The A B C of Relativity - Bertrand Russell - This is a new publication of Bertrand Russell's The A B C of Relativity. What makes it invaluable is that it is written by one of the greatest minds of the twentieth century with the intention to reach a wider circle of readers. The book should be also of interest to students of physics and philosophy of science as well as to all interested in one of the two great scientific discoveries of the twentieth century - the theory of relativity.
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Everybody knows that Einstein has done something astonishing, but very few people know exactly what it is that he has done. It is generally recognized that he has revolutionized our conception of the physical world, but his new conceptions are wrapped up in mathematical technicalities. It is true that there are innumerable popular accounts of the theory of relativity, but they generally cease to be intelligible just at the point where they begin to say something important. The authors are hardly to blame for this. Many of the new ideas can be expressed in non-mathematical language, but they are none the less difficult on that account. What is demanded is a change in our imaginative picture of the world—a picture which has been handed down from remote, perhaps pre-human, ancestors, and has been learned by each one of us in early childhood. A change in our imagination is always difficult, especially when we are no longer young. The same sort of change was demanded by Copernicus, when he taught that the earth is not stationary and the heavens do not revolve about it once a day. To us now there is no difficulty in this idea, because we learned it before our mental habits had become fixed. Einstein’s ideas, similarly, will seem easy to a generation which has grown up with them; but for our generation a certain effort of imaginative reconstruction is unavoidable.
In exploring the surface of the earth, we make use of all our senses, more particularly of the senses of touch and sight. In measuring lengths, parts of the human body are employed in pre-scientific ages: a “foot,” a “cubit,” a “span” are defined in this way. For longer distances, we think of the time it takes to walk from one place to another. We gradually learn to judge distances roughly by the eye, but we rely upon touch for accuracy. Moreover it is touch that gives us our sense of “reality.” Some things cannot be touched: rainbows, reflections in looking-glasses, and so on. These things puzzle children, whose metaphysical speculations are arrested by the information that what is in the looking glass is not “real.” Macbeth’s dagger was unreal because it was not “sensible to feeling as to sight.” Not only our geometry and physics, but our whole conception of what exists outside us, is based upon the sense of touch. We carry this even into our metaphors: a good speech is “solid,“ a bad speech is “gas,” because we feel that a gas is not quite “real.”
In studying the heavens, we are debarred from all senses except sight. We cannot touch the sun, or travel to it; we cannot walk round the moon, or apply a foot rule to the Pleiades. Nevertheless, astronomers have unhesitatingly applied the geometry and physics which they found serviceable on the surface of the earth, and which they had based upon touch and travel. In doing so, they brought down trouble on their heads, which it has been left for Einstein to clear up. It has turned out that much of what we learned from the sense of touch was unscientific prejudice, which must be rejected if we are to have a true picture of the world.
An illustration may help us to understand how much is impossible to the astronomer as compared to the man who is interested in things on the surface of the earth. Let us suppose that a drug is administered to you which makes you temporarily unconscious, and that when you wake you have lost your memory but not your reasoning powers. Let us suppose further that while you were unconscious you were carried into a balloon, which, when you come to, is sailing with the wind in a dark night—the night of the fifth of November if you are in England, or of the fourth of July if you are in America. You can see fireworks which are being sent off from the ground, from trains, and from aeroplanes traveling in all directions, but you cannot see the ground or the trains or the aeroplanes be cause of the darkness. What sort of picture of the world will you form? You will think that nothing is permanent: there are only brief flashes of light, which, during their short existence, travel through the void in the most various and bizarre curves. You cannot touch these flashes of light, you can only see them. Obviously your geometry and your physics and your metaphysics will be quite different from those of ordinary mortals. If an ordinary mortal is with you in the balloon, you will find his speech unintelligible. But if Einstein is with you, you will understand him more easily than the ordinary mortal would, because you will be free from a host of preconceptions which prevent most people from understanding him.
