  Paths in an appropriate geometry are usually used as trajectories of test
particles in geometric theories of gravity. It is shown that non-symmetric
geometries possess some interesting quantum features. Without carrying out any
quantization schemes, paths in such geometries are naturally quantized. Two
different non-symmetric geometries are examined for these features. It is
proved that, whatever the non-symmetric geometry is, we always get the same
quantum features. It is shown that these features appear only in the pure
torsion term (the anti-symmetric part of the affine connection) of the path
equations. The vanishing of the torsion leads to the disappearance of these
features, regardless of the symmetric part of the connection. It is suggested
that, in order to be consistent with the results of experiments and
observations, torsion term in path equations should be parametrized using an
appropriate parameter.
