Page:Relativity (1931).djvu/166



E can characterise the Lorentz transformation still more simply if we introduce the imaginary $$\sqrt{-1}. ct$$ in place of $$t$$, as time-variable. If, in accordance with this, we insert

and similarly for the accented system $$K'$$, then the condition which is identically satisfied by the transformation can be expressed thus:

That is, by the afore-mentioned choice of “coordinates” (11a) is transformed into this equation. We see from (12) that the imaginary time coordinate $$x_4$$, enters into the condition of transformation in exactly the same way as the space co-ordinates $$x_1$$, $$x_2$$, $$x_3$$. It is due to this fact that, according to the theory of relativity, the “time”