Page:Eddington A. Space Time and Gravitation. 1920.djvu/38

22 reader suppose that he is travelling through the aether at 161,000 miles a second vertically upwards; if he likes to make the positive assertion that this is his velocity, no one will be able to find any evidence to contradict him. For this speed the FitzGerald contraction is just $1⁄2$, so that every object contracts to half its original length when turned into the vertical position.

As you lie in bed, you are, say, 6 feet long. Now stand upright; you are 3 feet. You are incredulous? Well, let us prove it! Take a yard-measure; when turned vertically it must undergo the FitzGerald contraction, and become only half a yard. If you measure yourself with it, you will find you are just two—half-yards. "But I can see that the yard-measure does not change length when I turn it." What you perceive is an image of the rod on the retina of your eye; you imagine that the image occupies the same space in both positions; but your retina has contracted in the vertical direction without your knowing it, so that your visual estimates of vertical length are double what they should be. And so on with every test you can devise. Because everything is altered in the same way, nothing appears to be altered at all.

It is possible to devise electrical and optical tests; in that case the argument is more complicated, because we must consider the effect of the rapid current of aether on the electric forces and on waves of light. But the final conclusion is always the same; the tests will reveal nothing. Here is one illustration. To avoid distortion of the retina, lie on your back on the floor, and watch in a suitably inclined mirror someone turn the rod from the horizontal to the vertical position. You will, of course, see no change of length, and it is not possible to blame the retina this time. But is the appearance in the mirror a faithful reproduction of what is actually occurring? In a plane mirror at rest the appearance is correct; the rays of light come off the mirror at the same angle as they fall on to it, like billiard balls rebounding from an elastic cushion. But if the cushion is in rapid motion the angle of the billiard-ball will be altered; and similarly the rapid motion of the mirror through the aether alters the law of reflection. Precise calculation shows that the moving mirror will distort the image, so as to conceal exactly the changes of length which occur.