Classical Scale of Quantum Gravity

Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius rg. The role of this scale in quantum domain is discussed in the context of the low-energy effective theory. The question of whether quantum gravity effects appear already at rg leads to the question of correspondence between classical and quantum theories, which in turn can be unambiguously resolved considering the issue of general covariance. The O(h̄) loop contributions turn out to violate the principle of general covariance, thus revealing their essentially quantum nature. The violation is O(1/N), where N is the number of particles in the body. This leads naturally to a macroscopic formulation of the correspondence principle.