Gravitationally induced decoherence vs space-time diffusion: testing the quantum nature of gravity

TL;DR

This paper demonstrates that hybrid classical-quantum dynamics involving gravity necessarily cause decoherence and phase-space diffusion, providing testable predictions and experimental bounds on theories where gravity remains classical.

Contribution

It proves that classical-quantum coupling leads to unavoidable decoherence and diffusion, establishing a trade-off relation and constraining classical gravity theories through experimental data.

Findings

Decoherence is inevitable in hybrid classical-quantum systems.

A trade-off exists between decoherence rate and phase-space diffusion.

Experimental bounds restrict classical gravity theories interacting with quantum matter.

Abstract

We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here, we prove that such hybrid dynamics necessarily results in decoherence of the quantum system, and a breakdown in predictability in the classical phase space. We further prove that a trade-off between the rate of this decoherence and the degree of diffusion induced in the classical system is a general feature of all classical quantum dynamics; long coherence times require strong diffusion in phase-space relative to the strength of the coupling. Applying the trade-off relation to gravity, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric and its conjugate momenta. This provides an experimental signature of theories in which gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts with quantum matter. We find that part of the parameter space of such theories are already squeezed out, and provide figures of merit which can be used in future mass measurements and interference experiments.