Quantum Gravity Corrections to the Fall of the Apple

Abstract

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.

13 pages, LaTeX. v3: references added, expanded discussion

References in corpus (4)

• Signatures of the Quantization of Gravity at Gravitational Wave Detectors
• Quantum Mechanics of Gravitational Waves
• Electromagnetic and gravitational self-force on a relativistic particle from quantum fields in curved space
• Quantum Noise of Gravitons and Stochastic Force on Geodesic Separation

Cited by in corpus (12)

• Probing the quantum nature of gravity using a Bose-Einstein condensate
• Quantum Gravity Fluctuations in the Timelike Raychaudhuri Equation
• Quantum-gravitational noise correlation in nearby detectors
• Uncertainty principle from the noise of gravitons
• Entanglement and squeezing of gravitational waves
• Quantum-Gravitational Null Raychaudhuri Equation
• Apparent violations of the second law in the quantum-classical dynamics of interacting levitated nanoparticles
• Quantum gravity signatures in gravitational wave detectors placed inside a harmonic trap potential
• The shadows of quantum gravity on Bell's inequality
• Constraining a stochastic variation of the gravitational coupling with binary systems
• Quantum nature of gravity in a Bose-Einstein condensate
• Bose-Einstein condensate as a quantum gravity probe; "Erste Abhandlung"