When we derive the formula of time dilation using light clocks, we always consider the projected light pulse in direction perpendicular to spaceship. What if we take the direction of light pulse in same direction as aircraft ? Can someone derive the time dilation formula using the light pulse direction same as aircraft direction?(when we take direction same as spaceship then time for light pulse to reach the end of clock and return again is same for observer in spaceship but these 2 time intervals are different for observer outside the spaceship, why?)
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Does this answer your question? – joseph h Sep 12 '21 at 08:20
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Referring to the link given in the comments above, I suspect that Paul T's answer may be the one sought. The thought-experiment of the 'transverse arm light clock' depends for its simplicity on the frame-invariance of transverse lengths. This isn't always emphasised in introductory treatments of SR. – Philip Wood Sep 12 '21 at 11:16
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@joseph h thanks alot – Hououin Kyouma Sep 13 '21 at 15:28
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@Philip Wood His answer is really nice but i still have a doubt...... That is he derived the answer using both the time taken by pulse to reach the end of clock and the time taken to return again. Can you please show me how to derive the formula by just consider the time taken to reach the end of tube???? – Hououin Kyouma Sep 14 '21 at 01:38