Multivariance as a crucial property of microcosm
نویسنده
چکیده
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 P0 there are many vectors P0P1, P0P2,... which are equivalent to the vector Q0Q1 at the point Q0, but they are not equivalent between themselves. In the conventional (Euclidean) method the equivalence relation is transitive, whereas in a multivariant geometry the equivalance relation is intransitive, in general. It is a reason, why the multivariant geometries cannot be deduced from a system of axioms. However, the space-time geometry in microcosm is multivariant. In general, the multivariance is a property of the particle dynamics in microcosm, which is observed experimentally. Multivariance cannot be ignored. Multivariance may be prescribed either to space-time geometry, or to dynamics in the single-variant space-time geometry. In the first case the multivariance looks as a very natural property of the space-time geometry. In the second case it looks as a very artificial property of dynamics in itself.
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