lthough time plays a critical role in the theory of relativity and much of modern physics and chemistry, the nature of time remains a complete mystery. Since our subjectivity as conscious beings is all that distinguishes the present moment from all others, time cannot be fully explained without understanding the role of the observer. Conversely, because our perceptions of the world are fixed to the present moment, an understanding of time will most likely be required before we can fully understand consciousness. Time and consciousness are related in another way: time and information storage are both related to entropy, which is a measure of both thermodynamic disorder and information, and provides directionality or asymmetry to the temporal flow of events.

This book is a collection of articles by various eminent physicists, including luminaries like Murray Gell-Mann, John Wheeler, and Steven W. Hawking, on the subject of the quantum cosmological origins of time's 'arrow' and thermodynamic irreversibility and quantum decoherence as the fundamental characteristic, and perhaps a causal determinant, of the passage of time. The articles vary widely in style. Some, like the short article by Hawking, are anecdotal and intuitive in nature, making them accessible to the layman, while others are dense with Hamiltonians, density matrices, and Bose operators.

Time asymmetry is a little easier to examine than time itself, because a fundamental axiom of statistical thermodynamics is that entropy must increase over time in a closed system. The perception of the flow of time is thus nothing more than the perception of the world's inexorable increase in disorder. This is just another way of saying that psychological time always seems to move 'forward' instead of 'backward'. Because the very nature of information storage determines the directionality of perceived time, it is impossible to perceive the world as doing anything other than going to hell in a handbasket (at least in the physical sense).

However, entropy is not a fundamental property of space, but a property of collections of particles. Many systems are known where entropy decreases over time in small regions of space, yet within them time still moves forward. This increase in "real" physical entropy cannot therefore be the cause of physical time. In order to reverse time, not only the entropy but the momenta of all particles and fields in the region would have to be reversed. For the most part, the laws of physics are agnostic with respect to time, and most of the authors seem to agree that time, if it is a real phenomenon, could theoretically move in either direction, although we would never notice it. On a cosmological scale, expansion of space provides a driving force for irreversibility that emerges from solutions of the Wheeler-Dewitt equation in the semiclassical limit when a low-entropy boundary condition is imposed at one end. For example, the articles by H. D. Zeh's, L. S. Schulman, and others discuss a commonly-shared belief that time results from expansion in the Big Bang and defend Hawking's original introduction of a time-reversal during the contraction phase. This idea is, however, now vigorously disputed by Hawking as his ``greatest mistake''.

After reading this book it seems clear that, fascinating as it is, dragging in statistical mechanics, the theory of computation, and ergodic theory to explain the mystery of time has mostly provided, so far, descriptions of the effects of time on matter rather than shedding much light on the true nature of this slippery beast. The article by P.C.W. Davies is typical of the difficulty physics currently has in explaining the Second Law in a non-circular fashion with respect to time and in escaping from the idea that time must somehow therefore be an illusion. A major piece of the puzzle is still missing.

However, this book is definitely well worth taking the time to read because of the significance (dare I say `timeliness') of the topic. The articles are sufficiently independent to be read in a time-asymmetric sequence. There are a few annoyances, such as the frequent substitution of `<' and `>' for angle brackets  '⟨' and '⟩' , and the absence of an index. Perhaps, taking their cue from the `timelessness' of the article by J. B. Barbour, who argues that time does not really exist (and jokes of having doubts about the existence of quantum mechanics as well), the editors found that there simply was no time to write one.