Deformation principle as foundation of physical geometry and its application to space-time geometry 2004jbu | Rylov Yuri A.
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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