08-18-2014, 08:51 AM
One can also consider the Doppler shifts of the light from each twin to the other twin. It's true for both twins that when the other twin is seen to be moving away, the light will be Doppler redshifted. And when the other twin is seen to be approaching, the light will be Doppler blueshifted. But consider when each twin sees the other twin turn around from moving away to approaching. Because it is the travelling twin that actually turns around, he sees the redshift become blueshift immediately. By contrast, the stay-at-home twin only sees the redshift become blueshift when light from the travelling twin's turn-around reaches him. Therefore, the stay-at-home twin sees the travelling twin redshifted for a greater proportion of the journey than visa-versa, and this accounts for the travelling twin being unequivocally younger upon return.

A tensor equation that is valid in *any* coordinate system is valid in *every* coordinate system.