  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.
