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 accordance with the discussion contained in the preceding section, it follows that:

If $K$ is a Galileian co-ordinate system, then every other

co-ordinate system $K^{'}$ is a Galileian one, when, in relation to $K$ , it is in a condition of uniform motion of translation.

Relative to $K^{'}$ the mechanical laws of Galilei-Newton

hold good exactly as they do with respect to $K$ .

We advance a step farther in our generalisation when we express the tenet thus: If, relative to $K$ , $K^{'}$ is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to $K^{'}$ according to exactly the same general laws as with respect to $K$ . This statement is called the principle of relativity (in the restricted sense).

As long as one was convinced that all natural phenomena were capable of representation with the help of classical mechanics, there was no need to doubt the

validity of this principle of relativity. But in view of

the more recent development of electrodynamics and

optics it became more and more evident that classical

mechanics affords an insufficient foundation for the physical description of all natural phenomena. At this juncture the question of the validity of the principle of relativity became ripe for discussion, and it did not appear impossible that the answer to this question might be in the negative.

Nevertheless, there are two general facts which at the outset speak very much in favour of the validity of the principle of relativity. Even though classical mechanics does not supply us with a sufficiently broad basis for