# Non-commuting degrees of freedom in linear quantum gravity

## TL;DR

This paper proposes an experiment to detect non-commuting gravitational degrees of freedom, analogous to electromagnetic fields, using the weak-field limit of Einstein's General Relativity and the equivalence principle.

## Contribution

It identifies electric-like and magnetic-like components of Christoffel symbols as non-commuting gravitational degrees of freedom in the linear regime.

## Key findings

- Identification of gravitational electric-like and magnetic-like components as non-commuting.
- Proposal of experiments exploiting acceleration to explore quantum gravity.
- Analogy between electromagnetic and gravitational fields in the weak-field limit.

## Abstract

We analyse our recently proposed experiment to witness indirectly non-commuting degrees of freedom in gravity, in the light of the analogy between the electromagnetic and the gravitational field. We thereby identify the non-commuting gravitational degrees of freedom in the linear regime of Einstein's General Relativity. They are the electric-like and the magnetic-like components of the Christoffel symbol, in the weak limit of gravity. The equivalence principle can then be used to suggest further experiments of the quantum nature of gravity, exploiting acceleration only.