This paper presents a scalar-tensor extension of General Relativity in which the gravitational coupling strength depends on a coherence field C (x, t) that quantifies the degree of phase synchronization in an underlying complex scalar field ψ. The effective gravitational coupling takes the form Gₑff = G₀⟨C⟩, where ⟨C⟩ is a spatially averaged coherence that ranges from 0 (complete phase disorder) to 1 (perfect synchronization). The coherence field is sourced by the squared phase gradient |∇θ|², coupling gravitational strength to organizational structure. The theory recovers General Relativity when C = 1 and satisfies solar system constraints in gravitationally bound, organized systems where C ≈ 1. The central prediction is structure-dependent: at fixed baryonic mass, galaxies with higher morphological coherence (symmetric spirals with organized rotation) should exhibit stronger effective gravitational coupling, and therefore larger inferred dark matter fractions, than morphologically disordered systems (irregular galaxies). A testing protocol is developed using three independent coherence measures (kinetic organization ratio, rotational symmetry, and rotation curve smoothness) applied to mass-matched galaxy pairs in the SPARC database of 175 disk galaxies with Spitzer photometry and resolved rotation curves. The field equations are derived from a Hamiltonian Hψ, C, recovery of the Einstein field equations is demonstrated in the appropriate limit, and specific falsification criteria are defined.
Scott Costello (Sun,) studied this question.