expressed in the last equation of the Galileian transformation (t1 =
t)

The four-dimensional mode of consideration of the "world" is natural
on the theory of relativity, since according to this theory time is
robbed of its independence. This is shown by the fourth equation of
the Lorentz transformation:

eq. 24: file eq24.gif


Moreover, according to this equation the time difference Dt1 of two
events with respect to K1 does not in general vanish, even when the
time difference Dt1 of the same events with reference to K vanishes.
Pure " space-distance " of two events with respect to K results in "
time-distance " of the same events with respect to K. But the
discovery of Minkowski, which was of importance for the formal
development of the theory of relativity, does not lie here. It is to
be found rather in the fact of his recognition that the
four-dimensional space-time continuum of the theory of relativity, in
its most essential formal properties, shows a pronounced relationship
to the three-dimensional continuum of Euclidean geometrical
space.* In order to give due prominence to this relationship,
however, we must replace the usual time co-ordinate t by an imaginary
magnitude eq. 25 proportional to it. Under these conditions, the
natural laws satisfying the demands of the (special) theory of
relativity assume mathematical forms, in which the time co-ordinate
plays exactly the same role as the three space co-ordinates. Formally,
these four co-ordinates correspond exactly to the three space
co-ordinates in Euclidean geometry. It must be clear even to the