The Principle of Relativity (in the Restricted Sense)
In order to attain the greatest possible clearness, let us return to our example of the railway carriage supposed to be travelling uniformly. We call its motion a uniform translation (“uniform” because it is of constant velocity and direction, “translation” because although the carriage changes its position relative to the embankment yet it does not rotate in so doing). Let us imagine a raven ﬂying through the air in such a manner that its motion, as observed from the embankment, is uniform and in a straight line. If we were to observe the ﬂying raven from the moving railway carriage, we should ﬁnd that the motion of the raven would be one of diﬀerent velocity and direction, but that it would still be uniform and in a straight line. Expressed in an abstract manner we may say: If a mass m is moving uniformly in a straight line with respect to a co-ordinate system K, then it will also be moving uniformly and in a straight line relative to a second co-ordinate system K′, provided that the latter is executing a uniform translatory motion with respect to K. In
section, it follows that:
they do with respect to K.