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APPENDIX II

MINKOWSKI’S FOUR-DIMENSIONAL SPACE (“WORLD”) [Supplementary to Section XVII]

WE can characterise the Lorentz transformation still more simply if we introduce the imaginary in place of , as time-variable. If, in accordance with this, we insert

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

(12).

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

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