Deformation principle as a foundations of physical geometry and its application to the space-time geometry

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Sciences,

101-1, Vernadskii Ave., Moscow, 119526, Russia.


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Updated November 7, 2004

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 s =d2/2. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function s E .Any physical geometry G is obtained from the Euclidean geometry as a result of replacement s E by the world function s of 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).

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