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

This paper develops a structural and partially quantitative correspondence between two
historically independent theoretical frameworks: the Kaluza-Klein geometric unification of
gravity and electromagnetism, and the Kuramoto model of coupled oscillator
synchronization. We demonstrate that both frameworks share a common mathematical
substrate in U(1) phase dynamics, and that this shared structure permits a reinterpretation of
electromagnetic phenomena as collective synchronization patterns across spatial points, each
understood as a phase oscillator on the compactified fifth dimension. Within this framework,
the vacuum state corresponds to global phase synchronization, photons emerge as
perturbative phase waves propagating across the synchronized manifold, and electric charge
is reinterpreted as quantized angular momentum along the compact dimension. Going beyond
structural analogy, we show that the inertial (second-order) Kuramoto model on a spatial
lattice yields, in the continuum limit, a wave equation for phase perturbations of the
synchronized state, with a finite propagation speed cph = a√(K/m) determined by the coupling
strength K, lattice spacing a, and oscillator inertia m. This provides a concrete dynamical
mechanism for photon propagation within the synchronization picture. We further identify a
natural non-Abelian extension through the Lohe model of synchronization on compact Lie
groups, establishing a structural correspondence between SU(2) synchronization dynamics
and Yang-Mills gauge theory. The framework offers a novel intuitive account of the
observer-invariance of the speed of light: because observers are themselves embedded
constituents of the oscillating medium (spacetime), relative motion with respect to the
medium is undefined, rendering the propagation speed frame-independent. We situate the
work within prior research on emergent gauge fields, the Kuramoto–XY model
correspondence, and experimental realizations including Josephson junction arrays and
oscillator-network gauge theories, and identify the extension from scalar (site) to vectorial
(link) dynamics as the principal open problem.