  Several years ago the so-called quantum geometrodynamics in extended phase
space was proposed. The main role in this version of quantum geometrodynamics
is given to a wave function that carries information about geometry of the
Universe as well as about a reference frame in which this geometry is studied.
We consider the evolution of a physical object (the Universe) in ``physical''
subspace of extended configurational space, the latter including gauge and
ghost degrees of freedom. A measure of the ``physical'' subspace depends on a
chosen reference frame, in particular, a small variation of a gauge-fixing
function results in changing the measure. Thus, a transition to another gauge
condition (another reference frame) leads to non-unitary transformation of a
physical part of the wave function. From the viewpoint of the evolution of the
Universe in the ``physical'' subspace a transition to another reference frame
is an irreversible process that may be important when spacetime manifold has a
nontrivial topology.
