Non-commuting degrees of freedom in linear quantum gravity

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.