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

TL;DR

This paper proposes a stochastic mechanics approach to gravitation, modeling it as a quantum diffusion process in a Riemannian manifold, which explains the equivalence principle and the negative energy density of Newtonian gravity.

Contribution

It introduces a novel diffusion-based framework for gravity, linking quantum fluctuations to spacetime curvature and providing insights into the equivalence principle and energy density.

Findings

Quantum diffusion accelerates particles and frames independently of mass.

Gravitational curvature arises from quantum fluctuations in this model.

Negative energy density of Newtonian gravity is naturally explained.

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.