Institute for Problems in Mechanics, Russian Academy of Sciences
Updated November 21, 2005
It is shown that the generalized geometries may be obtained as a deformation of the proper Euclidean geometry. Algorithm of construction of any
proposition S of the proper Euclidean geometry E may
be described in terms of the Euclidean world function sigma_E
in the form S(sigma_E).
Replacing the Euclidean world function sigma_E
by the world function sigma of the geometry
G, one obtains the corresponding proposition S(sigma)
of the generalized geometry G. Such a construction of the generalized geometries (known as
T-geometries) uses well known algorithms of the proper Euclidean geometry and nothing besides. This method of the geometry construction is very simple
and effective. Using T-geometry as the space-time geometry, one can construct the 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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