Simple Derivation of the Lorentz Transformation [Supplementary to Section 11]

For the relative orientation of the co-ordinate systems indicated in Fig. 2, the xaxes of both systems permanently coincide. In the present case we can divide the problem into parts by considering first only events which are localised on the xaxis. Any such event is represented with respect to the co-ordinate system K by the abscissa x and the time t, and with respect to the system K′ by the abscissa x′ and the time t′. We require to find x′ and t′ when x and t are given.