(a) Suppose we have a tunnel of 800 feet long in its rest with doors on each end which can be used to seal the tunnel. The train is 1,000 feet long in its own rest frame, as shown in the illustration: Tunnel rest frame sliding door Train rest frame tunnel: 800 feet long in rest frame Lorentz contracted length - 600 feet Train rest frame If the train travels at v=0.8c, would it fit in the tunnel? Justify (calculate etc) (b) But what happens in the train's perspective? Is the tunnel too short? -Lorentz contracted 480 feet long- It is impossible for the entire train to be trapped inside the tunnel!! train: 1,000 feet long in rest frame Explain. (c) The solution to this paradox, as mentioned, was the breaking of simultaneity. If the doors were shut simultaneously in the tunnel's rest frame, what would be the time gap for the shutting doors in the train's frame? 0.8 c sliding door Doors slam shut simultaneously at -0, trapping entire train inside the tunnel -640 nsec -Lorentz contracted: 480 feet long. train: 1,000 feet long in rest frame 0 nsec (d) Argue that the train would stay intact even if the doors were to slam in the tunnel's frame.

(a) Suppose we have a tunnel of 800 feet long in its rest with doors on each end which can be used to seal the tunnel. The train is 1,000 feet long in its own rest frame, as shown in the illustration: Tunnel rest frame sliding door Train rest frame tunnel: 800 feet long in rest frame Lorentz contracted length - 600 feet Train rest frame If the train travels at v=0.8c, would it fit in the tunnel? Justify (calculate etc) (b) But what happens in the train's perspective? Is the tunnel too short? -Lorentz contracted 480 feet long- It is impossible for the entire train to be trapped inside the tunnel!! train: 1,000 feet long in rest frame Explain. (c) The solution to this paradox, as mentioned, was the breaking of simultaneity. If the doors were shut simultaneously in the tunnel's rest frame, what would be the time gap for the shutting doors in the train's frame? 0.8 c sliding door Doors slam shut simultaneously at -0, trapping entire train inside the tunnel -640 nsec -Lorentz contracted: 480 feet long. train: 1,000 feet long in rest frame 0 nsec (d) Argue that the train would stay intact even if the doors were to slam in the tunnel's frame.