Scale of non-locality for a system of $n$ particles

Abstract

Higher derivative theories of gravity are associated with a mass scale to insure the correct dimensionality of the covariant derivatives. This mass scale is known as the scale of non-locality. In this paper, by considering a higher derivative toy model, we show that for a system of $n$ particles the effective mass scale is inversely proportional to the square root of the number of particles. We demonstrate that as the number of particles increases the corresponding effective mass scale associated with the scattering amplitude decreases.