Abstract
The search for a quantum theory of gravity must include the recovery of the classical space-time. We consider some of the diculties that must be confronted in any such enterprise. These problems 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 not possible to assign a trajectory to a physical object and, on the other hand, according to the basic tenants of the geometrization of gravity, it is precisely the trajectories of localized objects that de ne the space-time geometry. This indicates that we should revise the standard geometrical concepts and explore the corresponding notions that could have, at least in principle, operational meaning and that would be at the heart of the above mentioned recovery. The insights gained in this analysis should be relevant to the quest for a quantum theory of gravity even before such theory is completely developed, and might help refocus some of its goals.
Yuri Bonder