Theory of Local Times

— 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.