Deformation principle as a foundation of physical geometry

Details Deformation principle as a foundation of physical geometry Deformation principle as a foundation of physical geometry

2003-12-08

arxiv.org/abs/math/0312160v3

Mathematics

General Mathematics

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

Scientific paper

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).

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