Confinement in Einstein's unified field theory

Abstract

After recalling the mathematical structure of Einstein's Hermitian extension of the gravitational theory of 1915, the problem, whether its field equations should admit of phenomenological sources at their right-hand sides, and how this addition should be done, is expounded by relying on a thread of essential insights and achievements by Schrödinger, Kursunoglu, Lichnerowicz, Hély and Borchsenius. When sources are appended to all the field equations, from the latter and from the contracted Bianchi identities a sort of gravoelectrodynamics appears, that totally departs from the so called Einstein-Maxwell theory, since its constitutive equation, that rules the link between inductions and fields, is a very complicated differential relation that allows for a much wider, still practically unexplored range of possible occurrences. In this sort of theory one can allow for both an electric and a magnetic four-current, which are not a physically wrong replica of each other, like it would occur if both these currents were allowed in Maxwell's vacuum. Particular static exact solutions show that, due to the peculiar constitutive equation, while electric charges with a pole structure behave according to Coulomb's law, magnetic charges with a pole structure interact with forces not depending on their mutual distance. The latter behaviour was already discovered by Treder in 1957 with an approximate calculation, while looking for ordinary electromagnetism in the theory. He also showed that in the Hermitian theory magnetic charges of unlike sign mutually attract, hence they are permanently confined entities. The exact solutions confirm this finding, already interpreted in 1980 by Treder in a chromodynamic sense.