On the Equivalence Principle and a Unified Description of Gravitation and Electromagnetism

We first investigate the form the general relativity theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence principle for the electromagnetic field. We argue that to each particle with a different electric charge-to-mass ratio in a gravitational and electromagnetic field there corresponds a spacetime manifold whose metric tensor gμν describes the dynamical actions of gravitation and electromagnetism. The possibility of exhibiting gravitation and electromagnetism in a unified geometrical representation has been pursued by many mathematicians and physicists. The first one to seek for a unified explanation of gravitation and electromagnetism was Riemann (see ref.[1]). This endeavor has really started as a full-fledged research area soon after the advent of Einstein’s general theory in 1916 [2]. The gauge-invariant unified theory of Weyl was based on a generalization of Riemannian geometry [3,4]. A generalization of Weyl’s theory was put forward by Eddington [5]. These unsuccessful attempts were followed by Kaluza who sought to include the electromagnetic field by increasing the number of components of the metric tensor by changing the number of dimensions to five [6], whose work was later revived and extended by Klein [7]. Generalizations of Kaluza’s theory were attempted by Einstein and coworkers [8-10]. another line of approach that produced the same field equations as in Kaluza’s theory was that of projective field theories [11,12]. Also worth mentioning is the work of Einstein based on Riemannian metrics and distant parallelism [13]. Since the electromagnetic field is described by a second rank antisymmetric tensor, the idea of employing a nonsymmetric metric tensor gμν whose antisymmetric part is to be associated with electromagnetism was exercised too [14].