The End of Certainty: Time, Chaos, and the New Laws of Nature

  • Ilya Prigogine
Free Press/Simon and Schuster: 1997228Pp. $24,£20.

In Search of Lost Time

  • Derek York
Institute of Physics Publishing: 1997Pp. £7.95,$15 (pbk).
J.B. Priestley's 1932 play Dangerous Corner illustrates, says Derek York, the key concept of chaos — sensitivity to initial conditions. In 1964, Priestley also published a book entitled Man and Time. (From a 1988 Shaw Festival playbill.)

Can physics explain the difference between past and future? The problem is that the laws of physics seem to be time-symmetric: if they allow a process with one temporal orientation, they allow it in reverse. Yet many ordinary processes seem to be irreversible. Ilya Prigogine calls this the ‘time paradox’, and argues that the solution lies in chaos theory and related methods pioneered by himself and his Brussels colleagues — a radical alternative, he believes, to a tradition due to Ludwig Boltzmann.

Prigogine paints with a broad brush. For example, he seems to equate explaining the thermodynamic asymmetry with finding a physical basis for the apparent flow of time. But these are different issues. Someone who treats time on a par with space, denying that there is objective flow, will still acknowledge that the Universe is asymmetric along its temporal axis, in the way described by the second law of thermodynamics. If Prigogine's methods do explain thermodynamic irreversibility, they simply account for this asymmetry — they do not give us objective flow.

Leaving flow to one side, what is it that actually needs to be explained about the asymmetry of thermodynamics? Ordinarily we say it is the fact that entropy increases. But whether entropy is increasing or decreasing depends on which we take to be the ‘positive’ direction of time. Reverse the scale on the graph, and an increase becomes a decrease.

Is one choice of scale objectively the right one? Is what we call the future objectively the sense of ‘positive’ time? If so, this objective fact must consist of something other than the thermodynamic asymmetry itself. Otherwise, asking why entropy increases is like asking why a snake's head is at the front end: it would be true more or less by definition.

So there is a dilemma for Prigogine. Either he needs to pull two rabbits out of the hat — one to account for the objective direction of time itself, and another to account for the thermodynamic asymmetry — or the puzzle about irreversibility is not what he thinks it is. It isn't that entropy increases per se, but rather that it increases in one direction and decreases in the other. (Analogously, the real puzzle about snakes is that the two ends are so different.)

In the latter case, Prigogine's methods are surely being applied to the wrong task. He suggests that the sensitivity of chaotic systems to initial conditions introduces unpredictability into physics, and hence explains why entropy is bound to increase. But the sensitivity applies whether we start with what we call initial conditions and work ‘forwards’ or start with final conditions and work ‘backwards’. The more chaos helps to convince us that entropy increase is inevitable in one direction, the more it ought to amaze us that we see decrease in the other direction (a fact that surely ought to give us pause about the reliability of the ‘explanation’ in the former case: how good is a method that gets things so badly wrong in one case out of a possible two?).

Boltzmann came this way in 1877, noting that it was a consequence of his new statistical methods that entropy ought to be higher in the past as well as in the future. The real ‘time paradox’ is that entropy goes down in one direction, not that it goes up in the other. Boltzmann may not have had a satisfactory solution, but — unlike Prigogine, I think — he certainly saw the significance of the problem.

So Prigogine's criticism of Boltzmann seems misplaced. To my mind, it is also counterproductive. One of the hardest things in this field is to set off on the right foot — to decide just what needs explaining. Clear directions are hard to find, and The End of Certainty lives up to its name in an unintended way: it isn't to blame for current uncertainty, but seems likely to prolong it.

In Derek York's book, by contrast, lack of a clear direction turns out to be an advantage. In Search of Lost Time is an engaging ramble through diverse topics temporal, by a man who has been dating for 40 years and seems to have loved every minute of it. I wish he had provided more references for readers inclined to explore on their own, but otherwise this is a delightful little book.