Gravitational effects in macroscopic quantum systems: a first-principles analysis

TL;DR

This paper investigates the weak-field limit of general relativity combined with quantum matter, revealing that certain proposed gravitational quantum phenomena do not involve true gravitational degrees of freedom and emphasizing the importance of a consistent quantisation approach.

Contribution

It provides a first-principles analysis of gravitational effects in macroscopic quantum systems, highlighting the nature of weak gravity as a parameterised field theory and discussing quantisation ambiguities.

Findings

Proposed gravitational quantum phenomena lack true gravitational degrees of freedom.

Weak gravity with matter is a parameterised field theory, not full GR.

Gauge-fixing quantisation introduces gauge dependence and the problem of time.

Abstract

We analyze the weak-field limit of General Relativity with matter and its possible quantisations. This analysis aims towards a predictive quantum theory to provide a first-principles description of gravitational effects in macroscopic quantum systems. This includes recently proposed experiments on the generation of (Newtonian) gravitational forces from quantum distributions of matter, and phenomena like gravity-induced entanglement, gravitational cat states, gravity-induced Rabi oscillations, and quantum causal orderings of events. Our main results include: (i) The demonstration that these phenomena do not involve true gravitational degrees of freedom. (ii) We show that, unlike full general relativity, weak gravity with matter is a parameterised field theory, i.e., a theory obtained by promoting spacetime coordinates to `dynamical' variables. (iii) Quantisation via gauge-fixing leads to an effective field theory that account for some phenomena, but at the price of gauge dependence that manifests more strongly on spacetime observables. This ambiguity is a manifestation of the problem of time that persists even in weak gravity. (iv) A consistent quantisation of parameterised field theories is essential for a predictive and spacetime covariant theory of weak gravity that describes gravitational effects in macroscopic quantum systems. We also discuss the implication of our results to gravitational decoherence theories, the notion of locality in gravity vis-a-vis quantum information theory, and the intriguing possibility that proposed solutions to the problem of time can be tested in weak-gravity quantum experiments.