Is Time Reversed in Special Relativity When Moving Opposite to Light?

[ghost34]

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?

 

[zhermes]

Excellent question ghost34, and welcome to PF.

You're right, the path length would be smaller in the second case, but that would not mean that the effect of time dilation would be reversed.

In special relativity, length contraction only occurs in the direction of motion. Thus, having a light beam traveling perpendicular to the direction of motion (i.e. up and down) makes sure that there is no length contraction effecting the experiment (i.e. the clock). Therefore the only observed effect is due to time dilation.

If you point the laser partially in the direction of motion then two effects are taking place; time dilation and length contraction---making the overall interpretation different.

 

[ghost34]

Ah, I see. Thank you very much, zhermes!

 

[jartsa]

No, if you move in the opposite direction of the light, then light moves faster in the opposite direction of you, therefore light must move slower in some other direction, which means light must travel a long distance in the direction of the fast motion, in order to travel a short distance in the direction of the slow motion.

It takes a long time to travel a long distance + a short distance

There may be a simple way to say this too.