Philosophy

We have seen that the world of the atom is a world of revolution rather than evolution: the electron which has been moving in one orbit hops quite suddenly into another, so that the motion is what is called “discontinuous”, that is to say, the electron is first in one place and then in another, without having passed over any intermediate places. This sounds like magic, and there may be some way of avoiding such a disconcerting hypothesis. At any rate, nothing of the sort seems to happen in the regions where there are no electrons and protons. In these regions, so far as we can discover, there is continuity, that is to say, everything goes by gradual transitions, not by jumps. The regions in which there are no electrons and protons may be called “æther” or “empty space” as you prefer: the difference is only verbal. The theory of relativity is especially concerned with what goes on in these regions, as opposed to what goes on where there are electrons and protons. Apart from the theory of relativity, what we know about these regions is that waves travel across them, and that these waves, when they are waves of light or electromagnetism (which are identical), behave in a certain fashion set forth by Maxwell in certain formulæ called “Maxwell’s equations”. When I say we “know” this, I am saying more than is strictly correct, because all we know is what happens when the waves reach our bodies. It is as if we could not see the sea, but could only see the people disembarking at Dover, and inferred the waves from the fact that the people looked green. It is obvious, in any case, that we can only know so much about the waves as is involved in their having such-and-such causes at one end and such-and-such effects at the other. What can be inferred in this way will be, at best, something wholly expressible in terms of mathematical structure. We must not think of the waves as being necessarily “in” the æther or “in” anything else; they are to be thought of merely as progressive periodic processes, whose laws are more or less known, but whose intrinsic character is not known and never can be. The theory of relativity has arisen from the study of what goes on in the regions where there are no electrons and protons. While the study of the atom has led us to discontinuities, relativity has produced a completely continuous theory of the intervening medium—far more continuous than any theory formerly imagined. At the moment, these two points of view stand more or less opposed to each other, but no doubt before long they will be reconciled. There is not, even now, any logical contradiction between them; there is only a fairly complete lack of connection. For philosophy, far the most important thing about the theory of relativity is the abolition of the one cosmic time and the one persistent space, and the substitution of space-time in place of both. This is a change of quite enormous importance, because it alters fundamentally our notion of the structure of the physical world, and has, I think, repercussions in psychology. It would be useless, in our day, to talk about philosophy without explaining this matter. Therefore I shall make the attempt, in spite of some difficulty. Common-sense and pre-relativity physicists believed that, if two events happen in different places, there must always be a definite answer, in theory, to the question whether they were simultaneous. This is found to be a mistake. Let us suppose two persons A and B a long way apart, each provided with a mirror and means of sending out light-signals. The events that happen to A still have a perfectly definite time-order, and so have those that happen to B; the difficulty comes in connecting A’s time with B’s. Suppose A sends a flash to B, B’s mirror reflects it, and it returns to A after a certain time. If A is on the earth and B on the sun, the time will be about sixteen minutes. We shall naturally say that the time when B received the light-signal is half way between the times when A sent it out and received it back. But this definition turns out to be not unambiguous; it will depend upon how A and B are moving relatively to each other. The more this difficulty is examined, the more insuperable it is seen to be. Anything that happens to A after he sends out the flash and before he gets it back is neither definitely before nor definitely after nor definitely simultaneous with the arrival of the flash at B. To this extent, there is no unambiguous way of correlating times in different places. The notion of a “place” is also quite vague. Is London a “place”? But the earth is rotating. Is the earth a “place”? But it is going round the sun. Is the sun a “place”? But it is moving relatively to the stars. At best you could talk of a place at a given time; but then it is ambiguous what is a given time, unless you confine yourself to one place. So the notion of “place” evaporates. We naturally think of the universe as being in one state at one time and in another at another. This is a mistake. There is no cosmic time, and so we cannot speak of the state of the universe at a given time. And similarly we cannot speak unambiguously of the distance between two bodies at a given time. If we take the time appropriate to one of the two bodies, we shall get one estimate; if the time of the other, another. This makes the Newtonian law of gravitation ambiguous, and shows that it needs restatement, independently of empirical evidence. Geometry also goes wrong. A straight line, for example, is supposed to be a certain track in space