Electrodynamic Spacetime Relativity: Extending Special Relativity and Maxwell's Equations based on the Electric Potential Limit Constant

 Abstract: This paper introduces the electric potential limit constant as a hypothesized new fundamental physical constant and explores its consequences for spacetime structure and classical electrodynamics. Based on the intrinsic symmetry between this constant and the intrinsic speed of light, the spacetime framework of Special Relativity is extended from the real domain to the complex and biquaternion domains, leading to a nine-dimensional spacetime framework termed Electrodynamic Spacetime Relativity (ESR). Within this formulation, standard Special Relativity and Electric Potential Relativity naturally emerge as two limiting sectors of a more general structure.

On this basis, a nonlinear electromagnetic framework compatible with Electric Potential Relativity is developed. Within the assumptions of the present model, the theory is formulated to preserve generalized gauge invariance while retaining the absolute invariance of electric charge and the fine-structure constant. The resulting modified Coulomb's law predicts a nonclassical short-distance behavior of the effective interaction. For the idealized point-charge model considered here, the corresponding electric field self-energy is naturally regularized to a finite value. This provides a rigorous geometric resolution to this long-standing fundamental difficulty in classical electrodynamics.

The framework also predicts macroscopic electric-potential-induced time dilation, redshift, and lensing-like effects, suggesting concrete experimental tests, including the concepts of an electric-potential telescope and an electric-potential Michelson interferometer. Possible implications for further extensions toward gravitation and quantum-scale physics are briefly discussed.

Keywords: Electrodynamic Spacetime Relativity; Electric Potential Relativity; electric potential limit constant; nonlinear Maxwell equations; idealized point-charge model; generalized gauge invariance.