The analysis of matter

COMMON sense starts with the notion that there is matter where we can get sensations of touch, but not elsewhere. Then it gets puzzled by wind, breath, clouds, etc., whence it is led to the conception of "spirit"—I speak etymologically. After "spirit" has been replaced by "gas," there is a further stage, that of the æther. Assuming the continuity of physical processes, there must be things happening between the earth and the sun when light travels from the sun to the earth; assuming the mediæval metaphysic of "substance," as all physicists did until recently, what is happening between the earth and the sun must be happening "in" or "to" a substance, which is called the æther.

Apart from metaphysical interpretations, what we may be said to know (using this word somewhat liberally) is that processes occur where there is no gross matter, and that these processes proceed, at least approximately, in accordance with Maxwell's equations. There does not seem any necessity to interpret these processes in terms of substance; indeed, I shall argue that processes associated with gross matter should also be interpreted so as not to involve substance. There must, however, remain a difference, expressible in physical terms, between regions where there is matter and other regions. In fact, we know the difference. The law of gravitation is different, and the laws of electromagnetism suffer a discontinuity when we reach the surface of an electron or proton. These differences, however, are not of a metaphysical kind. To the philosopher, the difference between "matter" and "empty space" is, I believe, merely a difference as to the causal laws governing successions of events, not a difference expressible as that between the presence or absence of substance, or as that between one kind of substance and another.

Physics, as such, should be satisfied when it has ascertained the equations according to which a process takes place, with just enough interpretation to know what experimental evidence confirms or confutes the equations. It is not necessary to the physicist to speculate as to the concrete character of the processes with which he deals, though hypotheses (false as well as true) on this subject may sometimes be a help to further valid generalizations. For the present, we are confining ourselves to the standpoint of physics. Whether anything further can be known or fruitfully conjectured is a matter which we shall discuss at a later stage. We want, therefore, to consider the difference in physical formulæ which is described as that between the presence and absence of matter, and also to consider briefly the difficulties as to the interchanges of energy between matter and empty space. I say "empty space" or "æther" indifferently; the difference seems to be merely one of words.

One way of approaching this subject is through the connection of mass with energy.[31] In elementary dynamics, the two are quite distinct, but nowadays they have become amalgamated. There axe two kinds of mass involved in physics, of which one may be called the "invariant" mass, the other the "relative" mass. The latter is the mass obtained by measurement, when the body concerned may be moving relatively to the observer; the former is the mass obtained when the body is at rest relatively to the observer. If we call the invariant mass and the relative mass , then, taking the velocity of light as unity, if is the velocity of the body relative to the observer, we have: Thus increases as increases; if is the velocity of light, becomes infinite if is finite. In fact, the invariant mass of light is zero, and its relative mass is finite. Wherever energy is associated with matter, there is a finite invariant mass ; but where energy is in "empty space", is zero. This might be regarded as a definition of the difference between matter and empty space.

It will be seen that, if is small, so that and higher powers can be neglected, the above equation becomes approximately Now is the kinetic energy. Thus the change of with changes of motion is the same as the change of the kinetic energy. But energy is fixed only to the extent of its changes, not in its absolute amount. Hence may be identified with the energy. And this suggests further that the usual definition of energy is only an approximation, which holds when is small. The accurate formula for energy is —i.e. accurately the same as .

The conservation of energy is the conservation of , not of ; also is approximately conserved, but not exactly. E.g. there is a loss of when four protons and two electrons combine to form a helium nucleus. The term "invariant" refers to changes of co-ordinates, not to constancy throughout time.

It is necessary to say something about the difficulties of reconciling the laws governing the propagation of light with those governing interchanges of energy between light and atoms. On this subject the present position of physics is one of perplexity, aptly summarized by Dr Jeans in Atomicity and Quanta (Cambridge, 1926) and by Dr C. D. Ellis in Nature, June 26, 1926, pp. 895-7. The wave theory of light accounts adequately for all phenomena in which only light is concerned, such as interference and diffraction; but it fails to account for quantum phenomena such as the photo-electric effect (see Chapter IV.). On the other hand, theories which account for the quantum phenomena seem unable to account for the very things which the wave theory explains perfectly.

Some of the difficulties of the light-quantum theory are set forth as follows by Dr Jeans (op. cit. pp. 29, 30):

The difficulties of the wave-theory, on the other hand, are illustrated by Dr Ellis as follows:

After setting forth the difficulties encountered by this theory in regard to interference and diffraction, Dr Ellis proceeds to the very interesting suggestion made by Professor G. N. Lewis in Nature, February 13, 1926, p. 236. "It is a striking fact," says Dr Ellis, summarizing this suggestion, "that while all the theories are directed towards explaining the propagation of light, one theory suggesting that it occurs in the form of waves, the other in the form of corpuscles, yet light has never been observed in empty space. It is quite impossible to observe light in the course of propagation; the only events that can ever be detected are the emission and absorption of light. Until there is some atom to absorb the radiation we must be unaware of its existence. In other words, the difficulty of explaining the propagation of light may be because we are endeavouring to explain something about which we have no experimental evidence. It might be more correct to interpret the experimental facts quite directly and to say that one atom can transfer energy to another atom although they may be far apart, in a manner analogous to the transference of energy between two atoms which collide."

