Page:Grundgleichungen (Minkowski).djvu/47

The new equations would now denote the transformation of a spatial co-ordinate system x, y, z to another spatial co-ordinate system x', y', z' with parallel axes, the null point of the second system moving with constant velocity in a straight line, while the time parameter remains unchanged.

We can, therefore, say that classical mechanics postulates a covariance of Physical laws for the group of homogeneous linear transformations of the expression

(1)	$-x^{2}-y^{2}-z^{2}+c^{2}t^{2}$

when $c=\infty$.

Now it is rather confusing to find that in one branch of Physics, we shall find a covariance of the laws for the transformation of expression (1) with a finite value of c, in another part for math>c = \infty</math>. It is evident that according to Newtonian Mechanics, this covariance holds for math>c = \infty</math> and not for c = velocity of light. May we not then regard those traditional co-variances for $c=\infty$ only as an approximation consistent with experience, the actual covariance of natural laws holding for a certain finite value of c?

I may here point out that by reforming mechanics, where instead of the Newtonian Relativity-Postulate with $c=\infty$ we assume a relativity-postulate with a finite c, then the axiomatic construction of Mechanics appears to gain considerably in perfection.

The ratio of the time unit to the length unit is chosen in a manner so as to make the velocity of light equivalent to unity.

While now I want to introduce geometrical figures in the manifold of the variables x, y, z, t, it may be convenient to leave y, z out of account, and to treat x and t as any possible pair of co-ordinates in a plane, refered to oblique axes.

A space time null point ($x,\ y,\ z,\ t=0,\ 0,\ 0,\ 0$) will be kept fixed in a Lorentz transformation. The figure

(2)	$-x^{2}-y^{2}-z^{2}-t^{2}=1,\ t>0$,