The Mossbauer effect and quasi-elastic neutron scattering (QENS) from hydrated proteins yield sharp elastic lines that are accompanied by broad wings. Conventionally, the elastic line and the broad wings are treated as separate phenomena. We show that there is no separation; the entire spectrum consists of Lorentzians with the natural line width. In protein crystals, the shifts of the individual lines from the elastic center above about 150 K are caused by beta fluctuations in the hydration shell. Vibrations cause shifts in the entire temperature range but are best seen below about 150 K. We construct a microscopic model for the dynamics that is based on a random walk of the proteins in their free-energy landscape. The model yields approximate values for the steps in the energy landscape. Remarkably, the quantum electrodynamic concept of gamma rays is needed to justify the model.