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The one that always got me:
The speed of light is constant regardless of the frame of reference, so, If there were a concave mirror - a bowl with a perfectly reflective inside surface - travelling through space at the speed of light with respect to the observer, and light were to hit that bowl, would it remain in the bowl? Would it pool in there? How would it appear to the observer?
Now, I have taken relativistic physics in college (not doing particularly well, but I did pass) and it still gets me. I understand that from the bowl's frame of reference, it's stationary, and light hitting it enters and leaves at the speed of light without a Doppler effect, but to the observer light hitting an object at the speed of light should have its wavelength compressed to zero.
So there you have it - a nagging problem with no application.
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Set a man on fire, and he will be warm for the rest of his life.
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