The theory of relativity depends, to a considerable extent, upon getting rid of notions which are useful in ordinary life but not to our drugged balloonist. Circumstances on the surface of the earth, for various more or less accidental reasons, suggest conceptions which turn out to be inaccurate, although they have come to seem like necessities of thought. The most important of these circumstances is that most objects on the earth’s surface are fairly persistent and nearly stationary from a terrestrial point of view. If this were not the case, the idea of going a journey would not seem so definite as it does. If you want to travel from King’s Cross to Edinburgh, you know that you will find King’s Cross where it always has been, that the railway line will take the course that it did when you last made the journey, and that Waverley Station in Edinburgh will not have walked up to the Castle. You therefore say and think that you have traveled to Edinburgh, not that Edinburgh has traveled to you, though the latter statement would be just as accurate. The success of this common sense point of view depends upon a number of things which are really of the nature of luck. Suppose all the houses in London were perpetually moving about, like a swarm of bees; suppose railways moved and changed their shapes like avalanches; and finally suppose that material objects were perpetually being formed and dissolved like clouds. There is nothing impossible in these suppositions: something like them must have been verified when the earth was hotter than it is now. But obviously what we call a journey to Edinburgh would have no meaning in such a world. You would begin, no doubt, by asking the taxi-driver: “Where is King’s Cross this morning?“ At the station you would have to ask a similar question about Edinburgh, but the booking-office clerk would reply: “What part of Edinburgh do you mean, Sir? Prince’s Street has gone to Glasgow, the Castle has moved up into the Highlands, and Waverley Station is under water in the middle of the Firth of Forth.” And on the journey the stations would not be staying quiet, but some would be travelling north, some south, some east or west, perhaps much faster than the train. Under these conditions you could not say where you were at any moment. Indeed the whole notion that one is always in some definite “place” is due to the fortunate immovability of most of the large objects on the earth’s surface. The idea of “place” is only a rough practical approximation: there is nothing logically necessary about it, and it cannot be made precise.
If we were not much larger than an electron, we should not have this impression of stability, which is only due to the grossness of our senses. King’s Cross, which to us looks solid, would be too vast to be conceived except by a few eccentric mathematicians. The bits of it that we could see would consist of little tiny points of matter, never coming into contact with each other, but perpetually whizzing round each other in an inconceivably rapid ballet-dance. The world of our experience would be quite as mad as the one in which the different parts of Edinburgh go for walks in different directions. If—to take the opposite extreme—you were as large as the sun and lived as long, with a corresponding slowness of perception, you would again find a higgledy-piggledy universe without permanence—stars and planets would come and go like morning mists, and nothing would remain in a fixed position relatively to anything else. The notion of comparative stability which forms part of our ordinary outlook is thus due to the fact that we are about the size we are, and live on a planet of which the surface is no longer very hot. If this were not the case, we should not find pre-relativity physics intellectually satisfying. Indeed, we should never have invented such theories. We should have had to arrive at relativity physics at one bound, or remain ignorant of scientific laws. It is fortunate for us that we were not faced with this alternative, since it is almost inconceivable that one man could have done the work of Euclid, Galileo, Newton, and Einstein. Yet without such an incredible genius physics could hardly have been discovered in a world where the universal flux was obvious to non-scientific observation.
In astronomy, although the sun, moon, and stars continue to exist year after year, yet in other respects the world we have to deal with is very different from that of everyday life. As already observed, we depend exclusively on sight: the heavenly bodies cannot be touched, heard, smelt or tasted. Everything in the heavens is moving relatively to everything else. The earth is going round the sun, the sun is moving, very much faster than an express train, towards a point in the constellation “Hercules,” the “fixed” stars are scurrying hither and thither like a lot of frightened hens. There are no well-marked places in the sky, like King’s Cross and Edinburgh. When you travel from place to place on the earth, you say the train moves and not the stations, because the stations preserve their topographical relations to each other and the surrounding country. But in astronomy it is arbitrary which you call the train and which the station: the question is to be decided purely by convenience and as a matter of convention.
