#### Physics geometrization in microcosm: discrete
space-time and

#### relativity theory

#### Yuri A. Rylov

*Institute for Problems in Mechanics, Russian Academy of Sciences*

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

* email: rylov@ipmnet.ru*

Web site: http://rsfq1.physics.sunysb.edu/~rylov/yrylov.htm

or mirror Web site: http://gasdyn-ipm.ipmnet.ru/~rylov/yrylov.htm

Updated July 27, 2011

#### abstract

The
presented paper is a review of papers on the microcosm physics geometrization
in the last twenty years. These papers develop a new direction of the microcosm
physics. It is so-called geometric paradigm, which is alternative to the
quantum paradigm, which is conventionally used now. The hypothesis on
discreteness of the space-time geometry appears to be more fundamental, than
the hypothesis on quantum nature of microcosm. Discrete space-time geometry
admits one to describe quantum effects as pure geometric effects. Mathematical
technique of the microcosm physics geometrization (geometric paradigm) is based
on the physical geometry, which is described completely by the world function.
Equations, describing motion of particles in the microcosm, are algebraic (not
differential) equations. They are written in a coordinateless form in terms of
world function. The geometric paradigm appeared as a result of overcoming of
inconsistency of the conventional elementary particle theory. In the suggested
skeleton conception the state of an elementary particle is described by its
skeleton (several space-time points). The skeleton contains all information on
the particle properties (mass, charge, spin, etc.). The skeleton conception is
a monistic construction, where elementary particle motion is described in terms
of skeleton and world function and only in these terms. The skeleton conception
can be constructed only on the basis of the physical geometry. Unfortunately,
most mathematicians do not accept the physical geometries, because these
geometries are nonaxiomatizable. It is a repetition of the case, when
mathematicians did not accept the non-Euclidean geometries of Lobachevsky-Bolyai.
As a result this review is a review of papers of one author. This situation has
some positive sides, because it appears to be possible a consideration not only
of papers, but also of motive for writing some papers..

There is text of the paper
in English (pdf,
ps) and in Russian (pdf,
ps).