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Paul Davies is certainly one of the most successful and influential science writers of our time. I have followed his books with great interest. Moreover he has edited a collection of essays, The New Physics (1984), which provides an excellent introduction to the main problems confronting today's physics. I therefore started to read his latest book, About Time, with great expectations. I must confess that I was disappointed.

My puzzle started with the comment, "When scientists began to explore the implications of Einstein's time for the universe as a whole, they made one of the most important discoveries in the history of human thought: that time, and hence all physical reality, must have had a definite origin in the past." Is this really so?

Davies is of course referring to the "Big Bang". We do indeed believe, since the discovery of the black body residual radiation 30 years ago, that the universe began in a state of high density and high temperature. But was this the beginning of time? There are many other possibilities compatible with this particular observation. For example the Big Bang could correspond to an instability leading to a phase transition from a pre-universe often called the "quantum vacuum" or the "meta-universe". After all, science generally deals with questions concerning classes of events, such as the birth of galaxies or of stars. The answers to such questions require the solution of the famous (or infamous) quantum gravity problem. It is premature to speak of the beginning of time as a "discovery" in the same sense that we speak of the "discovery" of the electron or the proton.

In chapter 2, "Time for a change", Davies writes:"In fact the very division of time into past, present and future seems to be physically meaningless." This conclusion is meant to be a consequence of Einstein's special relativity. But the distinction between past and future is an essential element of the Minkowski spacetime interval with respect to orthochronous Lorentz transformations. Davies's statement becomes even more opaque when he goes on to write, "this does not preclude our distinguishing in an absolute way between past and future directions in time". In order to reconcile these two statements, Davies speaks of two "subtly different ways". I have difficulty in following his argument. Special relativity simply expresses the idea that the laws of nature are identical for inertial observers moving at constant velocity with respect to each other: for each observer the distinction between past and future remains valid.

The vocabulary used throughout the book gives me a feeling of uneasiness. Chapter 4 is entitled "Black holes: gateways to the end of time", with subsections entitled "Warp factor infinity, a dark mystery", "Penetrating the magic circle", "A singular problem", "Beyond the end of time", "Are they really out there?" These are typical; and we hear also of "spooky signals" and "psychic particles".

This may be a question of taste, but on other matters Davies seems unaware of recent developments. In chapter 7, on "Quantum time", there is a section on "Watched kettles". Davies writes: ". . . if you look at the atom closely and continuously, . . . the very act of observation itself interferes with the decay processes." This is a most confusing statement. Both in classical and quantum physics the time evolution is determined by the Hamiltonian H (that means the total energy expressed in terms of coordinates and momenta; in quantum mechanics H is an operator). Is Davies implying that independently of the Hamiltonian the act of observation changes the time evolution? This was indeed the conclusion reached by W. M. Itano, D. J. Heinzen, J. J. Bollinger and D. J. Wineland in 1990 (in Physical Review). But subsequently various authors (including the author of this review) showed that the interesting effects observed by Itano et al can be deduced by conventional quantum mechanics, taking into account the modification of the Hamiltonian of the original system needed for the observation of the decay processes. As a result Itano et al retreated in 1991. No quantum mechanical "watched kettle effect" has been observed as of now.

After describing the "dark mystery of time" over most of the book, Davies comes to the crux only near the end. "It seems to me . . . there is an aspect of time of great significance that we have so far overlooked in our description of the physical universe." He means the aspect associated with the arrow of time. For Davies there are two camps, one of which claims that the orthodox laws of nature are wrong and the other which maintains that the answer lies in quantum physics and the "still mysterious processes in the brain".

He places the reviewer in the first camp, referring to my book From Being to Becoming. However I have never made such a claim. Indeed in my view the arrow of time is not a universal property. There is no reason to modify either the Newtonian description for integrable systems such as the sun-earth motion or the quantum mechanical description of harmonic oscillators. Irreversibility, the arrow of time, appears only at a certain level of "complexity" (eg resonances in non-integrable systems, deterministic chaos). These specific features have to be taken into account in the formulation of any microscopic theory of irreversible processes. The difficulty associated with irreversibility lies in the fact that the conventional formulation of the laws of physics does not take into account the breaking of time symmetry. Now, though, we are beginning to see the direction along which this difficulty may be overcome.

A simple instance, known for some years, are Gamow vectors, in which radioactivity manifests itself in the form of strictly exponential decay - something which is impossible, according to the conventional formulation of quantum mechanics. More generally, once instabilities and resonances are incorporated into the dynamical formulation, the dynamical groups - in which past and future are indistinguishable - are transformed into semi-groups, in which the time symmetry is broken (see, for instance my Les Lois du Chaos, 1994). This requires appropriate mathematical tools; we have to consider more general classes of functions ("rigged" Hilbert spaces, Gelfand spaces) than the "nice" functions (Hilbert spaces) of traditional quantum mechanics.

In short the basic laws of physics when applied to unstable dynamical systems break the symmetry between past and future, which leads to a probabilistic formulation. The basic laws no longer describe certainties but possibilities, as is appropriate for our evolving universe.

This is not the place for more detail. In my view two recent fields of physics and mathematics are essential for the scientific understanding of time. They are non-equilibrium physics which illustrates the constructive role of time and irreversibility, and which thereby leads to dissipative structures, self-organisation and the theory of dynamical systems. None of these is discussed by Davies.

It is indeed an urgent task to combine the results obtained in these fields with Einstein's general relativity. In this sense Davies's subtitle about "Einstein's unfinished revolution" acquires meaning. To "complete" Einstein's revolution we need a satisfactory solution of the quantum gravity problem (a version of the "unified theory" which was Einstein's supreme goal), but in addition we need a theory including the flow of time in order to take into account the evolutionary patterns of the universe.

I believe that some progress towards this theory has been realised. In Einstein's general relativity, which forms the theoretical basis of modern cosmology, one particular degree of freedom plays a special role - the "conformal factor" (see J. V. Narlikar and T. Padmanabhan, Gravity Gauge Theories and Quantum Cosmology, 1986). In simple cosmological models the spacetime interval is equal to the conformal factors multiplied by the Minkowski spacetime interval from special relativity. Now the conformal factor leads to negative energy, while matter is characterised by positive energies (remember Einstein's formula E = mc2!). This opens up some fascinating possibilities studied by many authors (among others E. P. J. Tryon, R. Brout, F. Englert, E. Gunzig, P. Nardone, and Padmanabhan) leading to irreversible processes that transform the negative gravitational energy into positive energy matter.

The difficulty with this approach has been that it was developed within the framework of classical (non-quantum) gravity. But very recently the quantum version of this model has been obtained (by V. V. Kocharovsky and Vl. V. Kocharovsky). Its basic difference from the usual quantum field theory is that there is no stable ground state. Remarkably enough this theory is renormalisable and singularity free. This suggests the possibility, to be confirmed in the near future, of a unified theory still including the arrow of time. Its concept of the universe (or of the meta-universe) is different: it is a universe which contains the cause of its non-equilibrium state. Usually non-equilibrium can be maintained only in open systems, hence the universe appears to be a "self-excitatory system". In this view the arrow of time would be eternal.

This picture of time is radically different from that advanced by Davies who, as already mentioned, believes in a definite origin of time. No final conclusion can be drawn. The problem of time's "origin" may stay with us still for a long time, perhaps forever. But it is important to know that at present various options for understanding it are open.

Ilya Prigogine, a Nobel laureate in chemistry, is director, Solvay Institutes for Physics and Chemistry, in Brussels, and director, Ilya Prigogine Center for Statistical Mechanics and Thermodynamics, University of Texas at Austin.