Minimal noise in non-quantized gravity

TL;DR

This paper classifies models of non-quantized gravity, showing that a minimal noise level is necessary to prevent entanglement, and proposes experimental tests to distinguish quantum from classical gravity.

Contribution

It provides a systematic classification of non-quantized gravity models and identifies a quantifiable noise threshold for non-entangling behavior.

Findings

Any non-entangling model must inject a minimal amount of noise.

Measuring below this noise threshold would imply gravity is entangling.

Analyzes classical-quantum gravity models and entropic force models in experimental setups.

Abstract

An elementary prediction of the quantization of the gravitational field is that the Newtonian interaction can entangle pairs of massive objects. Conversely, in models of gravity in which the field is not quantized, the gravitational interaction necessarily comes with some level of noise, i.e., non-reversibility. Here, we give a systematic classification of all possible such models consistent with the basic requirements that the non-relativistic limit is Galilean invariant and reproduces the Newtonian interaction on average. We demonstrate that for any such model to be non-entangling, a quantifiable, minimal amount of noise must be injected into any experimental system. Thus, measuring gravitating systems at noise levels below this threshold would be equivalent to demonstrating that Newtonian gravity is entangling. As concrete examples, we analyze our general predictions in a number of experimental setups, and test it on the classical-quantum gravity models of Oppenheim et al., as well as on a recent model of Newtonian gravity as an entropic force.