Simple Refutation of the Eppley-Hannah argument

Abstract

In an influential paper, Eppley and Hannah argued that gravity must necessarily be quantized, by proposing a thought experiment involving classical gravitational waves interacting with quantum matter. They argue the interaction must either violate the uncertainty principle or allow superluminal signalling. The feasibility of implementing their experiment in our universe has been challenged by Mattingly, and other limitations of the argument have been noted by Huggett and Callender and by Albers et al.. However, these critiques do not directly refute the claim that coupling quantum theories with a Copenhagen collapse postulate to unentanglable classical gravitational degrees of freedom leads to contradiction. I note here that if the gravitational field interacts with matter via the local quantum state, the Eppley-Hannah argument evidently fails. This seems a plausibly natural feature of a hybrid theory, whereas the alternative considered by Eppley-Hannah is evidently inconsistent with relativity.