Problem of parallelism in geometry and physics

Yuri A. Rylov

Institute for Problems in Mechanics, Russian Academy of Science
101-1, Vernadskii Ave., Moscow, 119526, Russia.
Updated December 22, 2002


Two different definitions of the two vectors parallelism are investigated
and compared. The first definitions is based on the principle of geometry
deformation, when any physical geometry is obtained as a result of some
deformation of the proper Euclidean geometry. The second definition is the
conventional definition of parallelism, which is used in the Riemannian
geometry. It is shown, that the second definition is inconsistent. It leads
to absence of absolute parallelism in Riemannian geometry and to
discrimination of outcome outside the framework of the Riemannian geometry
at description of the space-time geometry. The reason of the inconsistency
appearance is discussed. Problems of the inconsistency elimination and
consequences of this elimination for development of the microcosm physics
are considered.


English version of the paper in Postscript.
Russian  version of the paper in Postscript.