  Entropic dynamics (ED) is a general framework for constructing
indeterministic dynamical models based on entropic methods. ED has been used to
derive or reconstruct both non-relativistic quantum mechanics and quantum field
theory in curved space-time. Here we propose a model for a quantum scalar field
propagating in a dynamical space-time. The approach rests on a few key
ingredients: (1) Rather than modelling the dynamics of the fields, ED models
the dynamics of their probabilities. (2) In accordance with the standard
entropic methods of inference the dynamics is dictated by information encoded
in constraints. (3) The choice of the physically relevant constraints is
dictated by principles of symmetry and invariance. The first such principle
imposes the preservation of a symplectic structure which leads to a Hamiltonian
formalism with its attendant Poisson brackets and action principle. The second
symmetry principle is foliation invariance, which following earlier work by
Hojman, Kuchar, and Teitelboim, is implemented as a requirement of path
independence. The result is a hybrid ED model that approaches quantum field
theory in one limit and classical general relativity in another, but is not
fully described by either. A particularly significant prediction of this ED
model is that the coupling of quantum fields to gravity implies violations of
the quantum superposition principle.
