> There is at least one known mechanism that cause Doppler WITHOUT moving: when the observer is in a gravity well This is gravitational redshift, not Doppler s

> There is at least one known mechanism that cause Doppler WITHOUT moving: when the observer is in a gravity well This is gravitational redshift, not Doppler shift. Doppler shift specifically means redshift due to an object moving away--but to really be correct that definition has to be limited to flat spacetime, or to a small enough region in a curved spacetime that the curvature can be ignored.