Irreversibility

‘No one will take me seriously,’ complains the scientific pioneer, exploring far ahead of the pack. We fully sympathise: but it is not easy to ‘take seriously’ a surmise that seems wildly at variance with our comfortable notions of reality. ‘The Earth going round the sun? Fiddlesticks.’ ‘Men descended from Apes? Pshaw!’ ‘Drifting continents? Whatever next?’ How deplorable to scoff, and yet how difficult to pick out the one such idea in a thousand that is not, after all, as wrongheaded as it first seems.

To some degree we must be influenced by the reputation of the proponent. Galileo lost many friendly ears by seeming too clever by half, whereas a modest and sober scholar like Darwin had to be listened to carefully. The relevance of that reputation to the subject in question is also an important factor: many famous scientists have been tempted to blow the trumpet of their idiosyncratic prejudices far beyond their expert knowledge. But Ilya Prigogine won the 1977 Nobel Prize for Chemistry for precisely the sort of theoretical work on which this book is based. He is not only a Professor at both the Free University of Brussels and the University of Texas: he is also a man of wide cultural interests, very energetic and effective in public affairs related to science and education. His novel ideas concerning the time factor in fundamental physical theory must be taken very seriously indeed.

The manner of presentation also affects our response and Professor Prigogine presents his argument impeccably. I thought some of his diagrams were a little schematic, but I do not think he could have made his case in a more pleasing or convincing style.

That is not to say that this is a simple or easy book to understand. Philosophical arguments, expressed verbally, are interwoven with the concepts and theorems of advanced theoretical physics, expressed in the appropriate mathematical form. This mathematical symbolism and terminology is used without affectation or undue elaboration: it is quite essential to the theme of the book. The genuine clarity of its style might not be apparent even to ‘the general reader with some background in physical chemistry and thermodynamics’ to whom the book is somewhat optimistically addressed. The only approach to ‘the mystery of time’ through the physical sciences is a steep and narrow staircase of formal education, winding interminably upward to a viewpoint overlooking the classical quantal and statistical formulations of theoretical mechanics in sophisticated mathematical terms. The central problem is that ‘physical’ time is completely reversible. It is quite unlike ‘psychological’, ‘cultural’ or even ‘biological’ time, in that it has no arrow pointing inescapably from past to future. If we are to believe Newton’s Laws of Motion – and the whole immense apparatus of dynamical theory constructed upon them – ‘time’ is simply a co-ordinate which might equally go one way or the other. That which goes up might equally well be coming down; those things that are being done could as well be being undone. Forward and backward look alike: it just depends on which way you put the film into the projector – not on something intrinsic in the dynamics you portray. Indeed, as Prigogine puts it, the Newtonian universe is static – ‘a universe of being without becoming’ – frozen into a film whose successive frames could be run back and forth, at any speed, by the eternal, omniscient god of Christian theology.

Fortunately, life is not like that. Our deepest experience is of the reality of irreversibility: ‘The rose that once has blown forever dies.’ Running a film backwards produces farcical fantasy, not an acceptable, alternative tale. How can we accept a mathematical theory that seems to contradict this salient fact both of human existence and of the universe within which it has evolved?

The conventional answer to this challenge to classical mechanics was given, about a hundred years ago, by Ludwig Boltzmann, who drew attention to the practical irreversibility of any process generating disorder. For example, when a new pack is opened, the cards are in standard sequence, number by number and suit by suit: shuffle it a few times, and that order is lost. However long you go on shuffling the pack, up to zillions of times, the same sequence will never return: the transition from order to disorder could never be reversed. Yet each particular shuffle step, like each interaction between the particles of a gas or liquid, could perfectly well be run backward without looking absurd. In other words, the apparent asymmetry between past and future in the ordinary macroscopic world of clocks, chrysanthemums, cousins and chronologies is an illusion, and does not necessarily apply amongst atoms, electrons and similar ‘microscopic’ entities.

For almost all practical purposes, this answer has served quite adequately. In particular, Boltzmann showed the formal connection between this vague philosophical notion of growing disorder and the precise thermodynamic principle of ever-increasing entropy which had already been developed to explain an infinite diversity of natural and artificial processes – the weather, steam engines, electric batteries, chemical reactions and so on. One of the most gratifying moments in studying theoretical physics is to learn the proof of ‘Boltzmann’s H-Theorem’, which shows how a statistical approach to mechanics, where one averages over the properties of, say, the vast numbers of atoms in a tiny bubble of gas, leads precisely to the familiar equations between such everyday quantities as pressure and temperature, energy and volume, heat that flows away and work that might be done.

