The Newtonian understanding of the physical world pictured immutable atoms interacting with one another within the container of absolute space, each moving according to strictly deterministic laws whose ineluctable consequences unfolded with the even flow of absolute time. This conception led to Laplace's chilling conclusion that a calculating demon of unlimited capacity and total instant knowledge could completely predict the future and retrodict the past. For all its appearance of activity, the Newtonian world was, in reality, a realm of frozen being in which any true distinction between past, present and future had collapsed into an instant of timeless knowledge. It was a universe that contained rearrangements but generated no true novelty. In a word, it was a clockwork cosmos.

That world, so lifeless in its character, is no longer on the agenda of physical science. Einstein's discoveries of special and general relativity tied together space, time and matter into a single package and replaced absolutes with relational concepts. Yet Einstein - in so many ways the last of the ancients rather than the first of the moderns - clung to a deterministic account of reality, rejecting the probabilistic interpretation of modern quantum theory despite his having been that theory's intellectual grandfather through his 1905 discussion of the photoelectric effect. Einstein also believed firmly in the ultimate unreality of temporal experience, seeking to console the widow of his friend, Michele Besso, with the thought that for him and for Besso, as physicists, the distinction between past, present and future was an illusory trick of human psychological perspective. He believed that the true reality was the timeless block universe of the total spacetime continuum.

Many might consider such an atemporal view to be an example of what Alfred North Whitehead called "misplaced concreteness", the misleading preference for abstract theory over actual experience. Yet many perplexities remain for the scientist in trying to think about the nature of time. This is not simply because the equations of physics offer no natural accommodation for the concept of the "nowness" of the present moment. It is also because the fundamental laws of nature (with one small exception, significant in the very early universe but negligible today) are time-symmetric; they incorporate no distinction between past and future. From whence, then, arises our experience of "the arrow of time", pointing from a remembered past to an unknown future? The conventional answer has been to appeal to the second law of thermodynamics, which states that the entropy of an isolated system (the measure of its disorder) can never decrease, thereby defining time's arrow as pointing in the direction of increasing disorderliness. Thermodynamics describes the behaviour of matter in bulk; that is to say, it deals with complex systems made up of huge numbers of molecules. Its second law is not an iron necessity but an immensely reliable statistical generalisation. The reason that entropy tends to increase is that there are vastly many more ways of being disorderly than there are of being orderly. The odds are stacked against all the air molecules in a box ending up in one half of it (a more orderly state than their being spread out over the whole), but it is not absolutely impossible that this should happen.

One cannot claim that the nature of time is well understood in modern physics. There is an uneasiness in relying on thermodynamics, using the properties of bulk matter as a correction to the time-symmetric insights of what we are otherwise prone to label as "fundamental physics". Two further sources of uneasiness are also present in our physical thinking today.

One relates to the paradox that, although quantum theory has been used with superb success to calculate and explain a very great many phenomena, we still do not fully understand it. The nub of the difficulty is located in the act of measurement. It is notorious that quantum mechanics predicts only the relative probabilities of a variety of possible outcomes that might result from making an observation. Yet, on any particular occasion of measurement, one, and only one, of these possible results will be observed. How does it come about that on this occasion this result has been obtained? It is humiliating for a quantum physicist to have to admit that there is no widely agreed or obviously satisfactory answer to this very reasonable question. The "measurement problem" may well be linked in some way to our perplexities about the origin of time's arrow. After all, measurement is an irreversible process, with a clear distinction between past and future as ignorance is transformed into knowledge.

The second uneasiness in our physical thinking arises from the unexpected discovery, first recognised by Henri Poincare at the turn of the century and extensively explored in the past 40 years or so by means of "experiments" with computer modelling, that the intrinsic unpredictabilities present in nature go well beyond the probabilistic character of microscopic quantum events. It turns out that they are also present in much of macroscopic physics, where classical (Newtonian) systems often exhibit an exquisite sensitivity to the finest possible detail of their circumstances, with the consequence that their future behaviour is beyond our power to predict. The study of these effects has been given the name of "the theory of chaos", a title that is unfortunately inapt (but by now, unrevisable) since, though the phenomena look haphazard, their apparent randomness is contained within certain limits. An orderly disorder characterises chaotic dynamics. Despite the deterministic equations apparently describing their basic structure, these chaotic systems are intrinsically unpredictable. They are also intrinsically unisolatable, since their sensitivity makes them vulnerable to the slightest change in the surrounding environment.

