  Any acceptable quantum gravity theory must allow us to recover the classical
spacetime in the appropriate limit. Moreover, the spacetime geometrical notions
should be intrinsically tied to the behavior of the matter that probes them. We
consider some difficulties that would be confronted in attempting such an
enterprise. The problems we uncover seem to go beyond the technical level to
the point of questioning the overall feasibility of the project. The main issue
is related to the fact that, in the quantum theory, it is impossible to assign
a trajectory to a physical object, and, on the other hand, according to the
basic tenets of the geometrization of gravity, it is precisely the trajectories
of free localized objects that define the spacetime geometry. The insights
gained in this analysis should be relevant to those interested in the quest for
a quantum theory of gravity and might help refocus some of its goals.
