Cosmology and the arrow of time

Abstract

THE arrow of time manifests itself in three distinct ways: through the approach to equilibrium in closed systems containing a large number of interacting particles; through the phenomenon of memory in certain open systems; and through the expansion of the observable Universe. The approach to equilibrium in closed systems can occur through a wide variety of physical processes, including not only molecular transport processes like diffusion and conduction but also macroscopic processes like turbulence which convert ordered fields and motions into less highly ordered ones and ultimately into heat. All such processes generate entropy. By contrast, the accumulation and preservation of information about previous states of a system depend upon processes tha t generate information (negative entropy). As for the entropy changes associated with cosmic evolution, it can be argued tha t these too must be negative-in spite of the fact tha t the Universe is, by definition, a closed system, l~or, as will be explained below, there are reasons for believing tha t the structure of the Universe was simpler in the past than it is now. Thus it is clear tha t the second law of thermodynamics does not afford a sufficiently broad framework for an understanding of the arrow of time in all its aspects. I t is equally clear, however, tha t these aspects must be related, for irreversible processes in closed systems, memory in certain open systems, and the evolution of cosmic structure all define the same arrow. And there are indications tha t the three kinds of process are physically connected. For example, it is obvious tha t we cannot hope to understand why different systems show the same arrow so long as we confine our attention to isolated systems. Interactions with the environment play an essential par t in determining the initial conditions for closed systems, and some authors have suggested tha t they continue to play an essential par t in the subsequent development of what are regarded nominally as closed systems. The present communication outlines a unified theory of the arrow of time. Although it requires a ra ther drastic departure from currently accepted cosmological ideas, this theory is consistent with theories of the kind tha t have been developed by van Hove (:) and Prigogine (2) to describe the approach to equilibrium in closed systems. In fact, it clarifies certain assumptions in these theories tha t have previously been regarded as ambiguous or obscure. To fix ideas, let us recall how the transition from a reversible microscopic description to an irreversible macroscopic description is accomplished in non-equilibrium statistical mechanics. In the first place, it is necessary to suppose tha t the microscopic state of the system under consideration is specified by a probability distribution {10k} or, more generally, by a density matrix ~. The information associated with this description is defined by