  Due to its connection to the diffeomorphism group, nonlinear quantum
mechanics may play an important role in quantum geometry. The Doebner-Goldin
nonlinearity (arising from representations of the diffeomorphism group)
amplifies nonlocal signaling effects under extreme localization, suggesting
that even if greatly suppressed at low energies, such effects may be
significant at the Planck scale. This offers new perspectives on Planck-scale
physics.
