  A brief review of main features of the new approach named ``quantum
geometrodynamics in extended phase space'' is given and its possible prospects
are discussed. Gauge degrees of freedom are treated as a subsystem of the
Universe which affects the evolution of the physical subsystem. Three points
can be singled out when the gauge subsystem shows itself as a real constituent
of the Universe: a chosen gauge condition determines the form of equation for
the physical part of wave function, the form of density matrix and the measure
in physical subspace. An example is considered when a physically relevant
choice of gauge condition leads to almost diagonal density matrix. The analogy
between a transition to another reference frame (another basis in physical
subspace) and a transition to accelerating reference frame in Rindler space is
suggested.
