Distinguishing Quantum and Classical Gravity via Non-Stationary Test Mass Dynamics

TL;DR

This paper proposes a method to distinguish quantum and classical gravity by analyzing non-stationary test mass dynamics in optomechanical systems, using statistical inference to reduce experimental trials needed.

Contribution

It introduces a novel approach to detect SN theory signatures during non-stationary evolution and employs statistical inference to minimize experimental repetitions.

Findings

Non-stationary oscillatory behavior in test mass moments can indicate SN effects.

Additional peaks in the noise spectrum serve as signatures of SN evolution.

Statistical inference reduces required trials to 10 for reliable model distinction.

Abstract

Classical gravity theory predicts a state-dependent gravitational potential for a quantum test mass, leading to nonlinear Schrodinger-Newton (SN) state evolution that contrasts with quantum gravity. Testing the effect of SN evolution can provide evidence for distinguishing quantum gravity and classical gravity, which is challenging to realize in the stationary optomechanical systems as analyzed in previous works [Phys. Rev. D 107, 024004 (2023), Phys. Rev. D 111, 062004 (2025)]. This work is devoted to analyzing the possibility of capturing the signature of SN theory during the non-stationary evolution of the test mass under the optomechanical measurement, where the second-order moments of a test mass can exhibit a distinctive oscillatory behavior. We show that this feature manifest in the non-stationary noise spectrum of outgoing light as additional peaks structures, although resolving these structures in practical experiments requires a larger number of repetitive trials with our sampling parameters, which is cost-prohibitive. To address this issue, we further employ statistical inference methods to extract more comprehensive information, thereby reducing the required number of experimental repetitions. Through Mock-Data simulations, we demonstrate that only 10 experimental trials of 40 seconds each are sufficient to reduce the false alarm rate for distinguishing between the two models to below one percent.