A new linear theory of light and matter

A new theory is proposed with similar form and mechanics to the Dirac equation, but where the rest-mass is introduced in a more fundamental way. The new theory proves to encompass and extend classical electromagnetism, and reduce to it exactly in the field only case. A sharpening of the principle of relativity allows fully relativistic field only solutions, which take on some of the properties more usually associated with quantised states. The extended theory has four new solutions which exhibit a non-zero electric field divergence and a double-covering symmetry. These are necessarily charged, essentially fermionic states, two with positive and two with negative charge, differing by an inner spin symmetry. The new configurations are identified with the spin “up” and spin “down” electron and positron.