Timeflow Gravity: A Thermodynamic Theory of Spacetime

This paper presents Timeflow Gravity (TG), a framework in which gravity emerges as a thermodynamic, entropic force driven by the wave mechanics of a continuous $U(1)$ spacetime medium. Building on T. Jacobson’s derivation of Einstein’s equations from the Clausius relation, we derive the Einstein field equations as an emergent macroscopic equation of state. Within this framework, we interpret dark matter and dark energy effects as wave-mechanical projections of the underlying phase space. At galactic scales, constructive phase interference between baryonic matter and the vacuum recovers MOND-like dynamics. By incorporating kinematic phase decoherence, the theory offers a potential resolution to MOND’s mass discrepancy in galaxy clusters, as well as the spatial offset observed in the Bullet Cluster. On cosmological scales, conservation of the one-dimensional topological phase boundary yields parameter-free matter and vacuum density parameters, offering a possible resolution to the cosmological coincidence problem. This result yields a dynamical dark energy equation of state (\( w \approx -0.84 \)) consistent with recent DESI observations. Finally, we establish a falsifiability criterion: the intrinsic scatter of the Radial Acceleration Relation (RAR) should systematically anti-correlate with the local macroscopic kinematic entropy of the system.