I've just been introduced to special relativity and time dilation. I understand that if someone in a frame of reference X bounces a beam of light vertically within two parallel mirrors, I, in a frame of reference Y moving at a uniform velocity 'U' from X, will see the light beam moving across a hypotenuse (diagonally), and given the postulate that the speed of light is equal for all observers, it will take me more time to view this same beam of light, and the person in frame of reference X can say that my clocks are slowing down. But let's say that the person in frame of reference X intentionally shoots a beam of light diagonally across the same mirrors, so that the light is traveling diagonally within his own frame of reference. If I am moving at velocity U in the opposite direction of the light, is it not possible (if U isn't very large) that I'll see the beam of light traveling across a shorter distance? If this is true, is it not possible that the person in frame of reference X can rightly say that my time will be faster due to how the light appears in my reference frame?