The Velocity of Light

The A B C of Relativity by Bertrand Russells, is part of the HackerNoon Books Series. You can jump to any chapter in this book here. III. THE VELOCITY OF LIGHT

Most of the curious things in the theory of relativity are connected with the velocity of light. If the reader is to grasp the reasons for such a serious theoretical reconstruction, he must have some idea of the facts which made the old system break down.

The fact that light is transmitted with a definite velocity was first established by astronomical observations. Jupiter’s moons are sometimes eclipsed by Jupiter, and it is easy to calculate the times when this ought to occur. It was found that when Jupiter was unusually near the earth an eclipse of one of his moons would be observed a few minutes earlier than was expected; and when Jupiter was unusually remote, a few minutes later than was expected. It was found that these deviations could all be accounted for by assuming that light has a certain velocity, so that what we observe to be happening in Jupiter really happened a little while ago—longer ago when Jupiter is distant than when it is near.

Just the same velocity of light was found to account for similar facts in regard to other parts of the solar system. It was therefore accepted that light in vacuo always travels at a certain constant rate, almost exactly 300,000 kilometers a second. (A kilometer is about five-eighths of a mile.) When it became established that light consists of waves, this velocity was that of propagation of waves in the ether—at least they used to be in the ether, but now the ether has grown somewhat shadowy, though the waves remain. This same velocity is that of the waves used in wireless telegraphy (which are like light waves, only longer) and in X-rays (which are like light waves, only shorter). It is generally held nowadays to be the velocity with which gravitation is propagated, though Eddington considers this not yet certain. (It used to be thought that gravitation was propagated instantaneously, but this view is now abandoned.)

So far, all is plain sailing. But as it became possible to make more accurate measurements, difficulties began to accumulate. The waves were supposed to be in the ether, and therefore their velocity ought to be relative to the ether. Now since the ether (if it exists) clearly offers no resistance to the motions of the heavenly bodies, it would seem natural to suppose that it does not share their motion. If the earth had to push a lot of ether before it, in the sort of way that a steamer pushes water before it, one would expect a resistance on the part of the ether analogous to that offered by the water to the steamer. Therefore the general view was that the ether could pass through bodies without difficulty, like air through a coarse sieve, only more so. If this were the case, then the earth in its orbit must have a velocity relative to the ether.

If, at some point of its orbit, it happened to be moving exactly with the ether, it must at other points be moving through it all the faster. If you go for a circular walk on a windy day, you must be walking against the wind part of the way, whatever wind may be blowing; the principle in this case is the same. It follows that, if you choose two days six months apart, when the earth in its orbit is moving in exactly opposite directions, it must be moving against an ether wind on at least one of these days.

Now if there is an ether wind, it is clear that, relatively to an observer on the earth, light signals will seem to travel faster with the wind than across it, and faster across it than against it. This is what Michelson and Morley set themselves to test by their famous experiment. They sent out light signals in two directions at right angles; each was reflected from a mirror, and came back to the place from which both had been sent out. Now anybody can verify, either by trial or by a little arithmetic, that it takes longer to row a given distance on a river upstream and then back again, than it takes to row the same distance across the stream and back again.

Therefore, if there were an ether wind, one of the two light signals, which consist of waves in the ether, ought to have traveled to the mirror and back at a slower average rate than the other. Michelson and Morley tried the experiment, they tried it in various positions, they tried it again later. Their apparatus was quite accurate enough to have detected the expected difference of speed or even a much smaller difference, if it had existed, but not the smallest difference could be observed. The result was a surprise to them as to everybody else; but careful repetitions made doubt impossible. The experiment was first made as long ago as 1881, and was repeated with more elaboration in 1887. But it was many years before it could be rightly interpreted.

The supposition that the earth carries the neighboring ether with it in its motion was found to be impossible, for a number of reasons. Consequently a logical deadlock seemed to have arisen, from which at first physicists sought to extricate themselves by very arbitrary hypotheses. The most important of these was that of Fitzgerald, developed by Lorentz, and known as the Fitzgerald contraction hypothesis.

