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 12034 Shatabdi Express travelling from Agra to Kanpur?

Step-by-step solution

Let the ground frame be S and the train frame be S' . Let Agra be at the origin x = 0 and Kanpur be at x = L , where L > 0 . The train is travelling from Agra to Kanpur, so its velocity v is in the positive x -direction. The two births are simultaneous in the ground frame, so t_A = t_K = 0 . Using the Lorentz transformation for time, t' = ( t - vx c^2 ) . For the baby born in Agra: t'_A = ( 0 - v(0) c^2 ) = 0 . For the baby born in Kanpur: t'_K = ( 0 - vL c^2 ) = - vL c^2 . Since v > 0 and L > 0 , we have t'_K This