  A mathematically consistent procedure for coupling quasiclassical and quantum
variables through coupled Hamilton-Heisenberg equations of motion is derived
from a variational principle. During evolution, the quasiclassical variables
become entangled with the quantum variables with the result that the value of
the quasiclassical variables depends on the quantum state. This provides a
formalism to compute the backreaction of any quantum system on a quasiclassical
one. In particular, it leads to a natural candidate for a theory of gravity
coupled to quantized matter in which the gravitational field is not quantized.
