  In a previous paper, we presented new results on non-Riemannian geometry. For
an asymmetric connection, we showed that a projective change in the symmetric
part generates a vector field that is not arbitrary, but is the gradient of a
non-arbitrary scalar field. As a consequence, Weyl's geometry is a conformal
differential geometry and is associated with asymmetric geometry by this
projective change. In the present paper, important differences between
light-like and non-light-like intervals are analysed. We show that
integrability condition in Weyl's geometry implies microscopic spacetime
oscillations of Weyl's and Einstein's geometries. We show that the
integrability condition in Weyl's geometry, together with the condition that
null and massive particles interact locally in an Einstein spacetime. We
construct an equation for linear transverse waves and make a qualitative
application in a hydrogen atom, which, from qualitative viewpoint, agrees with
Bohr's hydrogen model and Schrodinger's quantum mechanics.
