Incompleteness of Classical Electrodynamics and Longitudinal Non-Local Electromagnetic Action as One of the Missing Elements

Abstract

There is no necessity to argue that classical electrodynamics is one of the corner-stones of modern physics and cradle of Relativity. At first stages the development of electromagnetic theory proceeded in accordance with Newtonian traditional outlook on the world. Faraday’s discovery of induction highlighted limited validity of that conception in describing electromagnetic phenomena. A notion of local field was proposed by Faraday not to incorporate but to replace Newtonian action at a distance. As a result, the state of electromagnetism in the middle of the past century was characterized by opposition of a few alternatives and a search for the most adequate one. Among them there were two radically different Weber’s action at a distance and Maxwell’s field approaches on one hand, and, on the other, a compromise theory of Helmholtz who admitted simultaneous coexistence of action at a distance in form of longitudinal instantaneous electric modes with transverse electric and magnetic waves (their velocity was slightly different from that predicted by Maxwell’s theory). Hertz’s discovery of electromagnetic waves excluded definitively Weber’s alternative whereas Maxwell’s as well as Helmholtz’s theory were conceptually consistent with Hertz’s crucial experiment.