Decoherence vs space-time diffusion: testing the quantum nature of gravity

Consistent dynamics which couples classical and quantum systems exists, provided it is stochastic. This provides a way to
study the back-reaction of quantum systems on classical ones and has recently been explored in the context of quantum fields back-reacting
on space-time. Since the dynamics is completely positive and circumvents various no-go theorems this can either be thought of as a fundamental theory, or as an effective theory describing the limit of quantum gravity where the gravitational degrees of freedom are taken to be classical. In this talk we explore some of the consequences of complete positivity on the dynamics of classical-quantum systems. We show that complete positivity necessarily results in the decoherence of the quantum system, and a breakdown of predictability in the classical-phase space. We prove there is a trade-off between the rate of this decoherence and the degree of diffusion in the metric: long coherence times require strong diffusion relative to the strength of the coupling, which potentially provides a long-distance experimental test of the quantum nature of gravity  We discuss the consequences of complete positivity on preparing superpositions of gravitationally different states. Each state produces different distributions of the gravitational field determined by the constraints of the theory. The overlap of these distributions imposes an upper bound on the degree of coherence of the superposition.