We consider two interacting systems when one is treated classically while the other remains quantum. Despite several
famous no-go arguments, consistent dynamics of this coupling exist, and we derive its most general form. We apply this framework
to general relativity, and present a theory of classical gravity coupled to quantum field theory. The theory doesn't suffer from
the pathologies of the semi-classical Einstein's equation and can be considered as a candidate for a fundamental theory, or one
which is effective. If any system is treated as fundamentally classical, the dynamics necessarily results in decoherence of
quantum systems and a breakdown in predictability in classical phase space. We prove that a trade-off between the rate of
decoherence and the degree of diffusion induced in the classical system is a general feature of all classical-quantum dynamics.
When the trade-off is saturated, the quantum state remains pure conditioned on the classical trajectory and the measurement
postulate and Born rule is not needed. Applying the trade-off, we find a relationship between the strength of
gravitationally-induced decoherence versus diffusion of the metric. This provides an experimental signature of theories in which
gravity is fundamentally classical. Bounds on decoherence rates arising from current interferometry experiments, combined with
precision measurements of mass, place significant restrictions on theories where Einstein's classical theory of gravity interacts
with quantum matter.
Based on joint work with Carlo Sparaciari, Barbara Šoda & Zachary Weller-Davies