## 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 27, 2013

#### abstract

The tachyon model of neutrino is constructed, basing on the statement that quantum description is a statistical description of stochastically moving particles. Besides, the tachyon model contains two conceptual points: (1) universal formalism of particle dynamics, describing uniformly all particles: deterministic, stochastic and quantum, (2) discrete space-time geometry and skeleton conception of particle dynamics. The universal formalism is a result of a logical reloading, when the statistical ensemble becomes to be the basic object of particle dynamics instead of a single particle. Such a reloading admits one to describe uniformly the quantum, stochastic and deterministic particles in terms of a statistical ensemble without a reference to principles of quantum mechanics. Besides, one uses a relativistic state of a particle, when the state is described by the particle skeleton (several space-time points) instead of the point in the phase space, what is nonrelativistic concept of the particle state. Representing the Dirac equation in terms of the statistical ensemble, one concludes that in the deterministic approximation the world line of the Dirac particle may be a spacelike helix with timelike axis. The rotational component of the relativistic Dirac particle is described nonrelativistically. It shows that the world line may be spacelike, and the Dirac particle may be a tachyon. Neutrino is a Dirac particle, and it is a tachyon. Free quantum particles appear to move stochastically, and this bring up the question, what is the reason of stochastic motion of free quantum particles. It appears, that the discrete space-time geometry is a multivariant geometry. It is a reason of stochastic particle motion. If the elementary length $\lambda _{0}$ of the discrete space-time geometry is connected with the quantum constant $\hbar$ by the relation $\lambda _{0}^{2}=\hslash /bc$, where $b$ is some universal constant, then statistical description of the free particle motion coincides with the quantum description in terms of the Schr\"{o}dinger equation.

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