Page:Relativity (1931).djvu/136

 the natural extension of the special principle of relativity. According to the special theory of relativity, the equations which express the general laws of nature pass over into equations of the same form when, by making use of the Lorentz transformation, we replace the space-time variables $$x$$, $$y$$, $$z$$, $$t$$, of a (Galileian) reference-body $$K$$ by the space-time variables $$x'$$, $$y'$$, $$z'$$, $$t'$$, of a new referencebody $$K'$$. According to the general theory of relativity, on the other hand, by application of arbitrary substitutions of the Gauss variables $$x_1$$, $$x_2$$, $$x_3$$, $$x_4$$, the equations must pass over into equations of the same form; for every transformation (not only the Lorentz transformation) corresponds to the transition of one Gauss co-ordinate system into another.

If we desire to adhere to our “old-time” three-dimensional view of things, then we can characterise the development which is being undergone by the fundamental idea of the general theory of relativity as follows: The special theory of relativity has reference to Galileian domains, i.e. to those in which no gravitational field exists. In this connection a Galileian reference-body serves as body of reference, i.e. a rigid body the state of motion of which is so chosen that the Galileian law of the uniform rectilinear motion of “isolated” material points holds relatively to it.