# Why does time dilation imply length contraction? [duplicate]

This is probably a nonsensical question, but I'm having trouble wrapping my head around it. I'm thinking of the classic scenario where a stationary observer is watching a spaceship move horizontally. It makes perfect sense to me that a beam of light bouncing up and down will appear to move more slowly vertically, since it has to also move horizontally. This produces the time dilation effect. However, I don't see why this same dilation factor has to apply to a beam of light moving horizontally. This is the way that I have seen length contraction derived. It sounds peculiar, but couldn't there be a different time dilation factor for objects moving horizontally versus vertically on the spaceship?

edit: I believe this can be explained by thinking about a beam of light moving diagonally on the spaceship, but I'll leave the question up in case someone has a better explanation.

• This answer seems relevant. And your question might be a duplicate of this question. – Alfred Centauri Jul 22 '20 at 17:07
• John Norton has a nice discussion on this: pitt.edu/~jdnorton/teaching/HPS_0410/chapters/… – PM 2Ring Jul 22 '20 at 17:18
• @PM2Ring That's it! What I was missing was that the clocks would have to go through the same number of ticks regardless of reference frame. – Jeff Bass Jul 22 '20 at 17:25
• @AlfredCentauri I agree that my question is a duplicate. That answer was perfect. – Jeff Bass Jul 22 '20 at 17:27
• As Norton points out in the section "All Moving Clocks Are Slowed by Motion", there's a short-cut to see that all clocks must experience the same dilation: if they didn't we could build a device to detect absolute motion, and that contradicts the principle of relativity that there's no such thing as absolute motion, as explained here – PM 2Ring Jul 22 '20 at 17:43