Local Time and the Unification of Physics Part II. Local System

As a continuation of Part I [8], a more precise formulation of local time and local system is given. The observation process is reflected in order to give a relation between the classical physics for centers of mass of local systems and the quantum mechanics inside a local system. The relation will give a unification of quantum mechanics and general relativity in some cases. The existence of local time and local motion is proved so that the stationary nature of the universe is shown to be consistent with the local motion. V. Definition of Local System As announced in Part I [8], we begin in this part II with stating a precise definition of local clock and local time, where as we have discussed in Part I, local clock is the local system itself in that every existence is clocking. (See section IV [8], especially recall the statement: In this sense, “clocking” is the natural activity of any local system.) Thus the purpose of this section is the definition of local system. To do so, we begin with introducing a stationary universe φ. By nature what is called the universe must be a closed universe, within which is all. We characterize it by a certain quantum-mechanical condition. Let H be a separable Hilbert space, and set