In this respect, it is interesting to contrast Einstein and Copernicus. Before Copernicus, people thought that the earth stood still and the heavens revolved about it once a day. Copernicus taught that “really” the earth rotates once a day, and the daily revolution of sun and stars is only “apparent.” Galileo and Newton endorsed this view, and many things were thought to prove it—for example, the flattening of the earth at the poles, and the fact that bodies are heavier there than at the equator. But in the modern theory the question between Copernicus and his predecessors is merely one of convenience; all motion is relative, and there is no difference between the two statements: “the earth rotates once a day” and “the heavens revolve about the earth once a day.” The two mean exactly the same thing, just as it means the same thing if I say that a certain length is six feet or two yards. Astronomy is easier if we take the sun as fixed than if we take the earth, just as accounts are easier in a decimal coinage. But to say more for Copernicus is to assume absolute motion, which is a fiction. All motion is relative, and it is a mere convention to take one body as at rest. All such conventions are equally legitimate, though not all are equally convenient.
There is another matter of great importance, in which astronomy differs from terrestrial physics because of its exclusive dependence upon sight. Both popular thought and old-fashioned physics used the notion of “force,” which seemed intelligible because it was associated with familiar sensations. When we are walking, we have sensations connected with our muscles which we do not have when we are sitting still. In the days before mechanical traction, although people could travel by sitting in their carriages, they could see the horses exerting themselves and evidently putting out “force” in the same way as human beings do. Everybody knew from experience what it is to push or pull, or to be pushed or pulled. These very familiar facts made “force” seem a natural basis for dynamics. But Newton’s law of gravitation introduced a difficulty. The force between two billiard balls appeared intelligible, because we know what it feels like to bump into another person; but the force between the earth and the sun, which are ninety-three million miles apart, was mysterious. Newton himself regarded this “action at a distance” as impossible, and believed that there was some hitherto undiscovered mechanism by which the sun’s influence was transmitted to the planets. However, no such mechanism was discovered, and gravitation remained a puzzle. The fact is that the whole conception of “force” is a mistake. The sun does not exert any force on the planets; in Einstein’s law of gravitation, the planet only pays attention to what it finds in its own neighborhood. The way in which this works will be explained in a later chapter; for the present we are only concerned with the necessity of abandoning the notion of “force,” which was due to misleading conceptions derived from the sense of touch.
As physics has advanced, it has appeared more and more that sight is less misleading than touch as a source of fundamental notions about matter. The apparent simplicity in the collision of billiard balls is quite illusory. As a matter of fact, the two billiard balls never touch at all; what really happens is inconceivably complicated, but is more analogous to what happens when a comet penetrates the solar system and goes away again than to what common sense supposes to happen.
Most of what we have said hitherto was already recognized by physicists before Einstein invented the theory of relativity. “Force” was known to be merely a mathematical fiction, and it was generally held that motion is a merely relative phenomenon—that is to say, when two bodies are changing their relative position, we cannot say that one is moving while the other is at rest, since the occurrence is merely a change in their relation to each other. But a great labor was required in order to bring the actual procedure of physics into harmony with these new convictions. Newton believed in force and in absolute space and time; he embodied these beliefs in his technical methods, and his methods remained those of later physicists. Einstein invented a new technique, free from Newton’s assumptions. But in order to do so he had to change fundamentally the old ideas of space and time, which had been unchallenged from time immemorial. This is what makes both the difficulty and the interest of his theory. But before explaining it there are some preliminaries which are indispensable. These will occupy the next two chapters.
A certain type of superior person is fond of asserting that “everything is relative.” This is, of course, nonsense, because, if everything were relative, there would be nothing for it to be relative to. However, without falling into metaphysical absurdities it is possible to maintain that everything in the physical world is relative to an observer. This view, true or not, is not that adopted by the “theory of relativity.” Perhaps the name is unfortunate; certainly it has led philosophers and uneducated people into confusions. They imagine that the new theory proves everything in the physical world to be relative, whereas, on the contrary, it is wholly concerned to exclude what is relative and arrive at a statement of physical laws that shall in no way depend upon the circumstances of the observer. It is true that these circumstances have been found to have more effect upon what appears to the observer than they were formerly thought to have, but at the same time Einstein showed how to discount this effect completely. This was the source of almost everything that is surprising in his theory.
