The analysis of matter

BEFORE embarking upon the epistemological discussions which will concern us in Part II., it will be well to draw some morals from our previous chapters. Throughout these chapters, I have carefully abstained from speculations which would have taken us outside the domain of physics; in particular, I have not sought to interpret the mathematically fundamental notions of physics in terms of entities not directly amenable to ordinary mathematical treatment. It seemed desirable to be clear first as to what physics has to say, before undertaking either the epistemological criticism of the evidence or the metaphysical interpretation of the logically primitive apparatus of physics. This is the purpose of the present chapter.

Physics started historically, and still starts in the education of the young, with matters that seem thoroughly concrete. Levers and pulleys, falling bodies, collisions of billiard balls, etc., are all familiar in everyday life, and it is a pleasure to the scientifically-minded youth to find them amenable to mathematical treatment. But in proportion as physics increases the scope and power of its methods, in that same proportion it robs its subject-matter of concreteness. The extent to which this is the case is not always realized, at any rate in unprofessional moments, even by the physicist himself; he may tell you that he can "see" an electron hitting a screen, which is of course a telescoped expression for a complicated inference. Dr Whitehead has done more than any other author to show the need of undoing the abstractions of physics. For the moment, I am not concerned with this need, but with the abstractions themselves.

Let us take space, time, light and matter as illustrative of the gradually increasing abstractness of physics. These four notions are all extracted from common sense. We see objects spread out in space, we can feel their shapes with our fingers; we know what it is to walk to a neighbouring town or travel to a neighbouring country. All this makes "space" seem something familiar and easy, until, in the course of education, we learn the puzzles to which it has given rise. Time seems equally obvious: we remember past events in a time-order we notice day and night, summer and winter, youth and age, we know that history relates events of previous epochs, we insure our lives in the confident expectation that we shall die in the future. Light, again, seemed in no way mysterious to the author of Genesis, as, indeed, how should it to anyone who had experienced the difference between night and day? Matter was equally obvious: it was primarily anything that we could touch, though the first step towards mystification was taken when Empedocles included air. However, we are conscious of air in the form of wind and as something that fills our lungs, so that less effort was required to admit air among the elements than to exclude fire.

From this happy familiarity with the everyday world physics has been gradually driven by its own triumphs, like a monarch who has grown too grand to converse with his subjects. The space-time of relativity is very far removed from the space and time of our unscientific experience; yet even space-time is nearer to common sense than the conceptions towards which physics is tending. "Space and time" says Eddington,[34] "are only approximate conceptions, which must ultimately give way to a more general conception of the ordering of events in nature not expressible in terms of a fourfold co-ordinate system. It is in this direction that some physicists hope to find a solution of the contradictions of the quantum theory. It is a fallacy to think that the conception of location in space-time based on the observation of large-scale phenomena can be applied unmodified to the happenings which involve only a small number of quanta. Assuming that this is the right solution it is useless to look for any means of introducing quantum phenomena into the later formulæ of our theory; these phenomena have been excluded at the outset by the adoption of a co-ordinate frame of reference." But even if space-time, as it appears in the general theory of relativity, were the last word as regards the physical order corresponding to our usual notions of space and time, it is evident that we should have travelled very far from those notions, and have arrived at a region in which pictorial imagination is useless.

The view of Locke, that the secondary qualities are subjective but not the primary qualities, was more or less compatible with physics until very recent times. There are spaces and times in our immediate experience, and there seemed no insuperable obstacle to identifying them with the spaces and times of the physical world. In regard to time, at least, practically no one doubted the rightness of this identification. There were doubts as regards space, but they came from psychologists rather than physicists. Now, however, both space and time, as they occur in immediate experience, are recognized by writers on relativity as something quite different from the space-time which physics requires. Locke's half-way house has therefore been definitely abandoned.

I come now to the relation of light as experienced to light in physics. Here the cleavage is older than in the case of space and time; indeed, it is already admitted in Locke's theory. It is impossible to exaggerate the importance of this cleavage in separating the world of physics from the world of common sense. With the exception of parts of our own body and bodies with which our own body is in contact, the objects which, according to common sense, we perceive, are known by means of light, sound, or odour. The last of these, though important to many species of animals, is relatively subordinate in the perceptions of human beings. Sound is less important than light, and in any case raises exactly the same problems in the present connection. We may therefore concentrate upon light as a source of our knowledge concerning the external world.

