On the Quantum Corrections to the Newtonian Potential

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.