  The model of a stationary universe and the notion of local times presented in
[10] are reviewed with some alternative formulation of the consistent
unification of the Riemannian and Euclidean geometries of general relativity
and quantum mechanics. The method of unification adopted in the present paper
is by constructing a vector bundle $X\times R^6$ or $X\times R^4$ with $X$
being the observer's reference frame and $R^6$ or $R^4$ being the unobservable
inner space(-time) within each observer's local system. Some applications of
our theory to two concrete examples of human size and of cosmological size are
discussed, as well as the uncertainty of time in our context is calculated.
