Geometrical unification of gravitation and electromagnetism

Abstract

A theory which unifies gravitation and electromagnetism (GUGE) is presented. This new theory is based on a recent redefinition of proper time. The 5-dimensional metric which arises is similar but not equivalent to the Kaluza-Klein (KK) one. Differences follow. The GUGE metric is deduced while the KK metric is postulated. In the GUGE field theory there is no need to impose either the "cylinder" or "curling of coordinates" conditions, because they are direct consequences of the GUGE formalism. The GUGE field equations are fully equivalent to Einstein-Maxwell equations, while KK field equations are not. The GUGE 5-dimensional (geodesic) equations are equivalent to the 4dimensional (non-geodesic) equations for a charged particle moving in the presence of gravitational and electromagnetic fields, unlike the KK 5-dimensional (geodesic) equations which are not. No extra scalar field appears in GUGE. The physical interpretation of the fifth dimension and of the role of the extra field in KK (internal coordinate in GUGE) are totally different in both approaches. Finally, GUGE results include electric charge conservation, electric charge quantization and electric charge contribution to the energy of charged particles even in the absence of electromagnetic fields, which implies (the observed fact) that there are no massless electrically charged particles in Nature, unlike the prevailing treatments of KK theories.