APPENDIX I
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 pernumently 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 K1 by the abscissa x'
and the time t'. We require to find x' and t' when x and t are given.
A light-signal, which is proceeding along the positive axis of x, is
transmitted according to the equation
x = ct
or
x - ct = 0 . . . (1).
Since the same light-signal has to be transmitted relative to K1 with
the velocity c, the propagation relative to the system K1 will be
represented by the analogous formula
x' - ct' = O . . . (2)
Those space-time points (events) which satisfy (x) must also satisfy
(2). Obviously this will be the case when the relation
(x' - ct') = l (x - ct) .
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