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One of the best ways to think about it is the <transversal time dilation> thought experiment.


Time dilation

{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!


Ciro Santilli @cirosantilli 37

 Incoming links: Transversal time dilation