The A B C of Relativity

that these mathematically-constructed quantities are what our senses are adapted for perceiving. But neither of these things is physics in the strict sense. The part of physics which cannot, at present, be brought within the scope of relativity is large and important. There is nothing in relativity to show why there should be electrons and protons; relativity cannot give any reason why matter should exist in little lumps. With this goes the whole theory of the structure of the atom. The theory of quanta also is quite outside the scope of relativity. Relativity is, in a sense, the most extreme application of what may be called next-to-next methods. Gravitation is no longer regarded as due to the effect of the sun upon a planet, but as expressing characteristics of the region in which the planet happens to be. Distance, which used to be thought to have a definite meaning however far apart two points might be, is now only definite for neighboring points. The distance between widely separated places depends upon the route chosen. We may, it is true, define the distance as the geodesic distance, but that can only be estimated by adding up little [Pg 188] bits, that is to say, by the method we use in estimating the length of a curve. What applies to distance applies equally to the straight line. There is nothing in the actual world having exactly the properties that straight lines were supposed to have; the nearest approach is the track of a light ray. Straight lines have to be replaced by geodesics, which are defined by what they do at each point, not all at once, like Euclidean straight lines. Measurement, in Weyl’s theory, suffers the same fate. We can only use a measuring rod to give lengths in one place: when we move it to another region, there is no knowing how it will alter. We do assume, however, that, if it alters, it alters bit by bit, gradually, continuously, and not by sudden jumps. Perhaps this assumption is unjustified. It belongs to the general outlook of relativity, which is that of continuity. No doubt it is owing to this outlook that relativity is unable to account for the discontinuities in physics, such as quanta, electrons and protons. Perhaps relativity will conquer these domains when it learns to dispense with the assumption of continuity. Finally we come to geography, in which I include history. The separation of history from geography rests upon the separation of time [Pg 189] from space; when we amalgamate the two in space-time, we need one word to describe the combination of geography and history. For the sake of simplicity, I shall use the one word geography in this extended sense. 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 [Pg 190] 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 [Pg 191] 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.