Research Introduction

Maxwell’s equations [1] and Special Relativity [2] together constitute one of the central foundations of modern theoretical physics. Their mutual consistency has profoundly shaped the modern understanding of fields, spacetime, and electromagnetic interactions. However, within classical electrodynamics, the idealized point-charge model gives rise to a long-standing difficulty: the electric potential and electric field diverge at the charge center, and the corresponding electromagnetic field self-energy becomes divergent [3, 15]. This self-energy problem remains one of the most persistent conceptual difficulties in the classical description of charged particles.

Quantum Electrodynamics (QED) addresses these divergent terms through renormalization procedures, achieving extremely accurate agreement with experiment. Nevertheless, renormalization does not by itself provide a geometric or spacetime-level explanation for the origin of these divergences in the idealized point-charge model. As emphasized by Dirac [4], the subtraction of infinities, although operationally successful, leaves open the question of whether a deeper structural reformulation may exist. This motivates a rigorous re-examination of electromagnetic theory at a more fundamental theoretical level.

In this paper, the electric potential limit constant, denoted by , is introduced as a hypothesized new fundamental physical constant. The central idea is that electric potential, much like velocity in Special Relativity, may possess an intrinsic upper bound. The purpose of this hypothesis is not to claim an experimentally established constant at the outset, but to thoroughly investigate the theoretical consequences of assuming such a bound for spacetime structure and classical electrodynamics. Within the idealized point-charge model considered here, this assumption logically leads to a finite upper bound for the potential, thereby yielding a finite electromagnetic field self-energy.

Based on this hypothesis, 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, velocity-based relativity (Special Relativity) and electric-potential-based relativity (Electric Potential Relativity) naturally emerge as two limiting sectors of a broader unified structure. On this basis, a nonlinear electromagnetic framework compatible with Electric Potential Relativity is developed. In contrast to the Born–Infeld theory [5] and the Heisenberg–Euler theory [6], which introduce nonlinearity phenomenologically through modified electromagnetic Lagrangians, the present construction is strictly motivated by the covariance requirements of the proposed high-dimensional spacetime framework.

Within the assumptions of the present model, the resulting theory is formulated to preserve generalized gauge invariance while retaining the absolute invariance of electric charge and the fine-structure constant. The modified Coulomb's law exhibits a nonclassical short-distance behavior of the effective interaction; consequently, for the idealized point-charge model considered here, the electromagnetic field self-energy is naturally regularized to a finite value. The framework also predicts macroscopic electric-potential-induced time dilation, redshift, and lensing-like effects, suggesting concrete experimental tests. Possible implications for further extensions toward gravitation and quantum-scale physics are briefly discussed, though these broader issues remain beyond the main scope of the present paper. 

The remainder of this paper is organized as follows. Section 2 introduces the hypothesis of the electric potential limit constant and develops the Electrodynamic Spacetime Relativity framework. Section 3 derives the corresponding nonlinear Maxwell's equations and discusses their main physical consequences. Section 4 presents concepts for possible experimental verification and astronomical observation. Section 5 summarizes the main results, and finally, Section 6 outlines directions for further investigation.