The paper is devoted to the description a measurable time-interval (``proper
time'') in the Hamiltonian version of general relativity with the Dirac-ADM
metric. To separate the dynamical parameter of evolution from the space metric
we use the Lichnerowicz conformally invariant variables. In terms of these
variables GR is equivalent to the conformally invariant
Penrose-Chernicov-Tagirov theory of a scalar field the role of which is played
by the scale factor multiplied on the Planck constant. Identification of this
scalar field with the modulus of the Higgs field in the standard model of
electroweak and strong interactions allows us to formulate an example of
conformally invariant unified theory where the vacuum averaging of the scalar
field is determined by cosmological integrals of motion of the Universe
evolution.Comment: 20 pages, latex, no figures, submited to General Relativity and
Garvitatio
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