Necessity of the general relativity revision and free motion of particles in non-Riemannian space-time geometry

TL;DR

This paper argues that the current gravitational theory, based solely on Riemannian geometry, is incomplete because physical space-time may have a more general multivariant geometry, affecting particle motion.

Contribution

It introduces the concept that physical space-time geometry is more general than Riemannian geometry and shows that free microparticle motion is inherently stochastic in such geometries.

Findings

Microparticle motion in non-Riemannian geometry is multivariant and stochastic.

Riemannian geometries are a small subset of possible physical geometries.

Current gravitational theory neglects the existence of non-Riemannian geometries.

Abstract

It is shown, that a free motion of microparticles (elementary particles) in the gravitational field is multivariant (stochastic). This multivariance is conditioned by multivariant physical space-time geometry. The physical geometry is described completely by a world function. The Riemannian geometries form a small part of possible physical geometries. The contemporary theory of gravitation ignores existence of physical geometries. It supposes, that any space-time geometry is a Riemannian geometry. It is a mistake. As a result the contemporary theory of gravitation needs a revision. Besides, the Riemannian geometry is inconsistent, and conclusions of the gravitational theory, based on inconsistent geometry may be invalid. Free motion of macroparticles (planets), consisting of many connected microparticles, is deterministic, because connection of microparticles inside the macroparticle averages stochastic motion of single macroparticles.