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) |
when .
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 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 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 () will be kept fixed in a Lorentz transformation. The figure
(2) | , |