When two observers perceive what is regarded as one occurrence, there are certain similarities, and also certain differences, between their perceptions. The differences are obscured by the requirements of daily life, because from a business point of view they are as a rule unimportant. But both psychology and physics, from their different angles, are compelled to emphasize the respects in which one man’s perception of a given occurrence differs from another man’s. Some of these differences are due to differences in the brains or minds of the observers, some to differences in their sense organs, some to differences of physical situation: these three kinds may be called respectively psychological, physiological, and physical. A remark made in a language we know will be heard, whereas an equally loud remark in an unknown language may pass entirely unnoticed. Of two men in the Alps, one will perceive the beauty of the scenery while the other will notice the waterfalls with a view to obtaining power from them. Such differences are psychological. The difference between a long-sighted and a short-sighted man, or between a deaf man and a man who hears well, are physiological. Neither of these kinds concerns us, and I have mentioned them only in order to exclude them. The kind that concerns us is the purely physical kind. Physical differences between two observers will be preserved when the observers are replaced by cameras or phonographs, and can be reproduced on the movies or the gramophone. If two men both listen to a third man speaking, and one of them is nearer to the speaker than the other is, the nearer one will hear louder and slightly earlier sounds than are heard by the other. If two men both watch a tree falling, they see it from different angles. Both these differences would be shown equally by recording instruments: they are in no way due to idiosyncrasies in the observers, but are part of the ordinary course of physical nature as we experience it.
The physicist, like the plain man, believes that his perceptions give him knowledge about what is really occurring in the physical world, and not only about his private experiences. Professionally, he regards the physical world as “real,” not merely as something which human beings dream. An eclipse of the sun, for instance, can be observed by any person who is suitably situated, and is also observed by the photographic plates that are exposed for the purpose. The physicist is persuaded that something has really happened over and above the experiences of those who have looked at the sun or at photographs of it. I have emphasized this point, which might seem a trifle obvious, because some people imagine that Einstein has made a difference in this respect. In fact he has made none.
But if the physicist is justified in this belief that a number of people can observe the “same” physical occurrence, then clearly the physicist must be concerned with those features which the occurrence has in common for all observers, for the others cannot be regarded as belonging to the occurrence itself. At least, the physicist must confine himself to the features which are common to all “equally good” observers. The observer who uses a microscope or a telescope is preferred to one who does not, because he sees all that the latter sees and more too. A sensitive photographic plate may “see” still more, and is then preferred to any eye. But such things as differences of perspective, or differences of apparent size due to difference of distance, are obviously not attributable to the object; they belong solely to the point of view of the spectator. Common sense eliminates these in judging of objects; physics has to carry the same process much further, but the principle is the same.
I want to make it clear that I am not concerned with anything that can be called inaccuracy. I am concerned with genuine physical differences between occurrences each of which is a correct record of a certain event, from its own point of view. When a man fires a gun, people who are not quite close to him see the flash before they hear the report. This is not due to any defect in their senses, but to the fact that sound travels more slowly than light. Light travels so fast that, from the point of view of phenomena on the surface of the earth, it may be regarded as instantaneous. Anything that we can see on the earth happens practically at the moment when we see it. In a second, light travels 300,000 kilometers (about 186,000 miles). It travels from the sun to the earth in about eight minutes, and from the stars to us in anything from three to a thousand years. But of course we cannot place a clock in the sun, and send out a flash of light from it at 12 noon, Greenwich Mean Time, and have it received at Greenwich at 12.08 p.m. Our methods of estimating the speed of light have to be more or less indirect. The only direct method would be that which we apply to sound when we use an echo. We could send a flash to a mirror, and observe how long it took for the reflection to reach us; this would give the time of the double journey to the mirror and back. On the earth, however, the time would be so short that a great deal of theoretical physics has to be utilized if this method is to be employed—more even than is required for the employment of astronomical data.
The problem of allowing for the spectator’s point of view, we may be told, is one of which physics has at all times been fully aware; indeed it has dominated astronomy ever since the time of Copernicus. This is true. But principles are often acknowledged long before their full consequences are drawn. Much of traditional physics is incompatible with the principle, in spite of the fact that it was acknowledged theoretically by all physicists.
