A no-go theorem on the nature of the gravitational Field beyond quantum theory

In this talk I will discuss some recent work with Thomas D. Galley and Flaminia Giacomini, in which we apply the formalism of generalised probabilistic theories to the study of the nature of the gravitational field. Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field. The formalism allows us to study this problem without having to make any precommitments to any particular model of gravity or ontological notions. By analysing these experiments within the framework of GPTs we prove that the following are inconsistent i) the gravitational field is the mediator of an interaction between two systems; ii) entanglement is generated between the two systems; iii) the field is classical. I will discuss the particularly interesting case which is a violation of condition (iii), a violation of which has commonly been viewed as evidence for the quantum nature of the gravitational field. From the perspective of GPTs, however, we see that there are other possibilities. That is, I will discuss other examples of non-classical but non-quantum theories which are nonetheless consistent with conditions (i) and (ii). This leaves an important open question, what evidence do we actually need in order to conclude that the gravitational field is quantum?