  Gravitation, according to General Relativity, is an attribute of space-time's
geometry and hence not a force in the Newtonian sense. This is a consequence of
Einstein's equivalence principle, which so far passed all experimental tests
with high precision. However, the search for possible violations continues, for
they, as the case may be, are expected to point towards more fundamental
theoretical extensions of General Relativity. In particular, it is expected
that useful insights are gained by studying the interaction between
gravitational fields and genuine quantum-mechanical systems, like atoms or
molecules. But this raises some fundamental issues, for General Relativity and
Quantum Theory rest on partially incompatible sets of concepts. This article
tries to explain in an elementary fashion how these issues recently entered
modern research in atom interferometry. A shorter and editorially adapted
version of this paper will appear in "Spektrum der Wissenschaft" -- the German
edition of "Scientific American".
