##

### Tubular geometry construction
as a reason for new revision of the

### space-time conception.

#### Yuri A. Rylov

*Institute for
Problems in Mechanics, Russian Academy of Sciences*

* 101-1 ,Vernadskii Ave., Moscow, 119526, Russia*

* email: rylov@ipmnet.ru*

Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm

or mirror Web site: http://gas-dyn.ipmnet.ru/~rylov/yrylov.htm

Updated April 5, 2005

#### abstract

The turbular geometry (T-geometry) is a
generalization of the proper Euclidean geometry, founded on the property of
sigma-immanence. The proper Euclidean geometry can be described completely in
terms of the world fuction $\sigma =\rho ^{2}/2$, where $\rho $ is the
distance. This property is called the sigma-immanence. Supposing that any
physical geometry is sigma-immanent, one obtains the T-geometry G, replacing
the Euclidean world function $\sigma _{\mathrm{E}}$ by\ means of $\sigma $ in
the sigma-immanent presentation of the Euclidean geometry. One obtains the T-geometry G, described by the world fucntion
$\sigma $. This method of the geometry construction is very simple and
effective. T-geometry has a new geometric property: nondegeneracy of geometry.
The class of homogeneous isotropic T-geometries is described by a form of a
function of one parameter. Using T-geometry as the space-time geometry one can
construct the deterministic space-time geometries with primordially stochastic
motion of free particles and geometrized particle mass. Such a space-time
geometry defined properly (with quantum constant as an attribute of geometry)
allows one to explain quantum effects as a result of the statistical
description of the stochastic particle motion (without a use of quantum
principles). Geometrization of the particle mass appears to be connected with
the restricted divisibility of the straight line segments in such a space-time
geometry. The statement, that the problem of the elementary particle mass
spectrum is rather a problem of geometry, than that of dynamics, is a corollary
of the particle mass geometrization.

There is text of the paper in English and in Russian,