|College of Science Physics Dept Tatsu Takeuchi Special Relativity Practice Problems|
Trains in a Tunnel
Two trains, 1 and 2, of equal lengths are traveling at the same speed in opposite directions inside a long, dark, and straight tunnel. At time t1 in the ground frame of reference, all the ceiling lights in the tunnel turn on simultaneously. Then, at time t2 in the ground frame of reference, they all turn off simultaneously.
In ground frame of reference, both trains are observed to be the same length (since they are both moving at the same speed) and both are immersed in light for the same amount of time. Therefore, an observer on the ground concludes that both trains are hit by the same number of photons.
However, an observer riding train 1 reasons that since train 1 is longer than train 2 in the train 1 frame of reference (since train 2 in shorter due to Lorentz contraction) train 1 must be hit by more photons than train 2. This seems to contradict the conclusion of the observer on the ground.
Answer the following questions: