Quantum Corrections to the Newton’s Law from the Galilean Limit of Quantum Gravity

In this work the author derives the Galilean limit of the quantum gravity obtained by using the hydrodynamic approach. The result shows that the quantum interaction generates, in the limit of weak gravity, a non-zero contribution. The paper derives the small deviation from the Newtonian law due to the quantum gravity and analyzes the experimental features to validate the theoretical model. The work also shows that in the frame of the quantum gravity the equivalence principle between the inertial and gravitational mass can be violated in very extreme conditions.