Unified Electromagnetism in Time-Scalar Field Theory (TSFT): Temporal Curvature, Vorticity, and the Mechanical Origin of Charge and Magnetism

Building on Farrell (2025), which derived Newtonian kinematics directly from temporal curvature, this paper reformulates electromagnetism as a mechanical manifestation of the scalar time field Θ(x) on the compact two-boundary manifold M4. Electric and magnetic fields emerge as shear and torsion modes of Θ, respectively, while charge and current correspond to curvature defects and temporal flux. Five theorems and supporting lemmas show that Maxwell’s equations, electromagnetic energy, and circuit dynamics arise as corollaries of the ten TSFT axioms, supplemented by a single Electrodynamic Axiom E1. The flat Θ limit reproduces classical electrodynamics exactly, while curved Θ predicts small but measurable scalar–vector couplings in strong-gravity or high-frequency regimes.