A classical channel model for gravitational decoherence

We show that, by treating the gravitational interaction between two mechanical resonators as a classical measurement channel, a gravitational decoherence model results that is equivalent to a model first proposed by Diosi. The resulting decoherence model implies that the classically mediated gravitational interaction between two gravitationally coupled resonators cannot create entanglement. The gravitational decoherence rate (and the complementary heating rate) is of the order of the gravitationally induced normal mode splitting of the two resonators. Failure to see this in an experiment would rule out treating gravitational interactions as purely classical.