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  • Open Access

Relativistic electrodynamics with a universal length scale

Tiemo Pedergnana*

Florian Kogelbauer

  • Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland and Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

  • Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland

  • *Contact author: tiemop@mit.edu
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Phys. Rev. Research 7, 033171 – Published 20 August, 2025

DOI: https://doi.org/10.1103/1fj9-qccb

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.

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Phys. Rev. Research 7, 033171– Published 20 August, 2025
  • Received 19 February 2025
  • Accepted 8 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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