Diffraction from moving gratings: negative energy solutions and relativistic effects

Diffraction from gratings moving at constant speed is calculated for electromagnetic, Klein-Gordon, and Schrödinger dispersion relations. Applicability of the results to relativistic and superluminal grating speeds is discussed. Negative total energy solutions for particles of non-zero rest mass are obtained along with static and near static inhomogeneous plane wavefunction solutions. A possible test of the Ehrenfest paradox, using a rotating radial grating, is also discussed.