A Derivation of the Classical Einstein-Dirac-Maxwell Equations From a Model of an Elastic Medium

TL;DR

This paper derives the coupled Einstein-Dirac-Maxwell equations from an elastic medium model, providing a novel physical interpretation of these fundamental equations in a new theoretical framework.

Contribution

It introduces a new derivation of Einstein-Dirac-Maxwell equations from an elastic medium model, linking classical elasticity to fundamental particle interactions.

Findings

Derived coupled Einstein-Dirac-Maxwell equations from elastic medium model

Obtained a 2D version by Fourier mode analysis in a periodic dimension

Discussed potential generalizations to higher dimensions

Abstract

Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to electromagnetic and gravitational type of interactions. A two dimensional version of these equations is obtained by starting with a model in three dimensions and deriving equations for the dynamics of the lowest fourier modes assuming one dimension to be periodic. Generalizations to higher dimensions are discussed.