Classical and extended electrodynamics

Abstract

Classical electrodynamics is modeled by Maxwell’s equations, as a system of eight scalar equations in six unknowns, thus appearing to be overdetermined. The no-magnetic- monopoles equation can be derived from the divergence of Faraday’s law, thus reducing the number of independent equations to seven. Derivation of Gauss’ law requires an assumption beyond Maxwell’s equations, which are then overdetermined as seven equations in six unknowns. This overdetermination causes well-known inconsistencies. Namely, the interface matching condition between two different media is inconsistent for a surface charge and surface current. Also, the irrotational component of the vector potential is gauged away, contrary to experimental measurements. These inconsistencies are resolved by extended electrodynamics (EED), as a provably unique system of 7 equations in 7 unknowns. This paper provides new physical insights into EED, along with preliminary experimental results that support the theory.