According to the station clocks, two babies are born at the exact same instant, one in Kanpur and the other in Agra. Who is elder in the reference frame of the 12033 Shatabdi Express travelling from Kanpur to Agra?

Step-by-step solution

Let the ground frame be S and the train frame be S' . Let Kanpur be at the origin x = 0 and Agra be at x = L , where L > 0 . The train moves from Kanpur to Agra with velocity v in the positive x -direction. The birth of the Kanpur baby is event K with coordinates (t_K, x_K) = (0, 0) . The birth of the Agra baby is event A with coordinates (t_A, x_A) = (0, L) . Using the Lorentz transformation for time, t' = ( t - vx c^2 ) . The time of birth of the Kanpur baby in the train frame is t'_K = ( 0 - v(0) c^2 ) = 0 . The