Theory of Local Times II. Another formulation and examples

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.