Teleparallel Space-Time with Defects yields Geometrization of Electrodynamics with quantized Charges

Abstract

In the present paper a geometrization of electrodynamics is proposed which makes use of a generalization of Riemannian geometry considered already by Einstein and Cartan in the 20ies. Cartan's differential forms description of a teleparallel space-time with torsion is modified by introducing distortion 1-forms which correspond to the distortion tensor in dislocation theory. Under the condition of teleparallelism, the antisymmetrized part of the distorsion 1-form approximates the electromagnetic field, whereas the antisymmetrized part of torsion contributes to the electromagnetic current. Cartan's structure equations, the Bianchi identities, Maxwell's equations and the continuity equation are thus linked in a most simple way. After these purely geometric considerations a physical interpretation, using analogies to the theory of defects in ordered media, is given. A simple defect, which is neither a dislocation nor disclination proper, appears as source of the electromagnetic field. Since this defect is rotational rather than translational, there seems to be no contradiction to Noether's theorem as in other theories relating torsion to electromagnetism. Then,congruences of defect properties and quantum behaviour that arise are discussed, supporting the hypothesis that elementary particles are topological defects of space-time. In agreement with the differential geometry results, a dimensional analysis indicates that the physical unit (lenght)^2 rather than As is the appropriate unit of the electric charge.