Page:Eddington A. Space Time and Gravitation. 1920.djvu/36

20 equilibrium would be contracted in just such a way and by just such an amount as FitzGerald's explanation requires.

The contraction in most cases is extremely minute. We have seen that when the ratio of the speed of the current to that of the swimmer is $3⁄5$, a contraction in the ratio $$\scriptstyle\sqrt{\left(1-\left(\frac{3}{5}\right)^2\right)}$$ is needed to compensate for the delay. The earth's orbital velocity is $1⁄10000$ of the velocity of light, so that it will give a contraction of $$\scriptstyle\sqrt{\left(1-\left(\frac{1}{10000}\right)^2\right)}$$, or 1 part in 200,000,000. This would mean that the earth's diameter in the direction of its motion is shortened by $2 1⁄2$ inches.

The Michelson-Morley experiment has thus failed to detect our motion through the aether, because the effect looked for—the delay of one of the light waves—is exactly compensated by an automatic contraction of the matter forming the apparatus. Other ingenious experiments have been tried, electrical and optical experiments of a more technical nature. They likewise have failed, because there is always an automatic compensation somewhere. We now believe there is something in the nature of things which inevitably makes these compensations, so that it will never be possible to determine our motion through the aether. Whether we are at rest in it, or whether we are rushing through it with a speed not much less than that of light, will make no difference to anything that can possibly be observed.

This may seem a rash generalization from the few experiments actually performed; more particularly, since we can only experiment with the small range of velocity caused by the earth's orbital motion. With a larger range residual differences might be disclosed. But there is another reason for believing that the compensation is not merely approximate but exact. The compensation has been traced theoretically to its source in the well-known laws of electromagnetic force; and here it is mathematically exact. Thus the generalization is justified, at least in so far as the observed phenomena depend on electromagnetic causes, and in so far as the universally accepted laws of electromagnetism are accurate.

The generalization here laid down is called the restricted Principle of Relativity:—It is impossible by any experiment to detect uniform motion relative to the aether.