Classical Scale of Quantum Gravity

TL;DR

This paper explores the classical length scale of quantum gravity effects, focusing on the role of the gravitational radius in the low-energy effective theory and its implications for the quantum-classical correspondence.

Contribution

It analyzes how quantum gravity effects relate to classical scales and discusses the violation of general covariance by quantum loop contributions, proposing a macroscopic correspondence principle.

Findings

Quantum loop contributions violate general covariance.

The violation scales as 1/N, with N being the number of particles.

A macroscopic formulation of the correspondence principle is proposed.

Abstract

Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius r_g. 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 r_g 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(\hbar^0) 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.