Classical Kaluza-Klein description of the hydrogen atom

Abstract

The vacuum field equations of the classical five-dimensional Kaluza-Klein theory are solved for a static, spherically symmetric system. It is shown that the projection of the solution into four-dimensional space-time represents the Reissner-Nordstrom solution and that the five-dimensional geodesic equation of a properly chosen free particle represents the equation of motion of an electron in the field of a proton, as given by the Einstein-Maxwell equations. The electrical field of a charged particle is interpreted as the rotational inertial-dragging field outside a rotating particle in five-dimensional space-time.