Answer d pl (a) Suppose we have a tunnel of 800 feet long in its rest with doors on each end whichcan be used to seal the tunnel. The train is 1,000 feet long in its own rest frame, asshown in the illustration:Tunnel restframesliding doorTrain restframetunnel: 800 feet long in rest frameTrain restframeLorentz contracted length = 600 feetIf 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 impossiblefor the entiretrain to betrapped inside thetunnel!!0.8 c——train: 1,000 feet long in rest frame0.8 c0.8 cExplain.(c) The solution to this paradox, as mentioned, was the breaking of simultaneity. If thedoors were shut simultaneously in the tunnel's rest frame, what would be the timegap for the shutting doors in the train's frame?sliding door-640 nsecDoors slam shutsimultaneously at-0, trappingentire train insidethe tunneltrain: 1,000 feet long in rest frame-Lorentz contracted: 480 feet long.0 nsec(d) Argue that the train would stay intact even if the doors were to slam in the tunnel'sframe.

Length of train = 1000 ft Speed of train = 0.8 c Tunnel width = 800 ft

(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 inrest frame Lorentz contracted length=600 feet Train rest frame It is impossible for the entire 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- train to be trapped inside the 0.8 c tunnel!! S train: 1,000 feet long in rest frame 0.8 c 0.8 c 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? sliding door -640 nsec Doors slam shut simultaneously at -0, trapping entire train inside the tunnel train: 1,000 feet long in rest frame -Lorentz contracted: 480 feet long. 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 inrest frame Lorentz contracted length=600 feet Train rest frame It is impossible for the entire 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- train to be trapped inside the 0.8 c tunnel!! S train: 1,000 feet long in rest frame 0.8 c 0.8 c 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? sliding door -640 nsec Doors slam shut simultaneously at -0, trapping entire train inside the tunnel train: 1,000 feet long in rest frame -Lorentz contracted: 480 feet long. 0 nsec (d) Argue that the train would stay intact even if the doors were to slam in the tunnel's frame.