Retarded potentials and the expansion of the universe

The observed irreversibility of radiation processes is traced to the asymmetry in time of the expanding universe. A similar idea has recently been proposed by Hogarth (1962), who applied the Wheeler-Feynman (1945) theory to various world-models in an attempt to discriminate between advanced and retarded potentials. Hogarth found that, while the steady-state model leads to the required retarded potentials, the Einstein-de Sitter model leads to advanced potentials. In addition to disagreeing with observation, this latter result implies that a uniform distribution of galaxies can give rise to an infinite intensity of radiation. By contrast, we work with the conventional Maxwell theory. By using Kirchhoff’s boundary-value formulation of this theory, the boundary conditions appropriate to nonstatic world-models can be introduced. Among the consequences of these boundary conditions are: (i) In the Einstein-de Sitter model there exist distributions of sources for which Maxwell’s theory leads to retarded potentials (but, in addition, to an arbitrary amount of source-free radiation). In these cases the Wheeler-Feynman theory breaks down. The actual galaxies may constitute such a distribution. (ii) In the steady-state model Maxwell’s theory is equivalent to the Wheeler-Feynman theory, and leads to retarded potentials. In this case there is no source-free radiation, in agreement with the (somewhat crude) observational data.