The A B C of Relativity

a second, be 186,000 miles from you. It would also be 186,000 miles from any other motor-car which happened to be passing or meeting you less rapidly at the previous second. This seems impossible: how can the car be at the same distance from a number of different points along the road? Let us take another illustration. When a fly touches the surface of a stagnant pool, it causes ripples which move outwards in widening circles. The center of the circle at any moment is the point of the pool touched by the fly. If the fly moves about over the surface of the pool, it does not remain at the center of the ripples. But if the ripples were waves of light, and the fly were a skilled physicist, it would find that it always remained at the center of the ripples, however it might move. Meanwhile a skilled physicist sitting beside the pool would judge, as in the case of ordinary ripples, that the center [Pg 38] was not the fly, but the point of the pool touched by the fly. And if another fly had touched the water at the same spot at the same moment, it also would find that it remained at the center of the ripples, even if it separated itself widely from the first fly. This is exactly analogous to the Michelson-Morley experiment. The pool corresponds to the ether; the fly corresponds to the earth; the contact of the fly and the pool corresponds to the light signal which Messrs. Michelson and Morley send out; and the ripples correspond to the light waves. Such a state of affairs seems, at first sight, quite impossible. It is no wonder that, although the Michelson-Morley experiment was made in 1881, it was not rightly interpreted until 1905. Let us see what, exactly, we have been saying. Take the man walking along a road and passed by a motor-car. Suppose there are a number of people at the same point of the road, some walking, some in motor-cars; suppose they are going at varying rates, some in one direction and some in another. I say that if, at this moment, a light flash is sent out from the place where they all are, the light waves will be 186,000 miles from each [Pg 39] one of them after a second by his watch, although the travelers will not any longer be all in the same place. At the end of a second by your watch it will be 186,000 miles from you, and it will also be 186,000 miles from a person who met you when it was sent out, but was moving in the opposite direction, after a second by his watch—assuming both to be perfect watches. How can this be? There is only one way of explaining such facts, and that is, to assume that watches and clocks are affected by motion. I do not mean that they are affected in ways that could be remedied by greater accuracy in construction; I mean something much more fundamental. I mean that, if you say an hour has elapsed between two events, and if you base this assertion upon ideally careful measurements with ideally accurate chronometers, another equally precise person, who has been moving rapidly relatively to you, may judge that the time was more or less than an hour. You cannot say that one is right and the other wrong, any more than you could if one used a clock showing Greenwich time and another a clock showing New York time. How this comes about, I shall explain in the next chapter. [Pg 40] There are other curious things about the velocity of light. One is, that no material body can ever travel as fast as light, however great may be the force to which it is exposed, and however long the force may act. An illustration may help to make this clear. At exhibitions one sometimes sees a series of moving platforms, going round and round in a circle. The outside one goes at four miles an hour; the next goes four miles an hour faster than the first; and so on. You can step across from each to the next; until you find yourself going at a tremendous pace. Now you might think that, if the first platform does four miles an hour, and the second does four miles an hour relatively to the first, then the second does eight miles an hour relatively to the ground. This is an error; it does a little less, though so little less that not even the most careful measurements could detect the difference. I want to make quite clear what it is that I mean. I will suppose that, in the morning, when the apparatus is just about to start, three men with ideally accurate chronometers stand in a row, one on the ground, one on the first platform, and one on the second. The [Pg 41] first platform moves at the rate of four miles an hour with respect to the ground. Four miles an hour is 352 feet in a minute. The man on the ground, after a minute by his watch, notes the place on the ground opposite the man on the first platform, who has been standing still while the platform carried him along. The man on the ground measures the distance on the ground from himself to the point opposite the man on the first platform, and finds it is 352 feet. The man on the first platform, after a minute by his watch, notes the point on his platform opposite to the man on the second platform. The man on the first platform measures the distance from himself to the point opposite the man on the second platform; it is again 352 feet. Problem: how far will the man on the ground judge that the man on the second platform has traveled in a minute? That is to say, if the man on the ground, after a minute by his watch, notes the place on the ground opposite the man on the second platform, how far will this be from the man on the ground? You would say, twice 352 feet, that is to say, 704 feet. But in fact it will be a little less, though so little less as to be inappreciable. The discrepancy is owing to the fact that the two watches do not keep perfect time, in spite of the fact that each is [Pg 42] accurate from its owner’s point of view. If you had a long series of such moving platforms, each moving four miles an hour relatively to the one before it, you would never reach a point where the last was moving with the velocity of light relatively to the ground, not even if you had millions of them. The discrepancy, which is very small for small velocities, becomes greater as the velocity increases, and makes the velocity of light an unattainable limit. How all this happens, is the next topic with which we must deal. Note. The negative result of the Michelson-Morley experiment has recently been called in question by Professor Dayton C. Miller, as a result of observations by what is said to be an improved method. His claim is set forth by Professor Silberstein in Nature, May 23, 1925, and discussed unfavorably by Eddington in the issue of June 6. The matter is sub judice, but it seems highly questionable whether the results bear out the interpretation which is put upon them.