  We formulate semi-classical field theory as an approximate
decoherence-free-subspace of a finite-dimensional quantum-gravity hilbert
space. A complementarity construction can be realized as a unitary
transformation which changes the decoherence-free-subspace. This can be
translated to signify that field theory on a global slice, in certain
space-times, is the simultaneous examination of two different superselected
sectors of a field theory. We posit that a correct course graining procedure of
quantum gravity should be WKB states propagating in a curved background in
which particles exiting a horizon have imaginary components to their phases.
The field theory appears non-unitary, but it is due to the existence of
approximate decoherence free sub-spaces. Furthermore, the importance of
operator spaces in the course-graining procedure is discussed. We also briefly
touch on Firewalls.
