Probing the Quantum Nature of Gravity through Classical Diffusion

Abstract

The question of whether gravity is fundamentally quantum remains one of the deepest open problems in modern physics. A recently explored approach consists of testing gravity's ability to entangle quantum systems, which requires preparing and controlling massive quantum states - a formidable experimental challenge. We propose an alternative strategy that circumvents the need for quantum state engineering. We show that, if gravity is classical, it must necessarily modify momentum statistics in a non-unitary way. We consider the corresponding linearized master equation for two harmonically trapped objects interacting gravitationally and establish a lower bound on the noise that any classical gravitational interaction must induce. We then outline an experimental protocol based on a high-precision torsion pendulum at millikelvin temperatures, showing that the predicted diffusion, if present, is in principle detectable with near-term technology. Our approach offers a novel route to testing the classical versus quantum nature of gravity without requiring macroscopic quantum superpositions or precise control of the system's quantum state, thereby significantly reducing the experimental complexity.