Relativistic electrodynamics with a universal length scale

• URL: http://arxiv.org/abs/2507.08872v2
• Date: Mon, 21 Jul 2025 02:57:26 GMT
• Title: Relativistic electrodynamics with a universal length scale
• Authors: Tiemo Pedergnana, Florian Kogelbauer,
• Abstract summary: We derive the analogues of the Dirac and Pauli equations from a spatially fourth-order Klein-Gordon equation with a universal length scale.<n>We illustrate an experimental test of the theory from the split lines of the electron beam in a Stern--Gerlach experiment.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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