Statistical Time Symmetry and Two-Time Boundary Conditions in Physics and Cosmology

The hypothesis of complete time symmetry in oscillating cosmologies in which there exist locally irreversible processes is examined. A time-symmetric formalism for purely statistical processes is developed, and all aspects of quantum and statistical mechanics are shown to be time-symmetric within this framework. We conclude from analysis of a simple example that in a completely time-symmetric oscillating cosmology, statistical processes which produce entropy in the expanding phase will reverse themselves in the contracting phase, although microscopic reversal of motion need not occur. The analysis provides a self-consistent formalism for general problems involving the coexistence of different entropic directions of time in the observable universe. Boltzmann's $H$ theorem is discussed in this framework.