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.

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