Professor Lewis's theory suggests that we should take seriously the fact that the interval between two parts of a light-ray is zero, so that its point of departure and its point of arrival may be regarded as, in some sense, in contact. In a passage quoted by Dr Ellis, he says:

In a later letter to Nature (December 18, 1926), Professor Lewis suggests that light is carried by corpuscles of a new sort, which he calls "photons." He supposes that, when light radiates, what happens is that a photon travels; but at other times the photon is a structural element within an atom. The photon, he says, "is not light, but plays an essential part in every process of radiation." He assigns to the photon the following properties: "(1) In any isolated system the total number of photons is constant. (2) All radiant energy is carried by photons, the only difference between the radiation from a wireless station and from an X-ray tube being that the former emits a vastly greater number of photons, each carrying a very much smaller amount of energy. (3) All photons are intrinsically identical.... (4) The energy of an isolated photon, divided by the Planck constant, gives the frequency of the photon.... (5) All photons are alike in one property which has the dimensions of action or of angular momentum, and is invariant to a relativity transformation. (6) The condition that the frequency of a photon emitted by a certain system be equal to some physical frequency existing within that system, is not in general fulfilled, but comes nearer to fulfilment the lower the frequency is." Professor Lewis promises to deal with difficulties in the way of his hypothesis on a future occasion.

Professor Lewis's view is perhaps less radical than the view which it suggests—namely, that nothing whatever happens between the emission of light by one atom and its absorption by another. Whether this view is Professor Lewis's or not, it deserves to be considered, for although it is revolutionary, it may well prove to be right. If so, "empty space" is practically abolished. There will be need of a considerable labour if physics is to be re-written in accordance with this theory, but what is said about the necessary absence of evidence concerning light in transit is a powerful consideration. It is common in science to find hypotheses which, from a theoretical point of view, are unnecessarily complicated, because people cannot sufficiently divest themselves of common-sense prejudices. Why should we suppose that anything at all happens between the emission of light and its absorption? One might be inclined to attach weight to the fact that light travels with a certain velocity. But relativity has made this argument less convincing than it once was. Everything that has to do with the velocity of light is capable of being interpreted in a "Pickwickian" sense, and in any case our prejudices must be shocked. It is of course premature to adopt such an hypothesis definitively, and I shall continue to suppose that light does really travel across an intervening region. But it will be wise to remember the possibility, and to bear in mind the great changes in our imaginative picture of the world that are compatible with our existing physical knowledge.

The picture presented by this development of Professor Lewis's suggestion would be something like this: the world contains bits of matter (electrons and protons) possessing various amounts of energy. Sometimes energy is transferred from one of these bits of matter to another; usually this process has been thought to be casual, like the wandering of thistledown, but it is found to be more like the parcels post, in the sense that the energy has a definite destination. It is now suggested that there is no postman, because, if there were, he would be as magical as Santa Claus; the alternative is to suppose that the energy passes immediately from one piece of matter to another. It is true that, by the clock, there is a lapse of time between the departure of the energy from the source and its arrival at its destination. But there is no interval in the relativity sense, and the lapse of time will vary according to the co-ordinate system employed—i.e. according to the way in which the clock is moving. I do not know how the view we are considering will account for the time taken by a double journey to a reflector and back, which is not purely conventional. Nor do I know what will happen to the conservation of energy if light cannot be radiated into the void. This latter argument, however, is not serious, since light which never hits a piece of matter is in any case purely hypothetical. I am not sure, either, that the theory is intended to be as radical as I have suggested; perhaps it is only meant that light never starts on a journey without having a destination in view. In this form, however, the theory would seem scarcely credible: we should have to suppose that matter could exercise a mysterious attraction from a distance, which would undo the gain derived from Einstein's theory of gravitation. Perhaps the theory may have gained undue plausibility from a belief that the whole geometry of space-time depended upon interval, whereas in fact there is a space-time order which is not derivable from interval, and which, as presupposed in relativity theory, does not regard as contiguous parts of a light ray which would ordinarily be regarded as widely separated.[32] Perhaps it may be possible to avoid these difficulties, but, if so, a very great theoretical reconstruction will be necessary. Meanwhile it must be regarded as still possible that some less revolutionary theory may solve the difficulties connected with the interchange of energy between light and bodies.

There are three papers by Einstein which discuss the possibility of obtaining quantum laws as consequences of a modified relativity theory.[33] These papers do not arrive at any definite conclusion confidently asserted; but they suffice to show that the problem of combining quantum laws with those of gravitational and electromagnetic fields is not a hopeless one, a view which is strengthened by Mr L. V. King's theory alluded to above (Chapter IV.). So long as it is not known to be hopeless, it is perhaps rash to fly to heroic solutions of the problem. And it is as yet by no means universally admitted that the wave-theory of light is inadequate in its own domain; Dr Jeans (loc. cit.), for example, regards the hypothesis of light-quanta as unnecessary for reasons which demand serious consideration. We must therefore await further knowledge before venturing upon a definite opinion.