Contemporary development of Einstein's ideas on space-time and Brownian   motion
  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 Schr\"{o}dinger equation). 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. 
Yuri A. Rylov