Theoretical Physics, Astrophysics and Cosmology

Zahid Zakir [2]

Abstract

      Inhomogeneous Nelson’s diffusion in flat spacetime with a tensor of diffusion can be described as a homogeneous one in a Riemannian manifold with this tensor of diffusion as a metric tensor. The influence of matter to the energy density of the stochastic background (vacuum) is considered. It is shown that gravitation can be represented as inhomogeneity of the quantum diffusion; the Einstein equations for the metrics can be derived as the equations for the corresponding tensor of diffusion.

PACS: 04.20.Cv, 03.65.Ta, 05.40.Jc, 04.62.+v

Key words: stochastic mechanics, tensor of diffusion, quantum fluctuations, gravitation, curvature
Vol. 4, No 1,  p. 6 – 9, v1,   19 March 2009

Online: TPAC: 3000-013 v2,  28 September 2012; DOI: 10.9751/TPAC.3000-013

Download  pdf 145 kb

Zahid Zakir [2]

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 multiplied to the diffusion coefficient. It is shown that such diffusion accelerates both a sample particle and local inertial frames such that their mean accelerations do not depend on their mass. This fact, explaining the principle of equivalence, allows one to represent the curvature and gravitation as consequences of the inhomogeneity 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 (with respect to a point at spatial infinity).

PACS: 04.20.Cv, 03.65.Ta, 05.40.Jc, 04.62.+v

Key words: stochastic mechanics, tensor of diffusion, quantum fluctuations, gravitation, curvature

Vol. 4, No 1,  p. 1 – 5, v1,   19 March 2009

Online: TPAC: 3000-012 v2,  28 September 2012; DOI: 10.9751/TPAC.3000-012

Download  pdf 259 kb