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 September 1, 2007
Physical
geometry studies mutual disposition of geometrical objects and points in space,
or space-time, which is described by the distance function $d$, or by the world
function $\sigma =d^{2}/2$. One suggests a new general
method of the physical geometry construction. The proper Euclidean geometry is
described in terms of its world function $\sigma _{\mathrm{E}}$.
Any physical geometry $\mathcal{G}$ is obtained from
the Euclidean geometry as a result of replacement of the Euclidean world
function $\sigma _{\mathrm{E}}$ by the world function $\sigma $ of
$\mathcal{G}$. This method is very simple and effective. It introduces a new
geometric property: nondegeneracy of geometry. Using this method, one can
construct 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).
There is
text of the paper in English and in Russian