Time symmetric electrodynamics and the arrow of time in cosmology

Abstract

This paper seeks to establish a connexion between the local arrow of time given by the electromagnetic radiation and the cosmological arrow of time given by the expansion of the universe. The Wheeler-Feynman absorber theory of radiation is applied to the expanding cosmological models. First, it is shown that the Schwarzschild-Tetrode-Fokker principle of direct interparticle action can be extended to the general Riemannian space-time. This generalization is considerably simplified in the conformally flat spaces—as all the Robertson—Walker spaces are. In the application of the absorber theory to various cosmological models, the refractive index turns out to play a crucial part. The ambiguities connected with the sign of the imaginary part of the refractive index are resolved if two conditions are fulfilled: (i) a search is made for a self-consistent solution with full retarded (or advanced) solutions (ii) in an elementary theory the origin of the imaginary part of the refractive index is traced to the radiative reaction itself and not to the collisional damping considered by Hogarth. It is shown that full retarded solutions are consistent in the steady-state cosmology and full advanced solutions in the Einstein-de Sitter cosmology. Full advanced solutions are not consistent in the former and full retarded solutions in the latter. Some interesting implications of this result in the C -field approach to the steady-state cosmology are considered.