The Arrow of Time, Entropy and the Expansion of the Universe

Abstract

Setting aside the guidance of consciousness, we discover a signpost for time in the physical world itself. The signpost is a rather peculiar one, and I would not venture to say that the discovery of the signpost amounts to the same thing as the discovery of an objective ‘going on of time’ in the universe. But at any rate it provides a unique criterion for discriminating between past and future, whereas there is no corresponding absolute distinction between right and left. The signpost depends on a certain measurable physical quantity called entropy. Take an isolated system and measure its entropy at two instants t ₁ and t ₂: the rule is that the instant which corresponds to the greater entropy is the later. We can thus find out by purely physical measurements whether t ₁ is before or after t ₂ without trusting to the intuitive perception of the direction of progress of time in our consciousness. In mathematical form the rule is that the entropy S fulfils the law: dS/dt is always positive. This is the famous Second Law of Thermodynamics.