Thanks for the reply Eugene. So say we had a observer frame \Sigma and a MCRF \Sigma'. At time time t=t'=0 \Sigma' is moving with velocity \vec{\beta} in some arbritary direction in \Sigma at say x_0=y_0=z_0=1 in \Sigma, with no rotation of \Sigma' in relation to \Sigma. Then by what you...