  In hybrid classical-quantum theories, the dynamics of the classical system
induce the classicality of the quantum system, meaning that such models do not
necessarily require a measurement postulate to describe probabilistic
measurement outcomes. It has recently been shown that covariant
classical-quantum dynamics can be constructed using path integral methods, with
the dynamics encoded in a combined action for the classical and quantum
variables. This work introduces a classical-quantum model whereby quantum
gravity interacts with a classical scalar field. The scalar field can be viewed
as fundamentally classical or effectively classical due to the decoherence of a
quantum gravity theory. The dynamics act to collapse quantum spacetimes
according to their Ricci scalar, with corresponding diffusion in the scalar
field due to the quantum back-reaction. In the classical limit, the diffusion
in the scalar field manifests itself via stochastic fluctuations in the
Newtonian potential. Because we couple a classical scalar field to perturbative
quantum gravity, we find the theory is not renormalizable but is instead to be
viewed as an effective field theory. However, it is an effective field theory
that does not necessarily require a measurement postulate. More generally, our
work shows it is possible to integrate collapse dynamics with high-energy
physics and covariance.
