The Principle of Equivalence, electrodynamics and General Relativity

Abstract

It is shown that the customary covariant formulation of electrodynamics in General Relativity is incompatible with the Einstein Principle of Equivalence. This is demonstrated for the case of a resistanceless current-carrying wire in a static spherically symmetric gravitational field—where the Einstein Principle of Equivalence implies the existence, in the vicinity of the wire, of a non-zero component of the electric field parallel to the wire, whereas the covariant form of Maxwell's equations does not. An experiment, involving a superconducting current-carrying wire segment placed in the Earth's gravitational field, is suggested. Whether or not a component of electric field parallel to the wire, at a point in the wire's vicinity, would be detected would resolve the issue.