  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).

General Mathematics