Question

Suppose that a train robber decides to stop a train inside a tunnel. The proper length of the train is 60 m, while the proper length of the tunnel is 50 m. The train is traveling at 4/5 the speed of light. According to proper lengths, the train would not fit inside the tunnel. But the robber plans to use relativity to his advantage. The robber believes, due to length contraction, that he can trap the train inside the tunnel (by simultaneously blocking both ends of the tunnel). The engineer knows that his 60-m train will not fit completely into the tunnel, and does not worry about the robber. The robber thinks that the train will fit, whereas the engineer is sure it will not. Who is correct? Will the train fit inside the tunnel or not? Explain your reasoning.

Answer 1

There are two correct answers, depending on whether you consider the train stopped or moving through the tunnel. The `moving' solution is basically the more interesting

If the train moves, then both are correct: the robber will indeed see the train go completely inside the tunnel (i.e. the front end of the train will still be inside the tunnel when the rear end enters the tunnel), and the engineer will see quite the opposite: the front end will exit the tunnel before the rear end enters it. This is because those two events - the front end exits the tunnel and the rear end enters it - are not causally connected and can happen in different order to different observers.

However, if the train stopped, the train and the tunnel will be in the same reference frame, and the train will not fit, since its length will be longer. In this case the engineer is correct.