Modified Gravity Derived from the Thermodynamics of a U(1) Gauge Symmetry

Jacobson (1995) showed that Einstein's field equations arise as a thermodynamic equation of state from the Clausius relation on local causal horizons. Building on this, we present a framework, Timeflow Gravity, formulating gravitation as an emergent thermodynamic phenomenon driven by the wave mechanics of a U(1) spacetime medium. Spacetime is modeled as a medium carrying a U(1) phase field φ, with the flow of time identified as the field's phase evolution.

Imposing energy and information conservation partitions the field into a coherent, structure-forming sector and an incoherent thermal sector. A variance-sum decomposition of the phase gradient yields a wave-mechanical efficiency function μ governed by the coherence angle θ between matter and the vacuum. Applying the Clausius relation to the partitioned energy flux, we modify Jacobson's derivation to obtain a state-dependent field equation, in which macroscopic curvature is sourced by the ensemble-averaged squared phase gradient.

The field equation decomposes into three components: classical matter, a repulsive cosmological background, and a wave-mechanical interference cross-term. In coherent, rotationally supported galaxies the framework reproduces the universal Radial Acceleration Relation and MOND-like dynamics without dark matter, and it explains the apparent absence of dark matter in dispersion-dominated systems. We present a strictly falsifiable prediction: the intrinsic scatter of the Radial Acceleration Relation correlates directly with the kinematic disorder of the baryonic source, parameterized by cosθ—a signature distinguishing this framework from both ΛCDM and standard MOND, testable with existing SPARC data.