right-hand side.
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
image031
in place of _t_, as time-variable. If, in accordance with this, we
insert
image050
and similarly for the accented system _K _, then the condition which is
identically satisfied by the transformation can be expressed thus:
_x_1 2 + _x_2 2 + _x_3 2 + _x_4 2 = _x_12 + _x_22 + _x_32 + _x_42 (12).
That is, by the afore-mentioned choice of coordinates, (11_a_) [see
the end of Appendix II] is transformed into this equation.
We see from (12) that the imaginary time co-ordinate _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 _x_4, enters into natural laws
in the same form as the space co ordinates _x_1, _x_2, _x_3.
A four-dimensional continuum described by the co-ordinates _x_1,
_x_2, _x_3, _x_4, was called world by Minkowski, who also termed a
point-event a world-point. From a happening in three-dimensional
space, physics becomes, as it were, an existence in the
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