Question

According to the station clocks, two babies are born at the same instant, one in Howrah and other in Delhi. (a) Who is elder in the frame of 2301 Up Rajdhani Express going from Howrah to Delhi? (b) Who is elder in the frame of 2302 Dn Rajdhani Express going from Delhi to Howrah.

Answer 1

The time interval recorded in a moving train, i.e. improper time is always greater than proper time (recorded in ground frame). The birth timings recorded by the station clocks is the proper time interval because it is the ground frame.
Also, the time recorded in the moving train is improper because it records time at two different places.

Hence, the proper time interval ∆T is less than that of improper, i.e. ∆T' = v∆T.

Thus,
(a) Delhi baby is elder in the frame of 2301 Up Rajdhani Express going from Howrah to Delhi.
(b) Howrah baby is elder in the frame of 2302 Dn Rajdhani express going from Delhi to Howrah.