The Theory of Stochastic Space-Time. 1. Gravitation as a Quantum Diffusion

Abstract

The Nelson stochastic mechanics of inhomogeneous quantum diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold where this tensor of diffusion plays the role of a metric tensor. It is shown that the such diffusion accelerates both a sample particle and a local frame such that their mean accelerations do not depend on their masses. This fact, explaining the principle of equivalence, allows one to represent the curvature and gravitation as consequences of the quantum fluctuations. In this diffusional treatment of gravitation it can be naturally explained the fact that the energy density of the instantaneous Newtonian interaction is negative defined.