After thinking about the Free-electron x-ray laser device a bit longer, I realize that it appears to demonstrate time dilation as well as Lorentz contraction rather neatly. In my earlier post I pointed out the excellent reference in Wikipedia about the Lorentz contraction being directly demonstrated by the output frequency of the laser. The mathematical contribution of the contraction enters directly into the calculation of the x-ray output frequency in a manner that is difficult to argue against.
It appears that the same is true for a demonstration of time dilation according to special relativity (SR). Here is one example of how time dilation is exhibited: The undulator is a structure that exists in our stationary frame of reference through which the relativistic electron beam propagates. It consists of a series of permanent magnets that alternate poles along its length such that the electrons are accelerated at right angles to their main high velocity path by a modest amount as they pass through the structure. We observe them moving up and down or right and left depending upon the design of the undulator. Since the device operates by using electrons that are traveling at very nearly the speed of light, we observe only a tiny change in frequency of that right angle motion as their speed creeps up toward the light speed limit. Here I am referring to what we see looking from the side of the undulator at the moving electrons. To put this measurement into perspective, very little difference is observed in the motion of the electrons even though the laser output frequency changes over an order of magnitude in frequency. We would conclude that the frequency of the up and down electron motion remains essentially unchanged as energy is imparted upon the electrons by the system. At the same time the actual measured output frequency of x-rays emitted changes over an order of magnitude according to real life systems. This can readily be explained by realizing that we are actually observing time dilation at work. This is evident because the observed change in velocity of the series of electrons approaches a limit of c while the time dilation increases without bounds as that limit is neared. I find this laser device to be one of the best demonstrations of SR that I have encountered. Here one device can be built which clearly shows how time dilation and length contraction occur with motion of relativistic electrons. Any reference to Doppler confusion is nothing but hand waving. An injection signal of very small amplitude is sometimes utilized to lock the high power output x-ray signal to its phase. This allows the operator to significantly reduce the noise that typically would be seen had the device been allowed to operate with the non uniform electron beam. Careful analysis of the operation and construction of this type of device should be adequate to explain SR to all but the most determined skeptics. Harry, your train thought experiment should be simulated by the operation of one of these devices. The track is replaced by the undulator and the electron beam can stand in for the train. Both Lorentz contraction and time dilation are demonstrated in a real world type of device. Refer to the article for an excellent description of this type of device: http://en.wikipedia.org/wiki/Free-electron_laser Dave
