Non-Riemannian geometry as a reason of the third modification of the   space-time geometry
  The third modification of the space-time geometry is considered. (The first modification is the spacial relativity, the second one is the general relativity.) After the third modification of the space-time geometry the motion of free particles become to be primordially stochastic (multivariant). This circumstance forces one to construct a multivariant dynamics. The multivariant dynamics is the classical dynamics in the non-Riemannian space-time geometry. The multivariant dynamics explains quantum effects without a reference to the quantum principles. Elimination of quantum principles admits one to solve the main problem of relativistic quantum theory: unification of the principles of relativity with the nonrelativistic quantum principles. 
Yuri A. Rylov