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

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 $\sigma$. 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 Schr\"{o}dinger 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.