By Huw Price

J. J. Halliwell, J. Pérez-Mercader and W. H. Zurek (eds.), Physical Origins of Time Asymmetry, Cambridge: Cambridge University Press, 1994. Pp. xx + 515. $190.00 HB.

In 1963 a group of physicists, mathematicians and philosophers of science assembled in Cornell to discuss the arrow of time. One of them was Richard Feynman, who drew attention to his comments in the published discussions by insisting that they not be attributed to him. (They appeared as the remarks of "Mr. X".) Twenty-eight years later Feynman was gone, but the mysteries of time asymmetry in physics remained as deep as ever. At the end of September, 1991, forty-five physicists and mathematicians assembled in Mazagon, Spain, for a second meeting on the arrow of time. This book is the proceedings of that meeting.

The Mazagon meeting was opened by Mr. X's Princeton supervisor and collaborator, John Wheeler. Wheeler's contribution provides an introductory chapter to the book, and some of the themes will be familiar to those who know Wheeler's rather Bohrian speculations on the role of the mind in creating reality. It is heady stuff, but the book soon settles down to more serious topics. There are six parts, each comprising four to eight chapters: Information, Computation and Complexity; Statistical Origins of Irreversibility; Decoherence; Time Asymmetry and Quantum Mechanics; Quantum Cosmology and Initial Conditions; and Time and Irreversibility in Gravitational Physics. There are thirty five chapters in all, in addition to Wheeler's introductory piece. The book as a whole is an invaluable addition to the literature on the physics of time asymmetry, and a very worthy successor to Thomas Gold's The Nature of Time (Ithaca: Cornell University Press, 1967), which the proceedings of the 1963 meeting.

The highlights of the book include Stephen Hawking's "The No Boundary Condition and the Arrow of Time", which he delivered under the title "My Greatest Mistake". It provides his definitive account of the episode in the mid-1980s, recounted earlier in his A Brief History of Time, in which he changed his mind about the question as to whether the arrow of time would reverse if the universe recollapsed to a "big crunch". Not everyone agrees that Hawking was right to change his mind. H. D. Zeh begins his contribution--"Time (A-)Symmetry in a Recollapsing Universe"-- with the words, "It is argued that Hawking's `greatest mistake' may not have been a mistake at all." (p. 390) (The printed discussion of Zeh's paper begins like this. "Hawking: Your symmetric initial condition for the wave function is wrong! Zeh: Do you mean it does not agree with [your] no-boundary condition? Hawking: Yes.") The chapter by Murray Gell-Mann and James Hartle ("Time Symmetries and Asymmetry in Quantum Mechanics and Quantum Cosmology") also explores the anti-Hawking option, while J. J. Halliwell's "Quantum Cosmology and Time Asymmetry" presents a useful overview of the debate.

One of the less technical papers is Paul Davies' "Stirring up Trouble", in which he discusses "the nature and origin of time asymmetry", with the aim of dispelling "some persistent misconceptions". Davies does a nice job of separating the issue of the temporal asymmetry of physical processes from that of the (apparent?) flow of time, or that of the status of the past-present-future distinctions. He then goes on discuss thermodynamics, criticising--correctly, in my view--the common suggestion that the disturbing influence of the environment plays a crucial role. Finally, he introduces cosmological issues, and here I think his discussion goes a little astray. He points out the important role of the expansion of the universe in producing the relatively low entropy state of the present universe: "As the universe expanded ... the maximal possible entropy rose. The actual entropy also rose, but less fast. In particular, the relaxation time for nuclear processes to allow the cosmological processes to keep pace with changing constraints (due to expansion) was much longer than the expansion time, so the material began to lag further and further behind equilibrium conditions (equilibrium meaning in the nuclear case that this material is in the form of the most stable element - iron)." (p. 127) Davies concludes that "we can legitimately say that an explanation for the origin of the arrow of time can be traced back to the expansion of the universe." (p. 128) However, he warns us not to "fall for trap, as some have done, of supposing ... that if the expansion reverses, then so must the arrow." (p. 128)

At this point Davies himself seems to have fallen for a old trap. If expansion itself were the crucial thing in producing the thermodynamic asymmetry we observe around us, then the second law would have to reverse in a recontracting universe. Why? Simply because a recontracting universe just is an expanding universe, viewed in reverse. If expansion guarantees an arrow of time, it guarantees it, inter alia, in those cases we think of as recontracting universes; for these have just as much claim as our own region of the universe to thought of as expanding. (To dispute this you have to argue that there is an objective sense in which our universe is expanding rather than contracting--a privileged time direction, in effect--and this is to assume a time asymmetry, not to explain one.)

What is wrong with the hypothesis that the second law would reverse in a recontracting universe? One problem is that recontraction alone does not seem sufficient to guarantee that all those nuclear processes will reverse themselves; that iron will transmute into less stable elements. But the right lesson to draw from this is that in order to explain the thermodynamic arrow at our end of the universe, we need to do a lot more than appeal to expansion. In particular, we need to explain why the matter in the universe doesn't start off as iron, given that this is its equilibrium state.

In other words, it isn't the expansion itself which is crucial, so much as the state of the universe as it begins to expand. Like generations of physicists before him, Davies seems to have fallen for the trap of underestimating the importance of very special initial conditions in explaining the observed thermodynamic asymmetry. (The mystery isn't so much why entropy goes up, as why it is ever low in the first place.) And in claiming both that expansion generates the arrow of time, and that contraction would not reverse it, he seems to have fallen for the trap of the temporal double standard. If the two temporal directions are allowed to begin on an equal footing, these two claims are simply inconsistent.

School of Philosophy
University of Sydney
Australia