A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a relative speed of 0.900c. A paint bomb in the engine room is set to explode (and cover everyone with blue paint) when the front of the train passes the far end of the tunnel (event FF). However, when the rear car passes the near end of the tunnel (event RN), a device in that car is set to send a signal to the engine room to deactivate the bomb. Train view: (a) What is the tunnel length? (b) Which event occurs first, FF or RN? (c) What is the time between those events? (d) Does the paint bomb explode? Tunnel view: (e) What is the train length? (f) Which event occurs first? (g) What is the time between those events? (h) Does the paint bomb explode? If your answers to (d) and (h) differ, you need to explain the paradox, because either the engine room is covered with blue paint or not; you cannot have it both ways. If your answers are the same, you need to explain why.
A relativistic train of proper length 200 m approaches a tunnel
of the same proper length, at a relative speed of 0.900c. A
paint bomb in the engine room is set to explode (and cover
everyone with blue paint) when the front of the train passes the
far end of the tunnel (event FF). However, when the rear car
passes the near end of the tunnel (event RN), a device in that car
is set to send a signal to the engine room to deactivate the bomb.
Train view: (a) What is the tunnel length? (b) Which event occurs
first, FF or RN? (c) What is the time between those events?
(d) Does the paint bomb explode? Tunnel view: (e) What is the
train length? (f) Which event occurs first? (g) What is the time
between those events? (h) Does the paint bomb explode? If your
answers to (d) and (h) differ, you need to explain the paradox,
because either the engine room is covered with blue paint or not;
you cannot have it both ways. If your answers are the same, you
need to explain why.
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