Until recently, Ilya Progogine’s theoretical investigations lay within this well-established paradigm. In particular, he immensely extended our conception of the role of irreversible thermodynamic processes in the natural world. The traditional association of such processes is with boring uniformity, decay and death. We had been warned of the inevitable decline in the temperature of the Sun, of the tendency in all things towards more and more disorder and randomness, culminating in the ‘heat death’ of a universe as empty and cold and dull as the canteen of a redundant factory on a Sunday evening in winter.

But Prigogine showed up the constructive role of such processes as the conduction of heat and electricity, or a succession of chemical transformations within a single fluid medium. Usually, these processes go ahead smoothly and uneventfully, but when they are driven hard, they often generate remarkable spatial patterns, such as the regular ‘streets’ of cumulus clouds that develop by convection on a sunny afternoon; or they may keep stopping and starting, with uncanny regularity, marking out time like a slowly beating heart. In other words, the forms of living beings are not static equilibrium patterns like the rows of atoms in a crystal, but are ordered dynamically and maintained in a steady state by the tremendous irreversible flux of energy from the Sun, passing through every cell in our bodies, to be lost in breath, and warmth, and bodily wastes. In the end, the heat death must surely come – but until then the eating and drinking and kissing need not stop.

This is a profound and inspiring insight whose fundamental truth is slowly diffusing into all branches of physics, chemistry and biology. But now Professor Prigogine wants to go further. The conjectural aspect of this book is the suggestion that the observed asymmetry of time, the familiar irreversibility of all natural phenomena, is more than a ‘statistical illusion’, and derives from some specific mathematical feature of the primary physical laws. At the ‘microscopic’ level, also, there should surely be as much of ‘becoming’ as there is of timeless ‘being’.

The conventional wisdom is certainly vulnerable at one point: Boltzmann’s ‘proof’ of the ‘H-Theorem’ is not quite sound. It is easy to see, for example, that, once in a zillion hands, the pack of cards can be shuffled back into its original order. There is a finite probability that the transition from order to disorder will have been reversed. In practice, this possibility can be discounted, but it cannot be ruled out in principle. This ‘scandal’ at the very heart of theoretical physics has been the theme of much careful research, but never fully resolved.

To exploit this weakness, Prigogine draws upon some quite new work on some quite old problems. The question is: does a dynamical system, such as a planet moving round the Sun or an atom bouncing around in a gas, go through all possible orbits in a more or less random manner, or does it tend, after a while, to repeat some previous path? This turns out to be a subtle question, whose answer depends extraordinarily sensitively on the exact set-up. Some systems are ‘integrable’, and thus effectively predictable. Others are ‘ergodic’, and hence would satisfy the conditions for the H-Theorem fairly well. Sometimes these two types of behaviour are mixed, so that some trajectories are cyclic whilst others are apparently random, depending upon the initial conditions. Think of a squash ball, endlessly bouncing around in a perfectly cubical court: if it were aimed absolutely squarely at one wall, then it would bounce back and forth along a single line – otherwise it would go all over the place, eventually passing through almost every point in space. Or remember the Mikado’s punishment for billiard sharpers – ‘on a cloth untrue, with a twisted cue, and elliptical billiard balls’.

This fascinating field of mathematical physics is only now being systematically explored. It certainly has very important consequences for statistical mechanics at the most fundamental level. But I am not fully convinced by the final steps in Prigogine’s argument that this opens the way to incorporating irreversibility into the basic equations of motion – into every collision between atoms, say, or into the formal description of an unstable elementary particle. He sketches a possible theoretical scheme, first making the standard transition from classical to quantum language and then defining an operator that could be identified physically with ‘entropy’ on the microscopic level. He and his collaborators seem to have made some progress in the mathematical representation of such a scheme, but I simply could not tell, without reference to the detailed literature on this subject, whether it will bear the weight of interpretation that he puts upon it. I am not even sure that I see the necessity for any such development: the essential unpredictability of every quantum process may already have built into it all the irreversibility of time we could ever want. Prigogine here moves from familiar hard ground out onto the thin ice of conjecture.

For the moment, I do not think he is asking us to accept uncritically the whole line of thought which he presents so reasonably and unpretentiously. But we should certainly make the effort to clarify and strengthen it at various points, extending the mathematical analysis and using his conceptual scheme wherever it helps our understanding of these very deep questions. For his part, it will be essential to go beyond a purely formal theory, which only transforms the conventional equations into more relations whose observable consequences are exactly the same as before. We shall be expecting from him some predictions of data or phenomena whose experimental verification might confirm – or disconfirm – his novel and imaginative hypothesis. Until that is done, the verdict on the theme of this book must remain ‘unproven’, for all the pleasure and enlightenment one may get from reading it.