Relativity
The Special and General Theory
Appendix II
Minkowski's Four-Dimensional Space ("World") [Supplementary to Section XVII]
WE can characterize the Lorentz transformation still more simply if we introduce the imaginary
·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:
| x1'2 + x2'2 + x3'2 + x4'2 = x12 + x22 + x32 + x42 |
(12) |
That is, by the afore-mentioned choice of "coordinates," (11a) is transformed into this equation.
We see from (12) that the imaginary time co-ordinate x4, enters into the condition of transformation in exactly the same way as the space co-ordinates x1, x2, x3. It is due to this fact that, according to the theory of
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