Quantum Geometrodynamics Creates New Problems

The development of last years in quantum geometrodynamics highlights new problems which were not obvious in its first formulation proposed by Wheeler and DeWitt. At the first stage the main task was to apply known quantization schemes to gravitational field or a certain cosmological model. This way has led to the realization of the fact that a quantum description of the Universe is impossible without implicit or explicit indication to a reference frame presented by some medium, filling the whole Universe, with its own equation of state and thermodynamical properties. Thus the questions arise, should one seek for a “privileged” reference frame or consider all the variety of gauge conditions and appropriate solutions for the wave function? It is worth noting that thermodynamical properties of such a quantum Universe would also depend on a chosen reference frame to some extent. So, we need a self-consistent quantum theoretical and thermodynamical description of the Universe. In this talk I would like to present my point of view on the problems of quantum geometrodynamics, as they can be seen now, forty years after the first significant attempt to construct full quantum theory of gravity made by DeWitt in 1967 [1]. As all of us well know, first attempts to apply quantum theory to gravitational field immediately faced enormous obstacles, and the aim of this my talk is to demonstrate the interrelation between those obstacles and the problems quantum geometrodynamics meets now. At the first stage the main task was to apply known quantization schemes to gravitational field or a certain cosmological model. It was realized that the main difficulty consisted in the nature of general relativity as a completely covariant theory that ran counter to efforts former Rostov State University