{{wiki=Time_dilation#Simple_inference_of_velocity_time_dilation}}

Light watch transverse to direction of motion. This case is interesting because it separates <length contraction> from <time dilation> completely.

Of course, as usual in <special relativity>, calling something "time dilation" leads us to <mind boggling> ideas of "symmetry breaking": if both frames have a light watch, how can both possibly observe the other to be time dilated?

And the answer to this, is the usual: in special relativity time and space are interwoven in a <fucked> up way, everything is just a spacetime event.

In this case, there are three spacetime events of interest: both clocks start at same position, your beam hits up at x=0, moving frame hits up at x>0.

Those two mentioned events are <spacelike-separated events>, and therefore even though they seem simultaneous to you, they are not going to be simultaneous to the moving observer!

If <Einstein synchronization>[little clock one meter away from you] tells you that at the time of some event (your light beam hit up) the moving light watch was only 50% up, this is just a number given by your one meter away watch!


Discussion on "Transversal time dilation" by Ciro Santilli 32