A Derivation of Dirac's Equation From a Model of an Elastic Medium

TL;DR

This paper derives Dirac's equation from an elastic medium model, showing that mass and electromagnetic interactions naturally emerge without being manually inserted, and explores extensions to higher dimensions.

Contribution

It introduces a novel physical model that derives Dirac's equation and its interactions from elasticity theory, providing a new perspective on fundamental particle equations.

Findings

Dirac's equation derived from elastic medium model

Mass and electromagnetic terms emerge naturally

Two-dimensional version obtained from Fourier mode analysis

Abstract

Starting from a model of an elastic medium, we derive equations of motion that are identical in form to Dirac's equation for a spin 1/2 particle with mass, coupled to electromagnetic and gravitational interactions. The mass and electromagnetic terms are not added by hand but emerge naturally from the formalism. A two dimensional version of this equation is derived 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.