Teaching about the relativistic background of synchrotron radiation: some intriguing aspects with strong didactic implications

Not fully grasping the concepts of relativity can lead to misunderstandings about the fundamental background of synchrotron emission. Here we deal with some intriguing cases, in which the relevant `speed of light' is not the invariant c but the speed with respect to a moving object. This specifically affects two pillars of synchrotron radiation: the Lorentz length contraction and the Doppler shift. We propose a teaching strategy relying on new versions of simple `thought' experiments. Besides putting synchrotron radiation on solid foundations, the approach amazingly leads to a unique link-described by Einstein as `remarkable'-between special relativity and quantum mechanics.