662 IX. ON EMPIRICAL AND VERBAL STRUCTURES
This last formula brings out a few remarkable issues. In terrestrial velocities the square of the velocity of the motionof the observer in the primed system S' is very small as compared with the square of the velocity of light c2, so the fractionis small,differs very little from unity but the whole
denominator is less than unity, and sois not equal to, but greater.
In other words, the interval of 'time' between the two events appears larger to the observer in the primed moving system than to the observer in the stationary unprimed system. In general, among all systems in a state of uniform relative motion, that one in which two events occur at one place, is characterized by the fact that the 'time' interval between the two events appears shortest to an observer in this system. The shortest interval means that to an observer in the system, the events run their course most rapidly. A process which, with reference to a given system, occurs in one place, appears to run its course most rapidly to an observer in that system, but more slowly to a moving observer in any other system.
The more rapid the relative motion, the slower the process will appear, and, in the limit, if an observer could move with the velocity of light,,
the denominator of our equation would become and would
become 'infinite' and all events would be at a standstill.
As the formulae for length, x and x', involve the 'times' and, as we see, the intervals of 'time' are dependent on the relative velocities, by a similar process of reasoning we find that the standards of length are also relative, and that the length V in the primed system is represented by In other words, to an observer who sees the rod in motion, it will appear 'shortened', and among all systems in a state of uniform relative motion, the one in which the rod is at rest is distinguished from all others by the fact that in it the rod appears longer than in any other system. For instance, a metre rod lying on the earth in the direction of its motion would appear to an observer on the sun to be shortened by. In the limit, when vc, the fraction
and L' =0, which means that to an observer moving with the velocity of light, a three-dimensional body would appear as two-dimensional,