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 Quote by Fredrik In A's rest frame, the mirrors are moving, so the light going from the top mirror to the bottom is going "diagonally". The distance between the mirrors is the same in both frames. Light going from the top mirror to the bottom travels a distance d=ct in B's frame, and ct' in A's frame (where t' is the time measured by A). The pythagoran theorem tells us that ##(ct')^2=(ct)^2+(vt')^2##. Solve this for t, and you get $$t=\frac{t'}{\sqrt{1-\frac{v^2}{c^2}}}=\gamma t'.$$.
Yes I thought about this too. But the result seems strange to me, because it now predicts that time goes slower in the rest frame and not in the moving frame, just because we changed the location of the experiment.

For example if we had done the experiment in frame A instead of B, t and t' would change place in the equation predicting opposite results, as such:

$$t'=\frac{t}{\sqrt{1-\frac{v^2}{c^2}}}.$$.

How is this possible?