APPENDIX I
SIMPLE DERIVATION OF THE LORENTZ TRANSFORMATION [Supplementary to Section XI]
FOR the relative orientation of the co-ordinate systems indicated in Fig. 2, the -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 -axis. Any such event is represented with respect to the coordinate system by the abscissa and the time , and with respect to the system by the abscissa and the time . We require to find and when and are given. A light-signal, which is proceeding along the positive axis of , is transmitted according to the equation
or
Since the same light-signal has to be transmitted relative to with the velocity , the propagation
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