A rocket of proper length flies at straight through a hangar of proper length that…
PHYSICS · Subjective · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics
Relativity and Gravitation, Ch Time dilation, length contraction and simultaneity
Problem
A rocket of proper length 40.0m flies at v=0.600c straight through a hangar of proper length 36.0m that has a door at each end. In the hangar frame S the two doors are shut simultaneously at the instant the rocket is judged to be wholly inside, and are opened again immediately. The rocket frame S′ is in standard configuration with S, and all times are coordinate times on the synchronised clocks of the frame named. Which single statement below is correct? (a) The rocket's true length is 32.0m; the crew's measurement of 40.0m is an artefact of their instruments, and that is why it fits. (b) In S the rocket is 32.0m long and both doors shut together; in S′ the hangar is 28.8m long and the far door shuts 90.1ns before the near door, so in S′ the rocket is never wholly enclosed. Both accounts are correct. (c) In S′ the far door shuts 72.0ns before the near door, because the door separation in S′ divided by the relative speed gives the offset. (d) The paradox is resolved by the rocket's deceleration inside the hangar: an accelerating frame is not inertial, so the disagreement is only apparent.