Light as Synchronization: Phase Waves, Gauge Fields, and the Kaluza-Klein/Kuramoto Correspondence

This paper develops a structural and partially quantitative correspondence between twohistorically independent theoretical frameworks: the Kaluza-Klein geometric unification ofgravity and electromagnetism, and the Kuramoto model of coupled oscillatorsynchronization. We demonstrate that both frameworks share a common mathematicalsubstrate in U(1) phase dynamics, and that this shared structure permits a reinterpretation ofelectromagnetic phenomena as collective synchronization patterns across spatial points, eachunderstood as a phase oscillator on the compactified fifth dimension. Within this framework,the vacuum state corresponds to global phase synchronization, photons emerge asperturbative phase waves propagating across the synchronized manifold, and electric chargeis reinterpreted as quantized angular momentum along the compact dimension. Going beyondstructural analogy, we show that the inertial (second-order) Kuramoto model on a spatiallattice yields, in the continuum limit, a wave equation for phase perturbations of thesynchronized state, with a finite propagation speed cph = a√(K/m) determined by the couplingstrength K, lattice spacing a, and oscillator inertia m. This provides a concrete dynamicalmechanism for photon propagation within the synchronization picture. We further identify anatural non-Abelian extension through the Lohe model of synchronization on compact Liegroups, establishing a structural correspondence between SU(2) synchronization dynamicsand Yang-Mills gauge theory. The framework offers a novel intuitive account of theobserver-invariance of the speed of light: because observers are themselves embeddedconstituents of the oscillating medium (spacetime), relative motion with respect to themedium is undefined, rendering the propagation speed frame-independent. We situate thework within prior research on emergent gauge fields, the Kuramoto–XY modelcorrespondence, and experimental realizations including Josephson junction arrays andoscillator-network gauge theories, and identify the extension from scalar (site) to vectorial(link) dynamics as the principal open problem.