Electrodynamics of direct interparticle action. I. The quantum mechanical response of the Universe

Abstract

The present paper is the first of a series that seeks to obtain results in agreement with experience from a completely time-symmetric electromagnetic theory—i.e. which does not permit an ad hoc restriction to retarded solutions of time-symmetric equations. It is remarkable that the development of a wholly time-symmetric theory must be along lines entirely different from the usual electrodynamics. While a first quantisation of the particles can readily be carried out, there can be no separate quantisation of the field, since the field is wholly determined by the particles. This raises the question of how practical results that have hitherto been thought to arise from field quantisation can be obtained. The most immediate problem of this kind concerns the spontaneous transitions of atoms. Much of the present paper is directed toward showing that this problem can indeed be solved without the need for field quantisation. Although this question might appear simple compared to other issues in quantum electrodynamics— e.g. vacuum polarisation— it is not trivial in its implication, for the establishment of one such case provides a critical precedent. The path integral method of first quantisation is used to demonstrate that provided the Universe is a perfect absorber along the future light cone the usual formulae for level shifts and for spontaneous transitions can be obtained in a steady-state model of the Universe, but not in open Friedmann models.