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.
CHAPTER II:
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 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.