-x² - y² - z² + c² (1)
when c = ∞.
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 c = ∞.
It is evident that according to Newtonian Mechanics, this covariance holds for c = ∞ and not for c = velocity of light.
May we not then regard those traditional covariances for c = ∞ 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 if instead of the Newtonian Relativity-Postulate with c = ∞, 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, referred to oblique axes.
A space time null point 0 (x, y, z, t = 0, 0, 0, 0) will be kept fixed in a Lorentz transformation.
The figure -x² - y² - z² + t² = 1, t > 0 ... (2)