On the Quantum Corrections to the Newtonian Potential

TL;DR

This paper calculates the quantum corrections to the Newtonian potential in quantum gravity, revealing how quantum effects modify gravitational interactions at long distances and reproduce classical post-Newtonian corrections.

Contribution

It provides a direct computation of the leading quantum correction to the Newtonian potential from graviton exchange diagrams, aligning with classical relativistic results.

Findings

Quantum corrections cause a slow increase in gravitational coupling with distance.

The calculation reproduces the classical post-Newtonian correction.

Quantum effects may influence gravity at large scales.

Abstract

The leading long-distance quantum correction to the Newtonian potential for heavy spinless particles is computed in quantum gravity. The potential is obtained directly from the sum of all graviton exchange diagrams contributing to lowest non-trivial order to the scattering amplitude. The calculation correctly reproduces the leading classical relativistic post-Newtonian correction. The sign of the perturbative quantum correction would indicate that, in the absence of a cosmological constant, quantum effects lead to a slow increase of the gravitational coupling with distance.