Gravitational Refraction in Quantum Diffusion: Recovering Schwarzschild Precession from Variable Substrate Diffusivity

In the Quantum Diffusion (QD) framework, spacetime is modeled as an emergent hydrodynamiclimit of an informational substrate with finite relaxation time τ. In this Letter, we extend this framework to include gravitational effects by proposing that the substrate’s diffusivity D is modulatedby the local information density. By adopting a linear ansatz for D(r) in terms of the Newtonianpotential, we demonstrate that the emergent speed of light c(r) = D(r)/τ naturally recovers theSchwarzschild metric components. Furthermore, we show that the resulting effective orbital potential contains the exact 1/r3 correction required to account for the anomalous precession of Mercury’sperihelion. This approach reinterprets gravity not as a geometric curvature of vacuum, but as arefractive effect in a non-homogeneous informational medium.