Bootstrapping Physics from Stationary Stochastic Processes: From the Fokker-Planck Equation to Quantum Mechanics, Thermodynamics, and General Relativity

This preprint presents a unifying framework that derives the mathematical structures of quantum mechanics, thermodynamics, and general relativity from the stationary Fokker-Planck (FP) equation under the Klimontovich-Hänggi consistency condition. By extending the diffusion coefficient to a complex, self-referential variable and identifying the coordinate with the log-odds of the probability it describes, the author demonstrates how the FP equation contains the structural apparatus of modern physics. Key results include: The Wick rotation as the unique solution preserving unitarity and self-consistency. The emergence of 3+1 dimensional Minkowski spacetime through a double Wick rotation for three perspectives. A complete thermodynamic framework: energy, temperature, all four laws of thermodynamics, the Landauer identity, and Verlinde’s entropic force. The derivation of the full nonlinear Einstein equation via Jacobson’s theorem, with all prerequisites verified. The emergence of U(1) gauge symmetry and spin-½ fermions from the Dirac operator on the Fisher sphere, yielding parameter-free mass ratios. A geometry-matter separation for three or more perspectives that mirrors general relativity, with the origin of nonlinearity traced to the self-referential feedback loop of the formalism. The framework is dimensionless, requiring only a single external scale to connect to experiment, from which fundamental constants such as Planck’s constant, the speed of light, and Newton’s gravitational constant emerge as dependent quantities. The paper also discusses testable predictions, including parameter-free numbers and structural constants, as well as open questions regarding the explicit construction of solutions and the identification of scale parameters. This work bridges stochastic processes, information geometry, and fundamental physics, offering a novel perspective on the origin of physical laws from statistical mechanics.