Deformation principle as a foundation of physical geometry

Abstract

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 $\sigma =d^2/2$. One suggests a new general method of the physical geometry construction. The proper Euclidean geometry is described in terms of its world function ${\sigma }_{\mathrm{E}}$. Any physical geometry $\mathcal{G}$ is obtained from the Euclidean geometry as a result of replacement of the Euclidean world function ${\sigma }_{\mathrm{E}}$ by the world function $\sigma$ 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).

18 pages, 0 figures, Addition of coordinateless definition of geometric objects

References in corpus (4)

• Model conception of quantum phenomena: logical structure and investigation methods
• Deformation principle and problem of parallelism in geometry and physics
• Asymmetric Nondegenerate Geometry
• Investigation methods in model conception of quantum phenomena

Cited by in corpus (1)

• Repeated dynamic quantization