When we "see" an object, we seem to have immediate knowledge of something external to our own body. But physics says that a complicated process starts from the external object, travels across the intervening region, and at last reaches the eye. What goes on between the eye and the brain is a question for the physiologists, and what finally happens when we "see" is a question for the psychologist. But without troubling ourselves about what happens after the light reaches the eye, it is evident that what the physicist has to say is destructive of the common-sense notion of "seeing." It makes no difference, in this matter, which of the possible theories we adopt as to the physical character of light, since all equally make it something utterly different from what we see. The data of sight, analyzed as much as possible, resolve themselves into coloured shapes. But the physical analogue of a colour is a periodic process of a certain frequency relative to the eye of the observer. The physical world, it seems natural to infer, is destitute of colour. Moreover, the correspondence between colours and their physical counterparts is peculiar: colours are qualities, which are static while they last, whereas their counterparts are periodic processes, which are in the medium between the eye and the object which we say we "see." What happens in the object itself, if it shines by its own light, is the sort of thing considered in Bohr's theory: a sudden jump of an electron from one orbit to another. This is very unlike a sensation of (say) red. And what looks to the eye like a continuous red surface is supposed to be really a volume whose apparent colour is due to the fact that some of the electrons in it are jumping in a certain way. When we say they are "jumping," we are saying something too pictorial. What we mean is that they possess an unknown quality called "energy," which is a known function of a certain number of small integers, and that one or more of these integers have suddenly changed their values. It may be claimed as a merit in such theories as Professor Lewis's, considered in the preceding chapter, that it makes the connection between this process and the eye rather less indirect than it appears on the undulatory theory. But even then the sort of sudden transition contemplated by Bohr is very unlike the perception of a red patch: it is prima facie quite dissimilar in structure, and unknown as regards its intrinsic properties.

I come now to the most serious of our questions: How is matter to be understood in modern physics? Educated common sense regards matter as the cause of sensations; broadly speaking, sensations private to one person are caused by the matter of that person's body—e.g. headaches and toothaches—while sensations common to several, or of a sort which is common to several in suitable circumstances, are attributed to causes external to the bodies of the persons experiencing the sensations. (I am not at present attempting to make these statements exact, but merely to interpret what common sense would reply if questioned.) We recognize the "same" piece of matter on different occasions by similarity in its qualities, though we admit that this is a rough-and-ready test which may lead us astray. We think, however, that, if we had observed closely and continuously, we could have distinguished between two similar objects by means of continuity in their perceived spatial relations. The three-card trick illustrates what I mean: if we watch the performer carefully, we can tell which is the card we saw a moment ago, by means of the spatio-temporal continuity of its positions. What common sense assumes may be expressed, in language foreign to common sense, by saying: A piece of matter is manifested by sensible qualities whose variations are continuous, and whose sensible spatial relations to other such continuous series of qualities are continuous functions of the time. In practice, the changes of sensible quality are often so slow as to be negligible, and this greatly facilitates the task of common sense in recognizing the "same" object on two different occasions.

On the common-sense level, there are difficulties in certain cases: a drop, in a sensibly homogeneous fluid in which there is a current, cannot be distinguished at a later moment from another drop which was near it at the earlier moment. Combustion also offers difficulties to common sense. Both these matters can, however, be dealt with on a common-sense basis. A small solid object floating in the water will show which way the water is moving, and the smoke shows, more or less, what happens to an object which is burned. The elaboration immediately suggested leads on naturally to elementary physics and chemistry, where it is still assumed, at least tacitly, that the objects concerned are of the same sort as sensible objects, but rather smaller. Often they can actually be seen under the microscope. Imaginatively, we continue to attribute this continuity with sensible objects to our scientific objects, our electrons and protons, thus concealing from ourselves the highly abstract character of our assertions. At moments, we realize this abstractness; but it does not make its due impression, because imagination reasserts itself as soon as we are off our guard.

