that is empirically equivalent to standard quantum mechanics. There is a discussion of quantum logic which ends, quite admirably, by pointing out that quantum logic won't solve our problems. But is it really necessary to lead a beginner down that particular dead end just to show that it doesn't work? Quantum theory has several foundational problems which can be stated quite sharply. Unfortunately, those sharp questions tend to be lost in the fog of fuzzy and incorrect claims that have been made about the theory through the years.

Philosophy of Physics is primarily designed as a tool for those who teach in the field, and it fills a need. If one wishes to cover the main branches of theoretical physics at an introductory level, Sklar has provided the backbone of a course. But those coming newly to the field would best take the long way round and work through Physics and Chance (and Space, Time, and Spacetime) rather than trying to glean everything from Philosophy of Physics.
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Author:Maudlin, Tim
Publication:The British Journal for the Philosophy of Science
Article Type:Book Review
Date:Mar 1, 1995
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