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physics of special relativity
1. Consider two inertial frames of reference associated with a platform (P) and a moving train (T). Denote the length of the train in its rest frame T by L. The train is moving with a speed u relative to the platform. Use the Lorentz transformation equations to derive the length contraction relation for the train from a) the perspective of the platform frame of reference P and b) from the perspective of the train frame of the reference T. Carry out a similar analysis for clocks at rest in the train frame of reference to derive the time dilation relation.