Relativistic electrodynamics with a universal length scale

TL;DR

This paper develops a relativistic electrodynamics framework incorporating a universal length scale, deriving Dirac and Pauli equations from a modified Klein-Gordon equation, and proposes an experimental test via electron beam split lines.

Contribution

It introduces a novel relativistic electrodynamics model with a universal length scale, deriving fundamental equations and suggesting experimental validation.

Findings

Derivation of Dirac and Pauli equations from a fourth-order Klein-Gordon equation.

Prediction of hyperfine splitting in electron beams.

Observation of particle-antiparticle asymmetry and oriented spacetime effects.

Abstract

We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein--Gordon equation with a universal length scale. Starting from a singularly perturbed variant of Maxwell's equations, we deduce a 32-dimensional variant of the Dirac equation for spin-$1/2$ particles through an algebraic factorization procedure. We illustrate an experimental test of the theory from the split lines of the electron beam in a Stern--Gerlach experiment. This hyperfine splitting leads to four distinct eigenvalues of the spin operator, which can be grouped into two pairs centered around the classic values of $\pm\hbar/2$. The modified electrodynamic framework features particle-antiparticle asymmetry and an oriented, micropolar spacetime.