According to this hypothesis, when a body is in motion it becomes shortened in the direction of motion by a certain proportion depending upon its velocity. The amount of the contraction was to be just enough to account for the negative result of the Michelson-Morley experiment. The journey up stream and down again was to have been really a shorter journey than the one across the stream, and was to have been just so much shorter as would enable the slower light wave to traverse it in the same time. Of course the shortening could never be detected by measurement, because our measuring rods would share it.

A foot rule placed in the line of the earth’s motion would be shorter than the same foot rule placed at right angles to the earth’s motion. This point of view resembles nothing so much as the White Knight’s “plan to dye my whiskers green, and always use so large a fan that they could not be seen.” The odd thing was that the plan worked well enough. Later on, when Einstein propounded his special theory of relativity (1905), it was found that the theory was in a certain sense correct, but only in a certain sense. That is to say, the supposed contraction is not a physical fact, but a result of certain conventions of measurement which, when once the right point of view has been found, are seen to be such as we are almost compelled to adopt. But I do not wish yet to set forth Einstein’s solution of the puzzle. For the present, it is the nature of the puzzle itself that I want to make clear.

On the face of it, and apart from hypotheses ad hoc, the Michelson-Morley experiment (in conjunction with others) showed that, relatively to the earth, the velocity of light is the same in all directions, and that this is equally true at all times of the year, although the direction of the earth’s motion is always changing as it goes round the sun. Moreover, it appeared that this is not a peculiarity of the earth, but is true of all bodies: if a light signal is sent out from a body, that body will remain at the center of the waves as they travel outwards, no matter how it may be moving—at least, that will be the view of observers moving with the body. This was the plain and natural meaning of the experiments, and Einstein succeeded in inventing a theory which accepted it. But at first it was thought logically impossible to accept this plain and natural meaning.

A few illustrations will make it clear how very odd the facts are. When a shell is fired, it moves faster than sound: the people at whom it is fired first see the flash, then (if they are lucky) see the shell go by, and last of all hear the report. It is clear that if you could put a scientific observer on the shell, he would never hear the report, as the shell would burst and kill him before the sound had overtaken him. But if sound worked on the same principles as light, our observer would hear everything just as if he were at rest. In that case, if a screen, suitable for producing echoes, were attached to the shell and traveling with it, say a hundred yards in front of it, our observer would hear the echo of the report from the screen after just the same interval of time as if he and the shell were at rest.

This, of course, is an experiment which cannot be performed, but others which can be performed will show the difference. We might find some place on a railway where there is an echo from a place further along the railway—say a place where the railway goes into a tunnel—and when a train is traveling along the railway, let a man on the bank fire a gun. If the train is traveling towards the echo, the passengers will hear the echo sooner than the man on the bank; if it is traveling in the opposite direction, they will hear it later. But these are not quite the circumstances of the Michelson-Morley experiment.

The mirrors in that experiment correspond to the echo, and the mirrors are moving with the earth, so that echo ought to move with the train. Let us suppose that the shot is fired from the guard’s van, and the echo comes from a screen on the engine. We will suppose the distance from the guard’s van to the engine to be the distance that sound can travel in a second (about one-fifth of a mile), and the speed of the train to be one-twelfth of the speed of sound (about sixty miles an hour). We now have an experiment which can be performed by the people in the train. If the train were at rest, the guard would hear the echo in two seconds; as it is, he will hear it in 2 and ²/₁₄₃ seconds. From this difference, if he knows the velocity of sound, he can calculate the velocity of the train, even if it is a foggy night so that he cannot see the banks. But if sound behaved like light, he would hear the echo in two seconds however fast the train might be traveling.

Various other illustrations will help to show how extraordinary—from the point of view of tradition and common sense—are the facts about the velocity of light. Every one knows that if you are on an escalator you reach the top sooner if you walk up than if you stand still. But if the escalator moved with the velocity of light (which it does not do even in New York), you would reach the top at exactly the same moment whether you walked up or stood still.

Again: if you are walking along a road at the rate of four miles an hour, and a motor-car passes you going in the same direction at the rate of forty miles an hour, if you and the motor-car both keep going the distance between you after an hour will be thirty-six miles. But if the motor-car met you, going in the opposite direction, the distance after an hour would be forty-four miles. Now if the motor-car were traveling with the velocity of light, it would make no difference whether it met or passed you: in either case, it would, after 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 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 ne 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.

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 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.