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


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,