## Multivariance
as a crucial property of microcosm

## 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://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated June 10, 2008

#### Abstract

The
conventional method of a generalized geometry construction, based on deduction
of all propositions of the geometry from axioms, appears to be imperfect in the
sense, that multivariant geometries cannot be constructed by means of this
method. Multivariant geometry is such a geometry, where at the point P there
are many vectors *PP’*, *PP”*,...
which are equivalent to the vector *QQ’*
at the point Q, but they are not equivalent between themselvesIn the
conventional (Euclidean) method the equivalence relation is transitive, whereas
in a multivariant geometry the equivalence relation is intransitive, in general. It is a reason,
why the multivariant geometries cannot be deduced from a system of axioms. The
space-time geometry in microcosm is multivariant. Multivariant geometry is a
grainy geometry, i.e. the geometry, which is partly continuous and partly discrete.
Multivariance is a mathematical method of the graininess description. The
graininess (and multivariance) of the space-time geometry generates a
multivariant (quantum) motion of particles in microcosm. Besides, the grainy
space-time generates some discrimination mechanism, responsible for discrete
parameters (mass, charge, spin) of elementary particles. Dynamics of particles
appears to be determined completely by properties of the grainy space-time
geometry. The quantum principles appear to be needless..

There is
text of the paper in English (pdf, ps)
and in Russian (ps, pdf)..