The weak field limit of quantum matter back-reacting on classical spacetime

TL;DR

This paper derives the Newtonian limit of classical-quantum gravity theories, showing how the potential diffuses with decoherence and proposing experimental tests to constrain such models.

Contribution

It provides a unified derivation of the weak field dynamics using path integral and master equation approaches, introducing stochastic equations and kernels for testing classical-quantum gravity.

Findings

Newtonian potential diffuses with a lower bound set by decoherence rate

Quantum and classical states evolve in lock-step with stochastic time flow

Framework enables experimental constraints on classical-quantum gravity models

Abstract

Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the Newtonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unravelled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic.