5 Tubular geometry construction as a reason for new revision of the space - time conception

Tubular geometry construction as a reason for new revision of the space-time conception. Abstract The tubular geometry (T-geometry) is a generalization of the proper Eu-clidean geometry, founded on the property of σ-immanence. The proper Eu-clidean geometry can be described completely in terms of the world function σ = ρ 2 /2, where ρ is the distance. This property is called the σ-immanence. Supposing that any physical geometry is σ-immanent, one obtains the T-geometry G, replacing the Euclidean world function σ E by means of σ in the σ-immanent presentation of the Euclidean geometry. One obtains the T-geometry G, described by the world function σ. This method of the geometry construction is very simple and effective. T-geometry has a new geometric property: nondegeneracy of geometry. The class of homogeneous isotropic T-geometries is described by a form of a function of one parameter. Using T-geometry as the space-time geometry one can construct the deterministic space-time geometries with primordially stochastic motion of free particles and geometrized particle mass. Such a space-time geometry defined properly (with quantum constant as an attribute of geometry) allows one to explain quantum effects as a result of the statistical description of the stochastic particle motion (without a use of quantum principles). Geometrization of the particle mass appears to be connected with the restricted divisibility of the straight line segments. The statement, that the problem of the elementary particle mass spectrum is rather a problem of geometry, than that of dynamics , is a corollary of the particle mass geometrization.