Relativistic electrodynamics with a universal length scale

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-$1\mathrm{/}2$ 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 $\pm \mathrm{\hslash }\mathrm{/}2$. The modified electrodynamic framework features particle-antiparticle asymmetry and an oriented, micropolar spacetime.