(sorry, you may have to zoom your browser out in order to see the whole animated graphic. Or find and click on the earlier link. For some reason, it appears much smaller there)
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(SNIP)
"I want you to imagine that you’ve got a clock, only instead of having a clock where a gear turns and the hands move, you have a clock where a single photon of light bounces up-and-down between two mirrors. If your clock is at rest, you see the photon bouncing up-and-down, and the seconds pass as normal. But if your clock is moving, and you look on it, how will the seconds pass, now?
A light clock moving close to the speed of light will appear to run slower relative to an observer at rest. Image credit: John D. Norton, via http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_clocks_rods/.
Quite clearly, it takes longer for the bounces to occur if the speed of light is always a constant. If time ran at the same rate for everyone, everywhere and under all conditions, then we’d see the speed of light be arbitrarily fast the faster something moved. And what’s even worse, is if something moved very quickly and then turned on a flashlight in the opposite direction, we’d see that light barely move at all: it’d be almost at rest.
Since light doesn’t do this — or change its speed-in-a-vacuum under any circumstances — we know this naive picture is wrong.