Page:The principle of relativity (1920).djvu/41

 length of the rod in the moving system" is equal to the length l of the rod in the stationary system.

The length which is found out by the second method, may be called '''the length of the moving rod measured from the stationary system.' This length is to be estimated on the basis of our principle, and we shall find it to be different from l''.

In the generally recognised kinematics, we silently assume that the lengths defined by these two operations are equal, or in other words, that at an epoch of time t, a moving rigid body is geometrically replaceable by the same body, which can replace it in the condition of rest.

Relativity of Time.

Let us suppose that the two clocks synchronous with the clocks in the system at rest are brought to the ends A, and B of a rod, i.e., the time of the clocks correspond to the time of the stationary system at the points where they happen to arrive; these clocks are therefore synchronous in the stationary system.

We further imagine that there are two observers at the two watches, and moving with them, and that these observers apply the criterion for synchronism to the two clocks. At the time t_{A}, a ray of light goes out from A, is reflected from B at the time t_{B}, and arrives back at A at time t´_{A}. Taking into consideration the principle of, constancy of the velocity of light, we have

t_{B} - t_{A} = r_{AB}/(c - v), and      t´_{A} - t_{B} = r_{AB}/(c + v),