## Geometrical
dynamics: spin as a result of rotation with superluminal speed

## 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 May 28, 2008

#### Abstract

Dynamics
is considered as a corollary of the space-time geometry. Evolution of a
particle in the space-time is described as a chain of connected equivalent
geometrical objects. Space-time geometry is determined uniquely by the world
function σ. Proper modification of the Minkowskian world function for
large space-time interval leads to wobbling of the chain, consisted of timelike
straight segments. Statistical description of the stochastic world chain
coincides with the quantum description by means of the Schrödinger equation.
Proper modification of the Minkowskian world function for small space-time interval
may lead to appearance of a world chain, having a shape of a helix with
timelike axis. Links of the chain are spacelike straight segments. Such a world
chain describes a spatial evolution of a particle. In other words, the helical
world chain describes the particle rotation with superluminal velocity. The
helical world chain associated with the classical Dirac particle, whose world
line is a helix. Length of world chain link cannot be arbitrary. It is
determined by the space-time geometry and, in particular, by the elementary
length. There exists some discrimination mechanism, which can discriminate some
world chains.

There is
text of the paper in English (pdf) and
in Russian (ps, pdf).
Figures fig.1.