  The experimental results that test Bell's inequality have found strong
evidence suggesting that there are nonlocal aspects in nature. Evidently, these
nonlocal effects, which concern spacelike separated regions, create an enormous
tension between general relativity and quantum mechanics. In addition, by
avoiding the coincidence limit, semiclassical gravity can also accommodate
nonlocal aspects. Motivated by these results, we study if it is possible to
construct geometrical theories of gravitation that are nonlocal in the sense of
Bell. We propose three constructions of such theories, which could constitute
an important step towards our understanding of the interplay between quantum
mechanics and gravitation.
