John Barrow (Vol. 383, No. 6597, 228--29) makes some generous remarks about my book Time's Arrow and Archimedes' Point, but has two reservations about my discussion of cosmological arrows of time. One turns on the idea that the visible universe might be "a finite part of [a] possibly infinite, highly inhomogeneous whole." If so, Barrow notes, "we might expect to inhabit a fluctuation with special feature that permit expansion to last long enough to create the conditions in which evolution of [life] is possible." I agree entirely, and indeed spend pages 97--99 of my book discussing this idea. Perhaps I should have given it more prominence, but my main concern in the relevant chapter is with errors of reasoning within more conventional cosmological frameworks.
This point aside, Professor Barrow's reservations concern the validity of the notion of the entropy of the universe as a whole. While I share these concerns, I think they are largely irrelevant to the most important issue about the role of cosmology in explaining the arrow of time. This issue turns on the fact that local manifestations of thermodynamic asymmetry are associated with the existence of stars and galaxies: roughly speaking, the sun is the "reservoir" of order on which most other order in our neighbourhood depends.
However, the formation of galaxies requires that the distribution of matter in the early universe be very homogeneous. If the early irregularities are too large, gravity produces black holes, not galaxies. This early homogeneity has recently been confirmed by the COBE observations of background radiation, but it remains very puzzling. In a system governed by an attractive force, a homogeneous distribution of matter is a highly unusual state. One way to see this is to note that unless there is some prior sense in which the Big Bang is the beginning rather than the end of the observed universe, we are equally entitled to regard it as the end result of a process of gravitational collapse---and yet from this viewpoint gravity would be expected to produce a very inhomogeneous distribution of matter.
Thus the puzzles of local thermodynamic asymmetry are traced to a single big puzzle about the early universe: Why is it so smooth? Thanks to writers such as Roger Penrose and Stephen Hawking, this is a familiar tale. My concern in the relevant chapter of my book is with the next stage, the attempt to find an explanation for the smooth early universe. (In particular, I argue that many contemporary proposals involve the same kind of errors of reasoning as infest discussions of time-asymmetry elsewhere in physics.) However, neither the familiar tale itself, nor my comments on current attempts to conclude it, seem to depend on the ideas that Barrow rightly finds problematic.
In sum, I agree with Professor Barrow that on these issues we are nearer the end of the beginning of the game than the beginning of the end--if anything, I suspect that I am even more pessimistic than he is about the current state of play. However, I think his reservations about my attempts to clarify the rules are misplaced.
School of Philosophy
University of Sydney