Obviously something happens when an image in a looking glass moves. From the point of view of sight, the event seems just as real as if it were not in a mirror. But nothing has happened from the point of view of touch or hearing. When the “real” top-hat falls, it makes a noise; the twenty or thirty reflections fall without a sound. If it falls on your toe, you feel it; but we believe that the twenty or thirty people in the mirrors feel nothing, though top-hats fall on their toes too. But all this is equally true of the astronomical world. It makes no noise, because sound cannot travel across a vacuum. So far as we know, it causes no “feelings,” because there is no one on the spot to “feel” it. The astronomical world, therefore, seems hardly more “real” or “solid” than the world in the looking glass, and has just as little need of “force” to make it move.
The reader may feel that I am indulging in idle sophistry. “After all,” he may say, “the image in the mirror is the reflection of something solid, and the top-hat in the mirror only falls off because of the force applied to the real top-hat. The top-hat in the mirror cannot indulge in behavior of its own; it has to copy the real one. This shows how different the image is from the sun and the planets, because they are not obliged to be perpetually imitating a prototype. So you had better give up pretending that an image is just as real as one of the heavenly bodies.”
There is, of course, some truth in this; the point is to discover exactly what truth. In the first place, images are not “imaginary.” When you see an image, certain perfectly real light waves reach your eye; and if you hang a cloth over the mirror, these light waves cease to exist. There is, however, a purely optical difference between an “image” and a “real” thing. The optical difference is bound up with this question of imitation. When you hang a cloth over the mirror, it makes no difference to the “real” object; but when you move the “real” object away, the image vanishes also. This makes us say that the light rays which make the image are only reflected at the surface of the mirror, and do not really come from a point behind it, but from the “real” object. We have here an example of a general principle of great importance. Most of the events in the world are not isolated occurrences, but members of groups of more or less similar events, which are such that each group is connected in an assignable manner with a certain small region of space-time. This is the case with the light rays which make us see both the object and its reflection in the mirror: they all emanate from the object as a center. If you put an opaque globe round the object at a certain distance, the object and its reflection are invisible at any point outside the globe. We have seen that gravitation, although no longer regarded as an action at a distance, is still connected with a center: there is, so to speak, a hill symmetrically arranged about its summit, and the summit is the place where we conceive the body to be which is connected with the gravitational field we are considering. For simplicity, common sense lumps together all the events which form one group in the above sense. When two people see the same object, two different events occur, but they are events belonging to one group and connected with the same center. Just the same applies when two people (as we say) hear the same noise. And so the reflection in a mirror is less “real” than the object reflected, even from an optical point of view, because light rays do not spread in all directions from the place where the image seems to be, but only in directions in front of the mirror, and only so long as the object reflected remains in position. This illustrates the usefulness of grouping connected events about a center in the way we have been considering.
When we examine the changes in such a group of objects, we find that they are of two kinds: there are those which affect only some member of the group, and those which make connected alterations in all the members of the group. If you put a candle in front of a mirror, and then hang black cloth over the mirror, you alter only the reflection of the candle as seen from various places. If you shut your eyes, you alter its appearance to you, but not its appearance elsewhere. If you put a red globe round it at a distance of a foot, you alter its appearance at any distance greater than a foot, but not at any distance less than a foot. In all these cases, you do not regard the candle itself as having changed; in fact, in all of them, you find that there are groups of changes connected with a different center or with a number of different centers. When you shut your eyes, for instance, your eyes, not the candle, look different to any other observer: the center of the changes that occur is in your eyes. But when you blow out the candle, its appearance everywhere is changed; in this case you say that the change has happened to the candle. The changes that happen to an object are those that affect the whole group of events which center about the object. All this is only an interpretation of common sense, and an attempt to explain what we mean by saying that the image of the candle in the mirror is less “real” than the candle. There is no connected group of events situated all round the place where the image seems to be, and changes in the image center about the candle, not about a point behind the mirror. This gives a perfectly verifiable meaning to the statement that the image is “only” a reflection. And at the same time it enables us to regard the heavenly bodies, although we can only see and not touch them, as more “real” than an image in a looking glass.
