  One of the most important problems in Physics is how to reconcile Quantum
Mechanics with General Relativity. Some authors have suggested that this may be
realized at the expense of having to drop the quantum formalism in favor of a
more general theory. However, as the experiments we can perform nowadays are
far away from the range of energies where we may expect to observe non-quantum
effects, it is difficult to theorize at this respect. Here we propose a
fundamental axiom that we believe any reasonable post-quantum theory should
satisfy, namely, that such a theory should recover classical physics in the
macroscopic limit. We use this principle, together with the impossibility of
instantaneous communication, to characterize the set of correlations that can
arise between two distant observers. Although several quantum limits are
recovered, our results suggest that quantum mechanics could be falsified by a
Bell-type experiment if both observers have a sufficient number of detectors.
