### Contemporary development of Einstein's ideas on space-time and

Brownian motion

###

#### 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://gas-dyn.ipmnet.ru/~rylov/yrylov.htm

Updated December 8, 2005

#### abstract

Development of the contemporary theory of physical phenomena in the microcosm is considered to be a result of development of Einstein's ideas on
a possibility of the event space modification and on a possibility of stochastic (Brownian) motion of free particles. One considers the space-time
modification, based on a new conception of geometry. In the framework of this conception any geometry is obtained as a result of the proper Euclidean
geometry deformation. In the framework of this conception it is possible such a space-time geometry, where the free particle motion appears to be
stochastic, although the geometry in itself remains to be deterministic. The stochasticity intensity depends on the particle mass. It is small for
particle of a large mass, and it is essential for the particle of a small mass. The space-time geometry may be chosen in such a way, that the
statistical description of random world lines of particles be equivalent to the quantum description (the
Schroedinger equation). At such a choice of the space-time geometry the world function depends on the quantum
constant, and the universal character of the quantum constant is a corollary of the
fact, that all physical phenomena take place in the space-time, whose

properties depend on the value of the quantum constant. The stochastic motion of free particles may be considered to be a kind of the relativistic
Brownian motion, whose properties are conditioned by the properties of the

space-time geometry. At such a description the quantum principles are not used. They can be obtained as a
corollaries of the statistical description of nonrelativistic stochastic particles. The nonrelativistic quantum
principles may not be used for description of relativistic phenomena. They are to be modified. This modification should be obtained from the
statistical description of the relativistic stochastic particles.

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