Page:The Meaning of Relativity - Albert Einstein (1922).djvu/39

Rh velocity; the rotation of the earth must be considered in writing down the equations of motion relatively to the earth. It appears, therefore, as if there were Cartesian systems of co-ordinates, the so-called inertial systems, with reference to which the laws of mechanics (more generally the laws of physics) are expressed in the simplest form. We may infer the validity of the following theorem: If $$K$$ is an inertial system, then every other system $$K'$$ which moves uniformly and without rotation relatively to $$K$$, is also an inertial system; the laws of nature are in concordance for all inertial systems. This statement we shall call the "principle of special relativity." We shall draw certain conclusions from this principle of "relativity of translation" just as we have already done for relativity of direction.

In order to be able to do this, we must first solve the following problem. If we are given the Cartesian co-ordinates, $$x_\nu$$, and the time $$t$$, of an event relatively to one inertial system, $$K$$, how can we calculate the co-ordinates, $$x_\nu'$$, and the time, $$t'$$, of the same event relatively to an inertial system $$K'$$ which moves with uniform translation relatively to $$K$$? In the pre-relativity physics this problem was solved by making unconsciously two hypotheses:—

I. The time is absolute; the time of an event, $$t'$$, relatively to $$K'$$ is the same as the time relatively to $$K$$. If instantaneous signals could be sent to a distance, and if one knew that the state of motion of a clock had no influence on its rate, then this assumption would be physically established. For then clocks, similar to one