# Newtonian self-gravity in trapped quantum systems and experimental tests

## TL;DR

This paper discusses the Schr"odinger-Newton equation as a semi-classical gravity model, exploring its potential for experimental tests to determine if gravity must be quantized, addressing a fundamental question in physics.

## Contribution

It analyzes the experimental feasibility of testing the Schr"odinger-Newton equation as an alternative to quantum gravity theories.

## Key findings

- The Schr"odinger-Newton equation introduces nonlinear modifications to quantum mechanics.
- Proposes experimental setups to test semi-classical gravity effects.
- Highlights the importance of such tests for understanding gravity's quantum nature.

## Abstract

No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling between classical gravity and quantum matter according to the semi-classical Einstein equations, yields a nonlinear modification of the Schr\"odinger equation. Here, effects of this so-called Schr\"odinger-Newton equation are discussed, which allow for technologically feasible experimental tests.