The Relation between Complex Fluctuations of the Metric, the Cosmological Constant Problem and Electrodynamics in Einstein's Unified Field Theory

Abstract

The interpretation of Einstein's unified field theory with sources as a gravoelectrodynamics in a polarizable continuum is considered, and the influence exerted on the background stress energy momentum content of spacetime and on the polarizability by complex fluctuations of the metric field is investigated. It is shown that certain assumptions about the fluctuating metric field which comply with the requirement of local Lorentz invariance for freely falling observers simultaneously provide a possible answer to the question of the cosmological constant and ensure that the macroscopic behaviour of weak electromagnetic inductions and fields is just the one occurring in Einstein·Maxweli electrodynamics. We do not believe that Einstein's unified field theory!) is a complete theory, capable of accounting for the behaviour of charged matter through everywhere regular solutions of its field equations. We rather hold the opinion that the tensor quantities on the left-hand sides of those equations provide definitions of properties of charged matter in terms of geometric entities, as it occurs for uncharged matter in the general relativity of 1915, and that the conservation identities express laws imposed on the properties of matter by the non-Riemannian geometric structure of the theory. We introduce a real four-dimensional manifold with coordinates Xi and write 2 ) the definitions of material properties in terms of a nonsymmetric tensor density gik and of a nonsy~metric affinity Til as follows: