  A model of a stationary universe is proposed. In this framework, time is
defined as a local and quantum-mechanical notion in the sense that it is
defined for each local and quantum-mechanical system consisting of finite
number of particles. The total universe consisting of infinite number of
particles has no time associated. It is a stationary bound state of the total
Hamiltonian of infinite degrees of freedom. The quantum mechanics and the
theory of general relativity are consistently united in this context if one
uses this notion of local and quantum-mechanical time. As one of the
consequences, the Einstein-Podolsky-Rosen paradox is resolved. The Hubble
red-shift is explained as a consequence of general relativity which is
consistent with quantum mechanics. This does not require us to argue on the
beginning nor the end of the universe. The universe just exists without time.
(published in Il Nuovo Cimento, Vol. 109 B, N. 3, 1994, pp. 281-302)

Astrophysics;General Relativity and Quantum Cosmology