The ABC of Relativity

Bertrand Russell

• Publisher: Open Road Media
• Year: 2021
• ISBN:
  9781504000994
• Topic: Scienze fisiche
• Subtopic: Relatività in fisica

The Nobel Prize winner offers "an ideal introduction to the theories of special and general relativity" in clear, comprehensible language ( Nature ). A renowned mathematician and philosopher, and as well as recipient of the Nobel Prize in Literature, Bertrand Russell was acclaimed for his ability to address complex subjects in accessible ways. In this classic reference book, Russell delves into physics and relativity, helping everyday readers grasp the genius and implications of Albert Einstein's theory. When originally published in 1925, The ABC of Relativity brought science to a more general audience—and it continues to do so in the twenty-first century. "A mind of dazzling brilliance." — The New York Times

Chapter 1

Touch and Sight: The Earth and the Heavens

Everybody knows that Einstein did something astonishing, but very few people know exactly what it was. It is generally recognised that he revolutionised our conception of the physical world, but the 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 prehuman, 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, who 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 easier to generations which grow up with them; but for us 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 distance 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 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 was not cleared up until relativity was discovered. It turned out that much of what had been 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 with someone 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 on 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 travelling in all directions, but you cannot see the ground or the trains or the aeroplanes because 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 were with you in the balloon, you would find his speech unintelligible. But if Einstein were with you, you would understand him more easily than the ordinary mortal would, because you would 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 on 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 has always 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 travelled to Edinburgh, not that Edinburgh has travelled 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. 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 s question about Edinburgh, but the booking-office clerk would reply: ‘What part of Edinburgh do you mean? 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 immobility 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 higgledypiggledy 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 not 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 person 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. 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 earlier astronomers 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 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 offeree’, 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 the Newtonian 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. Even Newton 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 ‘gravitational force’ is a mistake. The sun does not exert any force on the planets; in the relativity law of gravitation, the planet only pays attention to what it finds in its own neighbourhood. 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 ‘gravitational 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 enters the solar system and goes away again than to what common sense supposes to happen.

Most of what we have said hitherto was already recognised by physicists before the theory of relativity was invented. 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 labour was required in order to bring the actual procedure of physics into harmony with these new convictions. The technical methods of the old physics embodied the ideas of gravitational force and of absolute space and time. A new technique was needed, free from the old assumptions. For this to be possible, the old ideas of space and time had to be changed fundamentally. This is what makes both the difficulty and the interest of the theory. But before explaining it there are some preliminaries which are indispensable. These will occupy the next two chapters.

Chapter 2

WHat Happens and What is Observed

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 the theory of relativity shows how to discount this effect completely. This is the source of almost everything that is surprising in the 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 practical point of view they are as a rule unimportant. But both psychology and physics, from their different angles, are compelled to emphasise the respects in which one person’s perception of a given occurrence differs from another’s. Some of these differences are due to differences in the brains or minds of the observers, some to differences in their senseorgans, 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 travellers 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 differences between a long-sighted and a short-sighted person, or between a deaf person and someone 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 recording machines, and can be reproduced in a film or on the gramophone. If two people both listen to a third person 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 people 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 experi...