  The role of the time surface term in the ADM Hamiltonian formulation of
general relativity is investigated. We show that the variable contained in the
time surface term (the scale factor) plays the role of a time-like variable.
The conjugated variable represents the energy density in the reduced phase
space, where the Schr\"odinger like equation for a wave function is derived.
The contribution from the surface term to the phase of the wave function allows
us to define {\bf the phase time of the quantum Universe} so that it coincides
with {\bf the proper time as an invariant interval} for the classical dust
filled Universe. The quantum scenario of the evolution of the Universe filled
in by the Weinberg-Salam fields is considered. The wave function of the early
Universe as the functional from the Higgs fields and scale factor realizes the
unitary irreducible representation of the SO(4,1) group. The elementary
particle masses are determined by the angles of the scale--scalar field mixing.
