Measurable signatures of quantum mechanics in a classical spacetime

TL;DR

This paper proposes an optomechanical experiment to detect potential signatures of a classical gravity theory, specifically the Schroedinger-Newton equation, by analyzing the phase fluctuations of light interacting with macroscopic oscillators.

Contribution

It introduces a novel experimental setup to test the Schroedinger-Newton equation's predictions using optomechanics and analyzes measurement fluctuations considering non-linear effects.

Findings

Distinct phase fluctuation features predicted by the SN equation can be observed.

The experiment can differentiate SN effects from thermal and quantum noise.

State-of-the-art technology is sufficient to resolve the predicted signatures.

Abstract

We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schroedinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator's center of mass wavefunction differ from the predictions of standard quantum mechanics. This difference is largest for low-frequency oscillators, and for materials, such as Tungsten or Osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum's dynamics. Due to the non-linearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wavefunction collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light's phase fluctuations' spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.