Institute for Problems in Mechanics, Russian
Academy of Sciences
101-1 ,Vernadskii Ave., Moscow, 119526, Russia
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
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.