  We advance here a new gravity quantization procedure that explicitly utilizes
York's analysis of the geometrodynamic degrees of freedom. This geometrodynamic
procedure of quantization is based on a separation of the true dynamic
variables from the embedding parameters and a distinctly different treatment of
these two kinds of variables. While the dynamic variables are quantized
following the standard quantum mechanical and quantum field theoretic
procedures, the embedding parameters are determined by the "classical"
constraint equations in which the expectation values of the dynamic variables
are substituted in place of their classical values. This self-consistent
procedure of quantization leads to a linear Schrodinger equation augmented by
nonlinear "classical" constraints and supplies a natural description of time
evolution in quantum geometrodynamics. In particular, the procedure sheds new
light on the "problems of time" in quantum gravity.
