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Right now, I'm studying time dilation. I think I understand the thought experiment which involved a laser reflecting from a mirror in a train car, (Page 15 of Modern Physics, Serway, Moses, Moyer) and the derivation of

[tex]\Delta t = \gamma \Delta t_p[/tex]

using a right triangle.

My problem is, I made up a different (most probably flawed) thought experiment, through which I cannot arrive at the same formula. Here it is: There is a stationary observer in O, who has a light source which emits in +x direction, and I call his reference frame S. There is another observer in O, with a constant velocity u in +x direction. Call his reference frame S'. Now, after [tex]\Delta

t[/tex] time for a clock in S, the second observer has moved [tex]u \Delta t[/tex], the light [tex]c \Delta t[/tex]. So, the light went [tex](c - u)\Delta t[/tex] according to the observer in S'. If [tex]\Delta

t'[/tex] is the time passed in S', [tex]\frac{(c - u)\Delta t} {\Delta t'} = c[/tex] because the observer in S' should see the speed of light as c too. But this is not equivalent to [tex]\Delta t = \gamma \Delta t_p[/tex] mathematically. What am I missing here?

Thank you.

(I'm not experienced with LaTeX, so I will edit the post until the tex code is correct.)

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# Question About Time Dilation

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