Deformation principle as a foundation of physical geometry
| dc.creator | Rylov, Yuri A. | |
| dc.date | 2003-12-08 | |
| dc.date | 2004-04-30 | |
| dc.date.accessioned | 2026-07-07T05:03:39Z | |
| dc.date.available | 2026-07-07T05:03:39Z | |
| dc.description | 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 $σ=d^{2}/2$. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function $σ_{\mathrm{E}}$. Any physical geometry $\mathcal{G}$ is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function $σ_{\mathrm{E}}$ by the world function $σ$ of $\mathcal{G}$. 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). | |
| dc.description | 18 pages, 0 figures, Addition of coordinateless definition of geometric objects | |
| dc.identifier | https://arxiv.org/abs/math/0312160 | |
| dc.identifier | http://arxiv.org/abs/math/0312160 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69509 | |
| dc.subject | General Mathematics | |
| dc.subject | 51K05;00A05 | |
| dc.title | Deformation principle as a foundation of physical geometry | |
| dc.type | text |