There existed a set of rules which caused uneasiness to the philosophically minded, but were accepted by physicists because they worked in practice. Locke had distinguished “secondary” qualities—colors, noises, tastes, smells, etc.—as subjective, while allowing “primary” qualities—shapes and positions and sizes—to be genuine properties of physical objects. The physicist’s rules were such as would follow from this doctrine. Colors and noises were allowed to be subjective, but due to waves proceeding with a definite velocity—that of light or sound as the case may be—from their source to the eye or ear of the percipient. Apparent shapes vary according to the laws of perspective, but these laws are simple and make it easy to infer the “real” shapes from several visual apparent shapes; moreover, the “real” shapes can be ascertained by touch in the case of bodies in our neighborhood. The objective time of a physical occurrence can be inferred from the time when we perceive it by allowing for the velocity of transmission—of light or sound or nerve currents according to circumstances. This was the view adopted by physicists in practice, whatever qualms they may have had in unprofessional moments.
This view worked well enough until physicists became concerned with much greater velocities than those that are common on the surface of the earth. An express train travels about a mile in a minute; the planets travel a few miles in a second. Comets, when they are near the sun, travel much faster, and behave somewhat oddly; but they were puzzling in various ways. Practically, the planets were the most swiftly moving bodies to which dynamics could be adequately applied. With radio-activity a new range of observations became possible. Individual electrons can be observed, emanating from radium with a velocity not far short of that of light. The behavior of bodies moving with these enormous speeds is not what the old theories would lead us to expect. For one thing, mass seems to increase with speed in a perfectly definite manner. When an electron is moving very fast, a bigger force is required to have a given effect upon it than when it is moving slowly. Then reasons were found for thinking that the size of a body is affected by its motion—for example, if you take a cube and move it very fast, it gets shorter in the direction of its motion, from the point of view of a person who is not moving with it, though from its own point of view (i.e. for an observer traveling with it) it remains just as it was. What was still more astonishing was the discovery that lapse of time depends on motion; that is to say, two perfectly accurate clocks, one of which is moving very fast relatively to the other, will not continue to show the same time if they come together again after a journey. It follows that what we discover by means of clocks and foot rules, which used to be regarded as the acme of impersonal science, is really in part dependent upon our private circumstances, i.e. upon the way in which we are moving relatively to the bodies measured.
This shows that we have to draw a different line from that which is customary in distinguishing between what belongs to the observer and what belongs to the occurrence which he is observing. If a man is wearing blue spectacles he knows that the blue look of everything is due to his spectacles, and does not belong to what he is observing. But if he observes two flashes of lightning, and notes the interval of time between his observations; if he knows where the flashes took place, and allows, in each case, for the time the light took to reach him—in that case, if his chronometer is accurate, he naturally thinks that he has discovered the actual interval of time between the two flashes, and not something merely personal to himself. He is confirmed in this view by the fact that all other careful observers to whom he has access agree with his estimates. This, however, is only due to the fact that all these observers are on the earth, and share its motion. Even two observers in aeroplanes moving in opposite directions would have at the most a relative velocity of 400 miles an hour, which is very little in comparison with 186,000 miles a second (the velocity of light). If an electron shot out from a piece of radium with a velocity of 170,000 miles a second could observe the time between the two flashes, it would arrive at a quite different estimate, after making full allowance for the velocity of light. How do you know this? the reader may ask. You are not an electron, you cannot move at these terrific speeds, no man of science has ever made the observations which would prove the truth of your assertion. Nevertheless, as we shall see in the sequel, there is good ground for the assertion—ground, first of all, in experiment, and—what is remarkable—ground in reasonings which could have been made at any time, but were not made until experiments had shown that the old reasonings must be wrong.
There is a general principle to which the theory of relativity appeals, which turns out to be more powerful than anybody would suppose. If you know that one man is twice as rich as another, this fact must appear equally whether you estimate the wealth of both in pounds or dollars or francs or any other currency. The numbers representing their fortunes will be changed, but one number will always be double the other. The same sort of thing, in more complicated forms, reappears in physics. Since all motion is relative, you may take any body you like as your standard body of reference, and estimate all other motions with reference to that one. If you are in a train and walking to the dining-car, you naturally, for the moment, treat the train as fixed and estimate your motion by relation to it. But when you think of the journey you are making, you think of the earth as fixed, and say you