We can now begin to interpret the common sense notion of one body having an “effect” upon another, which we must do if we are really to understand what is meant by the abolition of “force.” Suppose you come into a dark room and switch on the electric light: the appearance of everything in the room is changed. Since everything in the room is visible because it reflects the electric light, this case is really analogous to that of the image in the mirror; the electric light is the center from which all the changes emanate. In this case, the “effect” is explained by what we have already said. The more important case is when the effect is a movement. Suppose you let loose a tiger in the middle of a Bank Holiday crowd: they would all move, and the tiger would be the center of their various movements. A person who could see the people but not the tiger would infer that there was something repulsive at that point. We say in this case that the tiger has an effect upon the people, and we might describe the tiger’s action upon them as of the nature of a repulsive force. We know, however, that they fly because of something which happens to them, not merely because the tiger is where he is. They fly because they can see and hear him, that is to say, because certain waves reach their eyes and ears. If these waves could be made to reach them without there being any tiger, they would fly just as fast, because the neighborhood would seem to them just as unpleasant.
Let us now apply similar considerations to the sun’s gravitation. The “force” exerted by the sun only differs from that exerted by the tiger in being attractive instead of repulsive. Instead of acting through waves of light or sound, the sun acquires its apparent power through the fact that there are modifications of space-time all round the sun. Like the noise of the tiger, they are more intense near their source; as we travel away they grow less and less. To say that the sun “causes” these modifications of space-time is to add nothing to our knowledge. What we know is that the modifications proceed according to a certain rule, and that they are grouped symmetrically about the sun as center. The language of cause and effect adds only a number of quite irrelevant imaginings, connected with will, muscular tension, and such matters. What we can more or less ascertain is merely the formula according to which space-time is modified by the presence of gravitating matter. More correctly: we can ascertain what kind of space-time is the presence of gravitating matter. When space-time is not accurately Euclidean in a certain region, but has a non-Euclidean character which grows more and more marked as we approach a certain center, and when, further, the departure from Euclid obeys a certain law, we describe this state of affairs briefly by saying that there is gravitating matter at the center. But this is only a compendious account of what we know. What we know is about the places where the gravitating matter is not, not about the place where it is. The language of cause and effect (of which “force” is a particular case) is thus merely a convenient shorthand for certain purposes; it does not represent anything that is genuinely to be found in the physical world.
And how about matter? Is matter also no more than a convenient shorthand? This question, however, being a large one, demands a separate chapter.
CHAPTER XIV:
WHAT IS MATTER?
The question “What is matter?” is of the kind that is asked by metaphysicians, and answered in vast books of incredible obscurity. But I am not asking the question as metaphysician: I am asking it as a person who wants to find out what is the moral of modern physics, and more especially of the theory of relativity. It is obvious from what we have learned of that theory that matter cannot be conceived quite as it used to be. I think we can now say more or less what the new conception must be.
There were two traditional conceptions of matter, both of which have had advocates ever since scientific speculation began. There were the atomists, who thought that matter consisted of tiny lumps which could never be divided; these were supposed to hit each other and then bounce off in various ways. After Newton, they were no longer supposed actually to come into contact with each other, but to attract and repel each other, and move in orbits round each other. Then there were those who thought that there is matter of some kind everywhere, and that a true vacuum is impossible. Descartes held this view, and attributed the motions of the planets to vortices in the ether. The Newtonian theory of gravitation caused the view that there is matter everywhere to fall into discredit, the more so as light was thought by Newton and his disciples to be due to actual particles traveling from the source of the light. But when this view of light was disproved, and it was shown that light consisted of waves, the ether was revived so that there should be something to undulate. The ether became still more respectable when it was found to play the same part in electromagnetic phenomena as in the propagation of light. It was even hoped that atoms might turn out to be a mode of motion of the ether. At this stage, the atomic view of matter was, on the whole, getting the worst of it.