  Semi-classical gravity attempts to define a hybrid theory in which a
classical gravitational field is coupled to a unitarily evolving quantum state.
Although semi-classical gravity is inconsistent with observation, a viable
theory of this type might be appealing, since it potentially might preserve the
basic features of our two most successful theories while unifying them. It
might also offer a natural solution to the quantum measurement problem. I
explore the scope for such "semi-quantum" hybrid theories, and note some
interesting, though daunting, constraints. Consistency with observation
generally requires pyschophysical parallelism with the classical gravitational
field rather than the quantum matter. Solvability suggests the gravitational
field at a point should be determined by physics in its past light cone, which
requires local hidden variables and predicts anomalously non-Newtonian
gravitational fields. These predictions could be tested by low energy, although
technologically challenging, experiments in which the Bell non-locality of the
gravitational field is verified by direct measurement.
