Geography, in this sense, includes everything that, as a matter of crude fact, distinguishes one part of space-time from another. One part is occupied by the sun, one by the earth; the intermediate regions contain light waves, but no matter (apart from a very little here and there). There is a certain degree of theoretical connection between different geographical facts; to establish this is the purpose of physical laws. It is thought that a sufficient knowledge of the geographical facts of the solar system throughout any finite time, however short, would enable an ideally competent physicist to predict the future of the solar system so long as it remained remote from other stars. We are already in a position to calculate the large facts about the solar system backwards and forwards for vast periods of time. But in all such calculations we need a basis of crude fact. The facts are interconnected, but facts can only be inferred from other facts, not from general laws alone. Thus the facts of geography have a certain independent status in physics. No amount of physical laws will enable us to infer a physical fact unless we know other facts as data for our inference. And here when I speak of “facts” I am thinking of particular facts of geography, in the extended sense in which I am using the term.
In the theory of relativity, we are concerned with structure, not with the material of which the structure is composed. In geography, on the other hand, the material is relevant. If there is to be any difference between one place and another, there must either be differences between the material in one place and that in another, or places where there is material and places where there is none. The former of these alternatives seems the more satisfactory. We might try to say: There are electrons and protons, and the rest is empty. But in the “empty” regions there are light waves, so that we cannot say nothing happens in them. Some people maintain that the light waves take place in the ether, others are content to say simply that they take place; but in any case events are occurring where there are light waves. That is all that we can really say for the places where there is matter, since matter has turned out to be a mathematical construction built out of events. We may say, therefore, that there are events everywhere in space-time, but they must be of a somewhat different kind according as we are dealing with a region where there is an electron or proton or with the sort of region we should ordinarily call empty. But as to the intrinsic nature of these events we can know nothing, except when they happen to be events in our own lives. Our own perceptions and feelings must be part of the crude material of events which physics arranges into a pattern—or rather, which physics finds to be arranged in a pattern. As regards events which do not form part of our own lives, physics tells us the pattern of them, but is quite unable to tell us what they are like in themselves. Nor does it seem possible that this should be discovered by any other method.
CHAPTER XIII:
THE ABOLITION OF “FORCE”
In the Newtonian system, bodies under the action of no forces move in straight lines with uniform velocity; when bodies do not move in this way, their change of motion is ascribed to a “force.” Some forces seem intelligible to our imagination: those exerted by a rope or string, by bodies colliding, or by any kind of obvious pushing or pulling. As explained in an earlier chapter, our apparent imaginative understanding of these processes is quite fallacious; all that it really means is that past experience enables us to foresee more or less what is going to happen without the need of mathematical calculations. But the “forces” involved in gravitation and in the less familiar forms of electrical action do not seem in this way “natural” to our imagination. It seems odd that the earth can float in the void: the natural thing to suppose is that it must fall. That is why it has to be supported on an elephant, and the elephant on a tortoise, according to some early speculators. The Newtonian theory, in addition to action at a distance, introduced two other imaginative novelties. The first was, that gravitation is not always and essentially directed what we should call “downwards,” i.e., towards the center of the earth. The second was, that a body going round and round in a circle with uniform velocity is not “moving uniformly” in the sense in which that phrase is applied to the motion of bodies under no forces, but is perpetually being turned out of the straight course towards the center of the circle, which requires a force pulling it in that direction. Hence Newton arrived at the view that the planets are attracted to the sun by a force, which is called gravitation.
This whole point of view, as we have seen, is superseded by relativity. There are no longer such things as “straight lines” in the old geometrical sense. There are “straightest lines,” or geodesics, but these involve time as well as space. A light ray passing through the solar system does not describe the same orbit as a comet, from a geometrical point of view; nevertheless each moves in a geodesic. The whole imaginative picture is changed. A poet might say that water runs down hill because it is attracted to the sea, but a physicist or an ordinary mortal would say that it moves as it does, at each point, because of the nature of the ground at that point, without regard to what lies ahead of it. Just as the sea does not cause the water to run towards it, so the sun does not cause the planets to move round it. The planets move round the sun because that is the easiest thing to do—in the technical sense of “least action.” It is the easiest thing to do because of the nature of the region in which they are, not because of an influence emanating from the sun.
The supposed necessity of attributing gravitation to a “force” attracting the planets towards the sun has arisen from the determination to preserve Euclidean geometry at all costs. If we suppose that our space is Euclidean, when in fact it is not, we shall have to call in physics to rectify the errors of our geometry. We shall find bodies not moving in what we insist upon regarding as straight lines, and we shall demand a cause for this behavior. Eddington has stated this matter with admirable lucidity. He supposes a physicist who has assumed the formula for interval which is used in the special theory of relativity—a formula which still supposes that the observer’s space is Euclidean. He continues:
Since intervals can be compared by experimental methods, he ought soon to discover that his (formula for the interval) cannot be reconciled with observational results, and so realize his mistake. But the mind does not so readily get rid of an obsession. It is more likely that our observer will continue in his opinion, and attribute the discrepancy of the observations to some influence which is present and affects the behavior of his test-bodies. He will, so to speak, introduce a supernatural agency which he can blame for the consequences of his mistake.... The name given to any agency which causes deviation from uniform motion in a straight line is force according to the Newtonian definition of force. Hence the agency invoked through our observer’s mistake is described as a “field of force.”... A field of force represents the discrepancy between the naturalgeometry of a co-ordinate system and the abstractgeometry arbitrarily ascribed to it.[15]
If people were to learn to conceive the world in the new way, without the old notion of “force,” it would alter not only their physical imagination, but probably also their morals and politics. The latter effect would be quite illogical, but is none the less probable on that account. In Newton’s theory of the solar system, the sun seems like a monarch whose behests the planets have to obey. In Einstein’s world there is more individualism and less government than in Newton’s. There is also far less hustle: we have seen that laziness is the fundamental law of Einstein’s universe. The word “dynamic” has come to mean, in newspaper language, “energetic and forceful”; but if it meant “illustrating the principles of dynamics,” it ought to be applied to the people in hot climates who sit under banana trees waiting for the fruit to drop into their mouths. I hope that journalists, in future, when they speak of a “dynamic personality,” will mean a person who does what is least trouble at the moment, without thinking of remote consequences. If I can contribute to this result, I shall not have written in vain.
It has been customary for people to draw arguments from the laws of nature as to what we ought to do. Such arguments seem to me a mistake: to imitate nature may be merely slavish. But if nature, as portrayed by Einstein, is to be our model, it would seem that the anarchists will have the best of the argument. The physical universe is orderly, not because there is a central government, but because every body minds its own business. No two particles of matter ever come into contact; when they get too close, they both move off. If a man were had up for knocking another man down, he would be scientifically correct in pleading that he had never touched him. What happened was that there was a hill in space-time in the region of the other man’s nose, and it fell down the hill.
The abolition of “force” seems to be connected with the substitution of sight for touch as the source of physical ideas, as explained in [Chapter I]. When an image in a looking glass moves, we do not think that something has pushed it. In places where there are two large mirrors opposite to each other, you may see innumerable reflections of the same object. Suppose a gentleman in a top-hat is standing between the mirrors, there may be twenty or thirty top-hats in the reflections. Suppose now somebody comes and knocks off the gentleman’s hat with a stick: all the other twenty or thirty top-hats will tumble down at the same moment. We think that a force is needed to knock off the “real” top-hat, but we think the remaining twenty or thirty tumble off, so to speak, of themselves, or out of a mere passion for imitation. Let us try to think out this matter a little more seriously.