Quantum geometrodynamics in extended phase space - I. Physical problems of interpretation and mathematical problems of gauge invariance

Abstract

The paper is the first of two parts of the work devoted to the investigation of constructing quantum theory of a closed universe as a system without asynptotic states. In Part I the role of asymptotic states in quantum theory of gravity is discussed, that enables us to argue that mathematically correct quantum geometrodynamics of a closed universe has to be gauge-noninvariant. It is shown that a gauge-noninvariant quantum geometrodynamics is consistent with the Copenhagen interpretation. The proposed version of the theory is thought of as describing the integrated system ``the physical object + observation means''. It is also demonstrated that introducing the observer into the theory causes the appearance of time in it.