A relativistic train of proper length 237 m approaches a tunnel of the same proper length, at a relative speed of 0.951c. 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? ans: 77.3m (b) Which event occurs first, FF or RN? ans: FF (c) What is the time between those events? ans: 5.74E-7 s (d) Does the paint bomb explode? ans: YES Tunnel view:(e) What is the train length? ans: 77.3m (f) Which event occurs first? RN (g) What is the time between those events? ans: 5.74E-9 s (h) Does the paint bomb explode? ans: YESIf 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.
The Attempt at a Solution
I got part a thru g correct, what I could not understand is the answer to part (h) is yes. I believe from the tunnel's point of view the train (L=77.3m) has its rear passes thru the near end of tunnel (L0=273m) before its front passes thru the far end. This indicates that the bomb is deactivated first.