The recent observation of gravitational wave signals from
coalescing binary black holes has been significantly helped, from
the theoretical side, by the availability of analytical results on the
motion and gravitational radiation of binary systems, notably via
the Effective One-Body (EOB) formalism. The extension of the
EOB Hamiltonian description to scattering states has opened a way
to transcribe classical gravitational dynamics into quantum gravitational
scattering amplitudes. We point out, however, the existence of
difficulties in extracting classical information from quantum amplitudes.
These difficulties affect the interpretation of the two-loop trans-Planckian results of
Amati, Ciafaloni and Veneziano (based on string theory), as well as the
recent two-loop results of Bern et al (based on double-copy and generalized-unitarity).