There has been much debate about what significance to attribute to "'deterministic chaos". Are we simply faced with an unavoidable epistemological deficiency (we cannot know what such systems' future behaviour will be), so that the lesson is that apparent randomness and complexity may be the result of an underlying deterministic simplicity? Or is this intrinsic unpredictability rather the signal of an ontological opportunity, telling us that reality is more supple than we had supposed? If the latter is the case, as some of us believe, the initial deterministic equations from which the discussion started can only have the status of approximations, in particular (isolatable) circumstances, to a more holistic and open physical reality.

All these important issues are the subject of this new book by Ilya Prigogine. He won his Nobel prize for pioneering work on the thermodynamics of systems far from equilibrium. (Classical thermodynamics had restricted its discussion to systems at or very near thermal equilibrium.) In such non-equilibrium regimes, surprising new phenomena are encountered, involving the spontaneous generation of large-scale order in both space and time. A striking example of this behaviour is the so-called "chemical clock", associated with the Belousov-Zhabotinski reaction. "Red" and "blue" chemicals that have complicated (technically, non-linear and reflexive) reactions with each other are fed into and out of a reaction tank. In certain circumstances, instead of the system settling down into a simple, equilibrium "purple" mixture, regular oscillations are set up between successive states of all "red" and all "blue". Such a process requires the correlated behaviour of trillions of molecules. Here we see the emergence of an "optimistic" arrow of time, involving the spontaneous generation of order, in contrast to the "pessimistic" arrow of the second law of thermodynamics, involving the increase of disorder. There is no fundamental contradiction between these two arrows, since the non-equilibrium systems that generate spontaneous order are "dissipative", that is to say, they are in continuous interaction with their environment, into which they export the entropy that they need to get rid of in order to be able to maintain their internal orderliness. This is the way in which living beings are able to maintain themselves. We breathe out entropy.

Prigogine is convinced of the importance of finding ways to incorporate holistic understanding and a dynamic acceptance of temporality into the fundamental formulations of science. He refuses to treat these properties simply as byproducts of a basically reductionist and reversible reality. Prigogine believes that "no formulation of the laws of nature that does not take into account the constructive role of time can ever be satisfactory". The radical rethinking required goes beyond merely further consideration of relativity and quantum theory. It also demands a radical revision of classical mechanics as well. The result, he believes, will be "the end of certainty", for it will bring about the construction of a thorough-going probabilistic physical theory.

The key steps in Prigogine's argument seem to be a rejection of the individual trajectory account of classical physics, together with a correlated enlargement of the scope of the mathematical entities considered appropriate for use in the formulation of theoretical physics. Classical mechanics, as developed by Newton, was linked with Sir Isaac's wonderful mathematical discovery of the calculus. This latter is a superb tool for the discussion of continuous variations, the kind of smoothly changing entities that we can readily represent by drawing a graph. It has already been recognised that chaotic dynamics has associated with it an altogether more jagged and stuttery behaviour. This finds expression in chaos theory's use of fractals, entities that display the same characteristics at every scale on which they are investigated, resulting in such endlessly proliferating structures as saw-teeth whose edges are themselves saw-toothed ad infinitum, or, more dramatically and aesthetically striking, the infinite riches of the Mandelbrot set as displayed on many a psychedelic poster.

Prigogine's argument proceeds by first moving from the description of a complex set of particles in terms of their separate trajectories, to a collective or ensemble description of the kind used in the formulation of statistical mechanics. If the discussion is restricted to mathematically "nice" functions, of the kind the calculus can accommodate, these two forms of description are equivalent. The holistic account can be reduced to a sum of contributions derived from the set of individual trajectories. If, however, the treatment is generalised to include non-integrable (jagged) functions, then the equivalence is broken. No reduction is possible to separate bits and pieces and, at the same time, the behaviour of the whole is irreducibly probabilistic in its character. In physical terms, this is interpreted as due to the presence in the complex systems of inherent instabilities, generated by resonances (uncontrollably large effects) between their supposedly distinct components. These resonances give rise to persistent and non-localisable interactions.

These difficult issues are clearly and interestingly discussed here for the case of classical mechanics, using the minimum of explicit mathematical technicality. However the implications for quantum theory, though claimed to be highly significant, are nowhere near as adequately set out and it is difficult for the reader to assess exactly what is being proposed. The book concludes with some cosmological speculations. Prigogine tells us of his conviction that "time precedes existence" and this leads him to develop his own version of the fashionable notion that our universe originated as an episodic event in an everlasting vacuum state.

The issues this book addresses are profound, important and highly contentious. We are given a generally accessible account of the ideas of a man who has made significant, but not uncontested contributions to our thinking about time and process. It deserves a wide readership.

John Polkinghorne is a fellow of Queens' College, Cambridge.

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

Author - Ilya Prigogine

ISBN - 0 684 83705 6

Publisher - Free Press

Price - £20.00

Pages - 228

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