  We re-examine the notions of time and evolution in the light of the
mathematical properties of the solutions of the Wheeler-DeWitt equation which
are revealed by an extended adiabatic treatment. The main advantage of this
treatment is to organize the solutions in series that make explicit both the
connections with the corresponding Schr\"odinger equation as well as the
modifications introduced by the quantum character of gravity. When the universe
is macroscopic, the ordered character of the expansion leads to connections
with the Schr\"odinger equation so precise that the interpretation of the
solutions of the Wheeler-DeWitt equation is unequivocally determined. On the
contrary, when the expansion behaves quantum mechanically, i.e. in the presence
of backscattering, major difficulties concerning the interpretation persist.
