2005/11/23 by Yuri A. Rylov, Rylov, Yuri A.
Engineering · Mathematics · #03B30 #51K99 #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications #math.GM #msc:03B30 #msc:51K99
paper · pdf · doi:10.48550/arxiv.math/0511575
22 pages, 0 figures
arxiv created 2005/11/23 · openalex publication_date 2005/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the generalized geometries may be obtained as a deformation of the proper Euclidean geometry. Algorithm of construction of any proposition S of the proper Euclidean geometry E may be described in terms of the Euclidean world function sigmaE in the form S(sigmaE). Replacing the Euclidean world function sigmaE by the world function sigma of the geometry G, one obtains the corresponding proposition S(sigma) of the generalized geometry G. Such a construction of the generalized geometries (known as T-geometries) uses well known algorithms of the proper Euclidean geometry and nothing besides. This method of the geometry construction is very simple and effective. 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).