In theoretical physics, what is an electron, and how do we decide whether two events belong to the history of the same electron? I am not asking how we decide in practice, but what is our theoretical definition. Ever since Minkowski, people have spoken of "world-lines," which are in fact the series of events constituting the history of one unit of matter but they have not always been as explicit as one could wish in telling us the criterion by which, in theory, it is decided that two events belong to one world-line. The test of identity between the parts of a world-line must obviously depend upon the laws of physics. These laws say that a material unit will move in such-and-such a way; inverting this statement, they say that what has moved in such-and-such a way is to count as one unit of matter. This is substantially the method pursued by Eddington. In Chapter IX. we considered the tensor which, as Eddington shows (§ 52), has the property of conservation—i.e. if the amount of it in any closed region varies, it does so by a flux across the boundaries. He identifies this quantity with matter, because of its property of conservation: "The quantity appearing in our theory is, on account of its property of conservation, now identified with matter, or rather with the mechanical abstraction of matter which comprises the measurable properties of mass, momentum and stress sufficing for all mechanical phenomena" (p. 146). And the above quantity, it will be remembered, is defined solely by means of the formula for small intervals. It will be admitted that matter, so defined, has become rather different from the matter in which common sense believes. If Dr Johnson had known Eddington's definition of matter, he might have been less satisfied with his practical refutation of Berkeley.

The exact form of Eddington's definition is not important for our present purposes; indeed, he himself somewhat generalizes it in a later passage. The point is that it is the sort of definition to which modern physics is bound to be led. Approximately, matter as conceived by common sense is conserved; wherever it appears to be destroyed or created, we can find ways of explaining away this appearance. Hence, as an ideal suggested by empirical facts, we adopt the view that matter is indestructible. We then turn round, and beginning from the formula for interval we construct a mathematical quantity which is indestructible. This, we say, we shall call "matter"; and no harm comes of our doing so. But whenever we take a step of this sort, we widen the gulf between mathematical physics and observation, and increase the problem of building a bridge between them. This problem has not been taken as seriously by physicists as it deserves to be taken. The reason is partly that it has arisen gradually. Physics and perception are like two people on opposite sides of a brook which slowly widens as they walk: at first it is easy to jump across, but imperceptibly it grows more difficult, and at last a vast labour is required to get from one side to the other. Another reason is that physiology and psychology, the two sciences concerned with perception, are less advanced than physics. The man accustomed to the beauty and exactitude of physics is liable to feel a kind of intellectual nausea when he finds himself among the uncertain and vague speculations of the less scientific sciences. He cannot be expected to admit that these sciences have a part to play in providing the premisses for his own precise mathematical deductions. Perhaps he is right, but prima facie physics, as an empirical study, derives its facts from perception, and cannot remain indifferent to any argument which throws doubt on the validity of perception, least of all when that argument is derived from physics itself. An argument designed to prove that a proposition is false is not invalidated by having that proposition among its premisses. Hence if modern physics invalidates perception as a source of knowledge about the external world, and yet depends upon perception, that is a valid argument against modern physics. I do not say that physics in fact has this defect, but I do say that a considerable labour of interpretation is necessary in order to show that it can be absolved in this respect. And it is because of the abstractness of physics, as developed by mathematicians, that this labour is required.

The inevitable specialism which is forced upon men of science by the very increase of scientific knowledge has had a good deal to do with obscuring this problem. Few men have been both physicists and physiologists. Helmholtz's researches concerning vision are a notable example of the combination of these studies, but there are not many others. Physiologists and psychologists are seldom well-informed in physics, and are apt to assume an old-fashioned physics which makes their problems look easier than they are. Moreover, even when the problem is realized, a man may not possess a mastery of the proper instrument for its solution—namely, mathematical logic. It is by means of mathematical logic that Dr Whitehead has been enabled to make his immense contribution to our problem. But, greatly as I admire his work, which I place far above anything else that has been written on the relation of abstract physics to the sensible world, I think there are points—and not unimportant points—where his methods break down for want of due attention to psychology and physiology. Moreover, there seem to be premisses in his construction which are derived rather from a metaphysic than from the actual needs of the problem. For these reasons, I venture to think that it is possible to obtain a solution less revolutionary than his, and somewhat simpler from a logical point of view. The solution, however, must wait until we have examined perception as a source of knowledge, which will be our topic in Part II. The metaphysic which reconciles the results of Part II. with the abstract physics which we have been considering in Part I. will be the subject of Part III.