Coherence as a Geometric Principle: A Potential Unification Path Linking Information Flow, Spacetime Structure, and Quantum Dynamics

We propose a geometric framework in which coherence—defined as the divergence of a 5- dimensional information vector field—acts as a unifying quantity linking spacetime geometry, information flow, and quantum dynamics. A single postulate, the Coherence Flow Principle, asserts that the evolution of physical fields maximizes the rate of increase of a coherence func- tional. From this, a natural Hodge decomposition of the information vector field generates gradient, curl, and harmonic components, giving rise respectively to: (i) coherence-maximizing flow, (ii) rotational or spiral dynamics, and (iii) large-scale geometric structure. A minimal 5D action yields field equations whose Kaluza–Klein reduction reproduces the Klein–Gordon equation in four dimensions and produces the Schr¨odinger equation in the non-relativistic limit. This structure suggests that what appears as quantum behavior in 4D may originate from geo- metric information dynamics in a higher-dimensional setting. We discuss potential implications for unification, including emergent persistence, attractor-like structure, the arrow of time, and the relationship between coherence and curvature.