Model of embedded spaces: the field equations

TL;DR

This paper extends the Model of Embedded Spaces using relativistic Finslerian geometry, deriving Einstein-Maxwell type equations that geometrize classical electrodynamics and matter sources, confirming Clifford's ideas.

Contribution

It derives the field equations of MES with relativistic Finslerian geometry, completing the geometrization of classical electrodynamics and matter sources.

Findings

Derivation of Einstein and Maxwell type equations for MES

Geometrization of field sources and matter

Confirmation of Clifford's field hypothesis

Abstract

A study of the Model of Embedded Spaces (MES) with a relativistic version of Finslerian geometry is continued. The field equations of the MES (Einstein and Maxwell types) are derived, and this formally completes geometrization of classical electrodynamics. The minimal action principle leads to geometrization of the field sources (the right-hand sides of the equations) and, as a consequence, to a field hypothesis of matter, a direct confirmation of W. Clifford's ideas.