Absence of gravitationally induced entanglement in certain semi-classical theories of gravity

TL;DR

This paper demonstrates that certain semi-classical gravity models, including the Newton-Schrödinger and Bohmian models, do not produce entanglement, contrasting with quantum gravity predictions.

Contribution

It provides a rigorous analysis showing that specific semi-classical gravity models cannot generate entanglement in proposed experiments, challenging their quantum nature.

Findings

Semi-classical models do not generate entanglement in the proposed experiment.

The Newton-Schrödinger and Bohmian models are included in the analysis.

Standard Newtonian gravity can generate entanglement, unlike the semi-classical models.

Abstract

Bose et al. and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schr\"odinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton-Schr\"odinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by D\"oner and Grossardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement.