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

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.

42 pages, 1 table, comments welcomed

References in corpus (11)

• A Spin Entanglement Witness for Quantum Gravity
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Lower and Upper Bounds on CSL Parameters from Latent Image Formation and IGM Heating
• Gravitationally Mediated Entanglement: Newtonian Field vs. Gravitons
• Underground test of gravity-related wave function collapse
• Optomechanical sensing of spontaneous wave-function collapse
• Heating of trapped ultracold atoms by collapse dynamics
• Bounds on quantum communication via Newtonian gravity
• On the Energy Increase in Space-Collapse Models
• Principle of least decoherence for Newtonian semi-classical gravity
• Constraining CSL strength parameter $\lambda$ from standard cosmology and spectral distortions of CMBR

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