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.

Fully revised manuscript with a mathematical formalization of the main argument