The predominant approaches to understanding how quantum theory and General Relativity are related to each other implicitly assume that both theories use the same concept of mass. Given that despite great efforts such approaches have not yet produced a consistent falsifiable quantum theory of gravity, this paper entertains the possibility that the concepts of mass in the two theories are in fact distinct. It points out that if the concept of mass in quantum mechanics is defined such that it always exists in a superposition and is not a gravitational source, then this sharply segregates the domains of quantum theory and of general relativity. This concept of mass violates the equivalence principle applied to active gravitational mass, but may still produce effects consistent with the equivalence principle when applied to passive gravitational mass (in agreement with observations) by the correspondence principle applied to a weak field in the appropriate limit. An experiment that successfully measures the gravity field of quantum objects in a superposition, and in particular of photons, would not only falsify this distinction but also constitute the first direct empirical test that gravity must in fact be described fundamentally by a quantum theory.