On the geometrization of electrodynamics

This paper develops the conjecture that the electromagnetic interaction is the manifestation of the torsion of spacetime. This conjecture is made feasible by the natural separation of the connection ^v into gravitational and electromagnetic parts ^v and ^v , respectively, related to the metric and to the torsion. When ^v is neglected in front of ^v , the affine geodesics are shown to become the equations of motion of charged particles with Lorentz force, for an appropriate choice of . Since ^v contains the factor q/m, neutral particles do not see the torsional part of the connection and behave as if were zero, i.e., as in Einstein's theory of gravity (the same effect is obviously obtained for charged particles when ^{v v} ).In addition to the factor q/m, the velocity of the test particle appears in . This indicates that the appropriate context for this problem is to be found in velocity-dependent connections. The velocities are now coordinates and become the actual velocities of the test particles only in the system of equations that one solves for obtaining the affine geodesics in connections of this type.When written with differential forms, the combination of Maxwell's equations and of the pertinent form of the torsion suggests geometric field equations for electrodynamics. As for the gravitational part of the connection, it can be made to obey equations similar in form to the Einstein field equations. A unified geometric theory of electrodynamics and gravitation spontaneously emerges. The present state of the theory does not yet permit us to ascertain whether the right-hand side of the fully geometric, gravitational field equations corresponds to the energy-momentum tensor.