Can one have a consistent theory
of classical systems coupled to quantum ones? Yes. We construct a theory of classical gravity
coupled to quantum field theory. The
theory doesn't suffer the pathologies of semi-classical gravity and reduces to
Einstein's equations in the appropriate limit. The assumption that gravity is
classical necessarily modifies the dynamical laws of quantum mechanics -- the
theory must be fundamentally information destroying involving finite sized and
stochastic jumps in space-time and in the quantum field. The measurement postulate of quantum
mechanics is not needed since the interaction of the quantum degrees of freedom
with classical space-time necessarily causes collapse of the wave-function. The
theory can be regarded as fundamental, or as an effective theory of the
backreaction of quantum fields on space-time.