## Granular
geometry of space-time as a result of Newtonian

## investigation
strategy

## 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 December 10,, 2008

#### abstract

The Newtonian
investigation strategy declares "Hypotheses non fingo!" In practice
it means that, having problems in the theory development, one looks for mistakes in
papers of predecessors and corrects them. Sometimes such an investigation
strategy admits one to solve the arising problems without a use of additional hypotheses.
The conventional method of a generalized geometry construction, based on
deduction of all propositions of the geometry from axioms, appears to be imperfect
(incomplete) 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 themselves.
In 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. As a
rule the multivariant geometry is a granular geometry, i.e. such a geometry,
which is partly continuous and partly discrete. Multivariance is a mathematical
method of the granularity description. The granularity (and multivariance) of
the space-time geometry generates a multivariant (quantum) motion of particles
in microcosm. Besides, the granular 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 granular space-time geometry. The quantum principles appear
to be needless.

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