Archive

Archive for the ‘2009 Volume 4’ Category

Oct
05

The theory of stochastic space-time.

2. Quantum theory of relativity[1]

Zahid Zakir [2]

Abstract

      Nelson’s stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented as the transformations of the systems of perturbing devices. It is argued that the physical spacetime has a stochastic nature and that quantum mechanics in Nelson’s formulation correctly describes this stochasticity.

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

Key words: stochastic mechanics, quantum fluctuations, measurements

Vol. 4, No 2,  p. 10 – 16, v1,   5 October 2009
Online: TPAC: 3200-014 v2,  28 September 2012; DOI: 10.9751/TPAC.3200-014

Download  pdf 266 kb


[1] The preprint of the paper has been presented in 1999:  Zakir Z. arXiv:hep-th/99010139.

[2] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Mar
19

Gravitation as a Quantum Diffusion [1]

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


[1] The preprint of the paper has been presented in 1999:  Zakir Z. arXiv:gr-qc/9906079.

[2] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org

Mar
19

The Theory of Stochastic Space-Time.

1. Gravitation as a Quantum Diffusion[1]

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

 


[1] The preprint of the paper has been presented in 1998:  Zakir Z. arXiv:hep-th/9812254.

[2] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org