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When we try to find a formula for time dilation, we think of a situation where the velocity of the other frame is perpendicular to the velocity of the light

(http://en.wikipedia.org/wiki/Time_dilation)

Why is this? I know if we try any other direction there is length contraction involve. But the proof of length contraction goes after that right?

why not derive the formula for time dilation by considering a situation where the frame and the light goes in the same direction and then think there is a 'length expansion' for all object in the other 2 dimensions other than the direction of travel (relative to us)?

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# Time dilation question

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