whose parts all exist simultaneously. We shall now find that what is a straight line for one observer is not a straight line for another. Therefore geometry ceases to be separable from physics. The “observer” need not be a mind, but may be a photographic plate. The peculiarities of the “observer” in this region belong to physics, not to psychology. So long as we continue to think in terms of bodies moving, and try to adjust this way of thinking to the new ideas by successive corrections, we shall only get more and more confused. The only way to get clear is to make a fresh start, with events instead of bodies. In physics, an “event” is anything which, according to the old notions, would be said to have both a date and a place. An explosion, a flash of lightning, the starting of a light-wave from an atom, the arrival of the light-wave at some other body, any of these would be an “event”. Some strings of events make up what we regard as the history of one body; some make up the course of one light-wave; and so on. The unity of a body is a unity of history—it is like the unity of a tune, which takes time to play, and does not exist whole in any one moment. What exists at any one moment is only what we call an “event”. It may be that the word “event”, as used in physics, cannot be quite identified with the same word as used in psychology; for the present we are concerned with “events” as the constituents of physical processes, and need not trouble ourselves about “events” in psychology. The events in the physical world have relations to each other which are of the sort that have led to the notions of space and time. They have relations of order, so that we can say that one event is nearer to a second than to a third. In this way we can arrive at the notion of the “neighbourhood” of an event: it will consist roughly speaking of all the events that are very near the given event. When we say that neighbouring events have a certain relation, we shall mean that the nearer two events are to each other, the more nearly they have this relation, and that they approximate to having it without limit as they are taken nearer and nearer together. Two neighbouring events have a measurable quantitative relation called “interval”, which is sometimes analogous to distance in space, sometimes to lapse of time. In the former case it is called space-like, in the latter time-like. The interval between two events is time-like when one body might be present at both—for example, when both are parts of the history of your body. The interval is space-like in the contrary case. In the marginal case between the two, the interval is zero; this happens when both are parts of one light-ray. The interval between two neighbouring events is something objective, in the sense that any two careful observers will arrive at the same estimate of it. They will not arrive at the same estimate for the distance in space or the lapse of time between the two events, but the interval is a genuine physical fact, the same for all. If a body can travel freely from one event to the other, the interval between the two events will be the same as the time between them as measured by a clock travelling with the body. If such a journey is physically impossible, the interval will be the same as the distance as estimated by an observer to whom the two events are simultaneous. But the interval is only definite when the two events are very near together; otherwise the interval depends upon the route chosen for travelling from the one event to the other. Four numbers are needed to fix the position of an event in the world; these correspond to the time and the three dimensions of space in the old reckoning. These four numbers are called the co-ordinates of the event. They may be assigned on any principle which gives neighbouring co-ordinates to neighbouring events; subject to this condition, they are merely conventional. For example, suppose an aeroplane has had an accident. You can fix the position of the accident by four numbers: latitude, longitude, altitude above sea-level, and Greenwich Mean Time. But you cannot fix the position of the explosion in space-time by means of less than four numbers. Everything in relativity-theory goes (in a sense) from next to next; there are no direct relations between distant events, such as distance in time or space. And of course there are no forces acting at a distance; in fact, except as a convenient fiction, there are no “forces” at all. Bodies take the course which is easiest at each moment, according to the character of space-time in the particular region where they are; this course is called a geodesic. Now it will be observed that I have been speaking freely of bodies and motion, although I said that bodies were merely certain strings of events. That being so, it is of course necessary to say what strings of events constitute bodies, since not all continuous strings of events do so, not even all geodesics. Until we have defined the sort of thing that makes a body, we cannot legitimately speak of motion, since this involves the presence of one body on different occasions. We must therefore set to work to define what we mean by the persistence of a body, and how a string of events constituting a body differs from one which does not. This topic will occupy the next chapter. But it may be useful, as a preliminary, to teach our imagination to work in accordance with the new ideas. We must give up what Whitehead admirably calls the “pushiness” of matter. We naturally think of an atom as being like