Two babies are born on a moving train; one is in the compartment adjacent to the engine and the other is in the compartment adjacent to the guard. According to the train frame, the babies are born at the exact same instant of time. Who is elder according to the ground frame?

Step-by-step solution

Let the train frame be S' moving with velocity v relative to the ground frame S in the positive x -direction. Let the position of the compartment adjacent to the guard (rear of the train) be x'₁ = 0 and the compartment adjacent to the engine (front of the train) be x'₂ = L , where L is the proper length of the train. According to the train frame, the babies are born at the exact same instant, so t'₁ = t'₂ = 0 . Using the Lorentz transformation for time, the time of an event in the ground frame is given by: t = (t'