Page:Relativity (1931).djvu/59

values $x'$, $y'$, $z'$, $t'$ of an event with respect to $K'$, when the magnitudes $x$, $y$, $z$, $t$, of the same event with respect to $K$ are given? Fig. 2.The relations must be so chosen that the law of the transmission of light in vacuo is satisfied for one and the same ray of light (and of course for every ray) with respect to $K$ and $K'$. For the relative orientation in space of the co-ordinate systems indicated in the diagram (Fig. 2), this problem is solved by means of the equations:

${\begin{aligned}x'&={\frac {x-vt}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}\\y'&=y\\z'&=z\\t'&={\frac {t-{\frac {v}{c^{2}}}\cdot x}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}\end{aligned}}$

This system of equations is known as the “Lorentz transformation.”^[1]

If in place of the law of transmission of light we had taken as our basis the tacit assumptions of the older mechanics as to the absolute character

1. A simple derivation of the Lorentz transformation is given in Appendix I.