Simple Derivation of the Lorentz Transformation [Supplementary to Section 11]
For the relative orientation of the co-ordinate systems indicated in Fig. 2, the x-axes 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 x-axis. 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.