Action-at-a-distance and Cosmology

Abstract

Action-at-a-distance is an alternative approach to eld theory in describing all the interactions. It is based on direct interactions between particles rather than through their coupling to a eld having in nite degrees of freedom. First formulated in a relativistically invariant manner by Schwarzschild, Tetrode and Fokker, action- at-a-distance in electrodynamics was provided a paradigm by Wheeler and Feynman through their absorber theory of radiation. This theory, formulated in static and at universe, uses advanced absorber response from the entire universe as the origin for radiation reaction but allows for both retarded and advanced interactions. In the rst part of this work (section 3), we study extension of this formulation in cos- mological models (using conformal invariance of electromagnetism). Self-consistency of advanced and retarded interactions is investigated in these models. Only those models can be considered to be viable which have only retarded interactions. It is found that steady-state and quasi-steady-state models satisfy this criterion while Friedman models don't. Thus the origin of arrow of time in electromagnetism can be attributed to the cosmological structure. In the second part (section 4), we study the formulation of action-at-a-distance electrodynamics in Riemannian space-times using Green's functions. Green's functions in curved space-times have a compon- ent which corresponds to propagation inside the light cone ( tail ), along with the usual propagation along the light cone. We evaluate the explicit expressions for Green's functions in de Sitter and Einstein-de Sitter space-times. This can be used in evaluating the tail in an electromagnetic signal.