Gravitational interaction through a feedback mechanism

TL;DR

This paper compares two models of quantum gravity via measurement and feedback, finds limitations in generalizing one model, and suggests the other as the most viable approach for implementing Newtonian gravity in quantum systems.

Contribution

It analyzes the generalization of KTM and TD models for multiple particles and identifies the TD model as the only consistent full-Newtonian implementation under simple conditions.

Findings

KTM model cannot be straightforwardly generalized to multiple particles without issues.

TD model does not reduce to KTM under certain approximations.

TD model is the only viable full-Newtonian gravity implementation via measurement and feedback.

Abstract

We study the models of Kafri, Taylor and Milburn (KTM) and Tilloy and Di\'osi (TD), both of which implement gravity between quantum systems through a continuous measurement and feedback mechanism. The first model is for two particles, moving in one dimension, where the Newtonian potential is linearized. The second is applicable to any quantum system, within the context of Newtonian gravity. We address the issue of how to generalize the KTM model for an arbitrary finite number of particles. We find that the most straightforward generalisations are either inconsistent or are ruled out by experimental evidence. We also show that the TD model does not reduce to the KTM model under the approximations which define the latter model. We then argue that under the simplest conditions, the TD model is the only viable implementation of a full-Newtonian interaction through a continuous measurement and feedback mechanism.