Quantum gravity corrections to the fall of an apple

We consider the motion of a massive particle in a static, weakly curved spacetime where the gravitational field is taken to be quantized. We find that Newton's law of free fall is modified by quantum-gravitational corrections, in addition to the known special-relativistic and post-Newtonian modifications. The quantum-gravitational corrections take the form of stochastic noise in the particle trajectory, where the statistical properties of the noise depend on the quantum state of the gravitational field.