Discrete space-time geometry
and skeleton conception of particle
Dynamics
Yuri A. Rylov
Updated October 15, 2011
It is shown
that properties of a discrete space-time geometry distinguish from properties of
the Riemannian space-time geometry. The discrete geometry is a physical
geometry, which is described completely by the world function. The discrete
geometry is nonaxiomatizable and multivariant. The equivalence
relation is
intransitive in the discrete geometry. The particles are described by world
chains (broken lines with finite length of links), because in the discrete
space-time geometry there are no infinitesimal lengths. Motion of particles is
stochastic, and statistical description of them leads to the
Schr\"{o}dinger equation, if the elementary length of the discrete
geometry depends on the quantum constant in a proper way.
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the text in English (pdf,, ps),
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