## Incompleteness
of the particle dynamics in microcosm and the skeleton

## conception of
elementary particles as overcoming of this incompleteness

## 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 16, 2011

#### abstract

The skeleton
conception of elementary particles is considered in the paper. Conventional
particle dynamics is formulated in an unaccomplished form, which is adequate
only in the continuous space-time geometry. The conventional differential
equations of the particle motion cannot be written in the discrete space-time
geometry. In the discrete space-time geometry the particle world line is
replaced by the world chain. The world chain links has a finite length (not
infinitesimal). The world chain appears to be stochastic. Statistical
description of stochastic world chains leads to the Schr\"{o}dinger equation, if the elementary length of the geometry
is chosen in a proper way. The quantum principles are founded by existence of
the discrete (and multivariant) space-time geometry and lose the role of prime physical
principles. In the skeleton conception the particle is described by its
skeleton (several rigidly connected space-time points). Skeleton conception of
the elementary particles realizes a proper description of the particle state,
which appears to be adequate in a discrete space-time geometry.
The particle dynamics takes the form of a monistic conception, which is
described completely in terms of the world function of the space-time geometry.
The skeleton conception accomplishes the transition from nonrelativistic
physics to the relativistic one and realizes the total geometrization of particle
dynamics.

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