Proper Time Dynamics in General Relativity and Conformal Unified Theory

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-Chernikov-Tagirov theory of a scalar field the role of which is played by the scale factor multiplied by 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 evolution of the universe.