(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 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!! 0.8 c 13 train: 1,000 feet long in rest frame 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? 5858. -0.8 c 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 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!! 0.8 c 13 train: 1,000 feet long in rest frame 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? 5858. -0.8 c 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.
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Answer c
Transcribed Image Text:(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
Train rest
frame
Lorentz contracted length = 600 feet
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!!
0.8 c
——
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.
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Can you explain step 2, how did you get 146.304 and 8.128*10^-7 and the formula used to get the final answer?
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