Relativistic electrodynamics with a universal length scale

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 ±ℏ/2. The modified electrodynamic framework features an oriented, micropolar spacetime.