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Problem 4 A train with length Lo, as measured in the train's rest frame S", is moving toward a tunnel with velocity B = v/c in the +x-direction. The tunnel has length Lo in the rest frame of the Earth, S. (a) For an observer standing on the side of the train tracks, or the S frame, what is the observed length of the train? From the point of view of the observer on the side of the tracks, will there be a point in time in which the train has completely disappeared into the tunnel (i.e., will there be a moment in which no part of the train is sticking out of the tunnel)? (b) For an observer within the train, or the S' frame, what is the observed length of the tunnel? From the point of view of the observer in the train, will there be a point in time in which the train has completely disappeared into the tunnel? The answers you've obtained should present a paradoxical situation. Suppose that within the reference frame of an observer at the side of the train tracks, two doors simultaneously open and close at each end of the tunnel, immediately after the back of the train enters the tunnel. (c) Suppose that the left-most tunnel door closes at t = t' = 0 and x = x =0. At what time and location does the right-most tunnel door close in the S frame? (d) At what time and location does the right-most tunnel door close in the S' frame? (e) How does this resolve the paradox we encountered