Direction of Time

Abstract

Time is directed, which is often thought to conflict with the fact that all laws in fundamental physics are symmetric under time reversal. This is however a confusion of two concepts. That time is directed is reflected in the asymmetry of the predicates ‘before’ and ‘after’. A reversal of the time parameter in physics, on the other hand, is a mere change of convention, from labelling later times with bigger numbers, to labelling them with decreasing numbers. Just as the directions of axes in spatial coordinate systems are mere conventions, the direction of the time axis is a mere convention and it is a fundamental requirement that fundamental physics be invariant under changes of such conventions. We can in many cases easily decide which of two events occurred before the other one without having any time measuring device or any memory of these events. Many physical systems change state irreversibly, this is the basis for the asymmetry of the predicates ‘before’ and ‘after’. It is further shown that a universal direction of time does not require any universal clock undergoing irreversible changes. It suffice that there are a number of partly isolated physical systems, each existing for some time and undergoing irreversible changes. If they partly overlap in time we can construct a universal time parameter beginning with Big Bang. A universal time direction can thus be constructed without using the second law of thermodynamics.