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

**Abstract:** We consider two interacting systems when one is treated classically while the other remains quantum. Despite several famous no-go arguments, consistent dynamics of this coupling exist, and we derive its most general form. We apply this framework to geneneral relativity, and present a consistent theory of classical gravity coupled to quantum field theory. The theory can be considered effective or fundamental, and doesn't suffer from the pathalogies of the semi-classical Einstein's equation. If any system is treated as fundamentally classical, the dynamics necessarily results in decoherence of quantum systems, and a breakdown in predictability in classical phase space. We prove that a trade-off between the rate of decoherence and the degree of diffusion induced in the classical system is a general feature of all classical-quantum dynamics. When the trade-off is saturated, the quantum state remains pure conditioned on the classical trajectory and the measurement postulate and Born rule is not needed. Applying the trade-off, we find a relationship between the strength of gravitationally-induced decoherence versus diffusion of the metric. 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.

Based on joint work with Carlo Sparaciari, Barbara Šoda & Zachary Weller-Davies

https://arxiv.org/abs/1811.03116

https://arxiv.org/abs/2203.01332

https://arxiv.org/abs/2203.01982

https://arxiv.org/abs/2208.11722