Abstract

Maxwell's equations possess a certain generic structural property which is well-known, but rarely discussed. By considering this property as primary, we are able to derive the complete mathematical structure of Maxwell's equations described in terms of the orthogonality properties defined between certain spaces of linear operators. But, we find that the classical theory, whilst recovered intact here, is incomplete in the sense that the recovered Maxwell field is irreducibly associated with an additional massive vector field. In the overall context, this massive vector field can only be interpreted as a manifestation of a classical massive photon. One immediate consequence is that the Lorentz force law must be generalized and can be trivially made perfectly Newtonian once the massive vector field is accounted for.