2003/12/08 by Yuri A. Rylov, Rylov, Yuri A.
Mathematics · Physics and Astronomy · #00A05 #51K05 #Advanced Mathematical Theories and Applications #FOS: Mathematics #General Mathematics (math.GM) #Quantum Mechanics and Applications #Relativity and Gravitational Theory #math.GM #msc:00A05 #msc:51K05
paper · pdf · doi:10.48550/arxiv.math/0312160
18 pages, 0 figures, Addition of coordinateless definition of geometric objects
openalex publication_date 2003/12/08 · arxiv created 2004/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function σ=d2/2. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function σE. Any physical geometry G is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function σE by the world function σ of G. This method is very simple and effective. It introduces a new geometric property: nondegeneracy of geometry. Using this method, one can construct 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).