Gravitational entanglement and the mass contribution of internal energy in nonrelativistic quantum systems

TL;DR

This paper explores the interplay between gravitational entanglement and the mass contribution of internal energy in nonrelativistic quantum systems, highlighting conceptual inconsistencies and the need for a rigorous derivation from first principles.

Contribution

It demonstrates that combining gravitational entanglement with internal energy contributions leads to inconsistencies, emphasizing the importance of deriving the nonrelativistic limit from fundamental quantum gravity principles.

Findings

Identifies conceptual inconsistencies in combining gravitational entanglement with internal energy contributions.

Highlights the necessity of a first-principles derivation for nonrelativistic quantum gravity.

Reinforces the importance of rigorous theoretical foundations for quantum gravity models.

Abstract

Recently, interest has increased in the entanglement of remote quantum particles through the Newtonian gravitational interaction, both from a fundamental perspective and as a test case for the quantization of gravity. Likewise, post-Newtonian gravitational effects in composite nonrelativistic quantum systems have been discussed, where the internal energy contributes to the mass, promoting the mass to a Hilbert space operator. Employing a modified version of a previously considered thought experiment, it can be shown that both concepts, when combined, result in inconsistencies, reinforcing the arguments for the necessity of a rigorous derivation of the nonrelativistic limit of gravitating quantum matter from first principles.