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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.

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    $\begingroup$ This answer seems relevant. And your question might be a duplicate of this question. $\endgroup$ – Alfred Centauri Jul 22 '20 at 17:07
  • $\begingroup$ John Norton has a nice discussion on this: pitt.edu/~jdnorton/teaching/HPS_0410/chapters/… $\endgroup$ – PM 2Ring Jul 22 '20 at 17:18
  • $\begingroup$ @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. $\endgroup$ – Jeff Bass Jul 22 '20 at 17:25
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    $\begingroup$ @AlfredCentauri I agree that my question is a duplicate. That answer was perfect. $\endgroup$ – Jeff Bass Jul 22 '20 at 17:27
  • $\begingroup$ 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 $\endgroup$ – PM 2Ring Jul 22 '20 at 17:43
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Think of a relativistic train passing you. to measure its length you have two color spraying pistols in a distance d, then spray at the same moment of time. then you would say the two colospots have the distance d, bu the people on the train will not agree, the measure a different distance an tell you , the spraying was not dane at the same moment. (the length perpendicular to the movement is not changed it is the same in both systms.) The thought experiment , you are talking about, is not so good, since it is not symmetrical in the two systems, but it does not depend on the clocks being perpendicular to the movement.

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