The Analysis of Matter

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,[Pg 124] 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): "If, however, radiation is to be compared to rifle bullets, we know both the number and size of these bullets. We know, for instance, how much energy there is in a cubic centimetre of bright sunlight, and if this energy is the aggregate of the energies of individual quanta, we know the energy of each quantum (since we know the frequency of the light) and so can calculate the number of quanta in the cubic centimetre. The number is found to be about ten millions. By a similar calculation it is found that the light from a sixth magnitude star comprises only about one quantum per cubic metre, and the light from a sixteenth magnitude star, only about one quantum per ten thousand cubic metres. Thus if light travels in indivisible quanta like bullets, the quanta from a sixteenth magnitude star can only enter a terrestrial telescope at comparatively rare intervals, and it will be exceedingly rare for two or more quanta to be inside the telescope at the same time. A telescope of double the aperture ought to trap the quanta four times as frequently, but there should be no other difference. This, as Lorentz pointed out in 1906, is quite at variance with our everyday experience. When the light of a star passes through a telescope and impresses an image on a photographic plate, this image is not confined to a single molecule or to a close cluster of molecules as it would be if individual quanta left their marks like bullets on a target. An elaborate and extensive diffraction pattern is formed; the intensity of the pattern depends on the number of quanta, but its design depends on the diameter and also on the shape of the object-glass. Moreover, the design does not bear any resemblance whatever to the 'trial and error' design which is observed on a target battered by bullets. It seems impossible to reconcile this with the hypothesis that quanta travel like[Pg 125] bullets directly from one atom of the star to one molecule of the photographic plate." The difficulties of the wave-theory, on the other hand, are illustrated by Dr Ellis as follows: "To take a definite case, suppose X-rays are incident on a plate of some material, then it is found that electrons are ejected from the plate with considerable velocities. The number of the electrons depends on the intensity of the X-rays and diminishes in the usual way as the plate is moved farther from the source of X-rays. The velocity or energy of each electron, however, does not vary, but depends only on the frequency of the X-rays. The electrons are found to have the same energy whether the material from which they come is close to the X-ray bulb or whether it is removed away to any distance. "This is a result which is quite incompatible with the ordinary wave-theory of radiation, because as the distance from the source increases the radiation spreading out on all sides becomes weaker and weaker, the electric forces in the wave-front diminishing as the inverse square of the distance. The experimental result that the photo-electron always picks up the same amount of energy from the radiation could only be accounted for by giving it the power either to collect energy from a large volume or to collect energy for a long time. Both of these assumptions are unworkable, and the only conclusion is that the radiated energy must be localized in small bundles. "This is the basis of the light-quantum theory. Light of frequency is considered to consist of small bundles or quanta of energy all identical and of magnitude , being Planck's constant. These quanta travel through space, being unaffected by each other, and preserving their own individuality until they make a suitable collision with an atom." 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[Pg 126] 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: "I shall make the contrary assumption that an atom never emits light except to another atom, and that in this process, which may rather be called a transmission than an emission, the atom which loses energy and the atom which gains energy play co-ordinate and symmetrical parts." 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[Pg 127] 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[Pg 128] 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