The R.I. Pimenov unified gravitation and electromagnetism field theory as semi-Riemannian geometry

TL;DR

This paper develops a unified field theory of gravitation and electromagnetism using semi-Riemannian geometry, which models different physical quantities as distinct geometrical objects within a fibered space, avoiding issues of traditional Kaluza-Klein theories.

Contribution

It introduces a semi-Riemannian geometric framework for unifying gravity and electromagnetism, differing from Kaluza-Klein models by avoiding scalar fields and related defects.

Findings

Semi-Riemannian geometry models multiple physical quantities as distinct geometrical objects.

The theory provides a unified description of gravitation and electromagnetism.

It overcomes the scalar field issues present in Kaluza-Klein theories.

Abstract

More then forty years ago R.I. Pimenov introduced a new geometry -- semi-Riemannian one -- as a set of geometrical objects consistent with a fibering $ pr: M_n \to M_m.$ He suggested the heuristic principle according to which the physically different quantities (meter, second, coulomb etc.) are geometrically modelled as space coordinates that are not superposed by automorphisms. As there is only one type of coordinates in Riemannian geometry and only three types of coordinates in pseudo-Riemannian one, a multiple fibered semi-Riemannian geometry is the most appropriate one for the treatment of more then three different physical quantities as unified geometrical field theory. Semi-Euclidean geometry $^{3}R_5^4$ with 1-dimensional fiber $x^5$ and 4-dimensional Minkowski space-time as a base is naturally interpreted as classical electrodynamics. Semi-Riemannian geometry $^{3}V_5^4$ with the general relativity pseudo-Riemannian space-time $^{3}V^4,$ and 1-dimensional fiber $x^5,$ responsible for the electromagnetism, provides the unified field theory of gravitation and electromagnetism. Unlike Kaluza-Klein theories, where the 5-th coordinate appears in nondegenerate Riemannian or pseudo-Riemannian geometry, the theory based on semi-Riemannian geometry is free from defects of the former. In particular, scalar field does not arise. PACS: 04.50.Cd, 02.40.-k, 11.10.Kk