A Continuum Mechanics Formalism of Electrodynamics: Redefining Maxwell's Equations via Elastic Aether Dynamics and Stationary Light Theory

Repository Target: Zenodo (Open Access Open Science Repository) Abstract Classical electrodynamics, while exceptionally successful in engineering applications, relies on reductionist field simplifications that omit the mechanical properties of the vacuum substrate. This paper reconstructs Maxwell’s foundational formulations by modeling the vacuum as an isotropic, high-stiffness elastic continuum (an elastic aether). We integrate Stationary Light Theory (SLT) and the Unified Vortex & Entropy Hypothesis (UVEH), redefining electric charge as volumetric eigenstrain, magnetic potential as local displacement velocity, and vorticity as the magnetic field vector. By embedding these continuous mechanical relations with a Mod 9 invariant and a vacuum fatigue evolution parameter, we resolve longstanding circularities in electrodynamic theory and provide a rigorous predictive framework for macroscopic vacuum-matter interactions, planetary expansion scaling, and structural lattice limits.