Title: Any consistent coupling between classical gravity and quantum matter is fundamentally irreversible

Abstract: When gravity is sourced by a quantum system, there is tension between its role as the mediator of a fundamental interaction, which is expected to acquire nonclassical features, and its role in determining the properties of spacetime, which is inherently classical. Fundamentally, this tension should result in breaking one of the fundamental principles of quantum theory or general relativity, but it is usually hard to assess which one without resorting to a specific model. Here, we answer this question in a theory-independent way using General Probabilistic Theories (GPTs). We consider the interactions of the gravitational field with a single matter system, and derive a no-go theorem showing that when gravity is classical at least one of the following assumptions needs to be violated: (i) Matter degrees of freedom are described by fully non-classical degrees of freedom; (ii) Interactions between matter degrees of freedom and the gravitational field are reversible; (iii) Matter degrees of freedom back-react on the gravitational field. We argue that this implies that theories of classical gravity and quantum matter must be fundamentally irreversible, as is the case in the recent model of Oppenheim et al. [1]. We show that Mielinik’s statement in [2] that “either gravity is quantum or the electron is classical” holds only under the assumption of reversibility and argue that this assumption plays a key role in arguments for the quantisation of the gravitational field. Finally we will relate our result to existing work on quantum-classical couplings, such as [3], highlighting the operational framework used in our work and the advantages of a theory independent approach.