Unified Electromagnetic and Gravitational Geometrodynamics from Phase Harmony and Fermi-Walker Transport

We prove that standard electromagnetism precisely originates from local spacetime geometrodynamics, without postulating gauge invariance, in a way that is complementary and unified with respect to ordinary gravitational geometrodynamics. According to the Hamilton–Jacobi optomechanical analogy ("phase harmony"), interactions admit a dual reading: dynamically, as local changes of four-momentum; geometrically, as local modulations of spacetime recurrences. Spacetime curvature induces redshift and ruler deformation, resulting in gravitational interaction. In parallel, position-dependent local isometries, implemented as Fermi–Walker transport of tetrads, induce precession in particle’s dynamics. The corresponding abelian holonomy defines a $U(1)$ connection and yields electromagnetism, with the Lorentz force appearing as a Coriolis-like effect. This construction also introduces an $S^1$ fiber attached to every spacetime point and thus the Maxwell kinetic term from a purely 4D reinterpretation of the Kaluza-Klein mechanism. Electromagnetic effects, such as Larmor/Thomas precession, Zeeman effect, synchrotron radiation, gravitomagnetism, are consistently described within this geometrodynamical scheme.