Matter and Light. The New Physics (1937), ch. III: Light and Radiation
Among old and new perspectives in the Theory of Light, we present here chapter III of Louis de Broglie’s pioneering work Matière et Lumière, originally published in 1937. In the first section of this excerpt, the French scientist offers a nice historical survey of the theory of light, starting from 17th century Optics, which dates back to the works carried out by Descartes, Newton, Snell, Fermat, Roemer. The majority of these authors bent towards a corpuscular understanding of light, that is, light as matter; while Huyghens, and later Fresnel, put the basis for a wave theory of light. However, wave theory was originally introduced endorsing the idea that “waves” were oscillations occurring into a pervasive medium called ether. It was Maxwell who, based on the previous work by Faraday, first suggested a field theory of light, which gave rise to his electromagnetic field equations. At the down of the 20th Century, Planck’s results on the quantum nature of energy opened the door to contemporary quantum mechanics, which rules the interactions between energy and matter, and is able to interpret light as both matter and energy.
In the second section of de Broglie’s text, the paradoxes associated to wave and matter understanding of light are reviewed, emphasizing their importance to achieve a more comprehensive idea of what light is. Here are de Broglie’s words: “It is here, more clearly than perhaps anywhere else, that the century-old struggle between the corpuscular and the undulatory conceptions of Light has shown how contradictory hypotheses, both based on experimental facts, can both contain a part of the truth, and how the advance of Science has on many occasions been effected through the synthesis of opposed points of view.” After a history four centuries long, we then arrive to contemporary notion of “photon” as quantum of light. High energy experiments in 21th Century particle accelerators are expected to write the next pages of this exciting tale. As de Broglie concludes, “the Theory of Light, then, has a long and striking history; and a fine career lies before it.
The history of modern optics begins in the seventeenth century. Of course this does not mean that the scientists of the seventeenth century had no forerunners in the sphere of optics. In the evolution of the human mind it is wrong to make too clean a cut, and there can be no doubt that no step was ever taken in the advance of Science which was not based on the work of earlier periods. Setting aside, however, certain questions of priority which could be resolved only by specialist studies, one may fairly say that the real advancement of modern optics dates from the first half of the seventeenth century and may largely be identified with the great name of René Descartes.
Some time before Descartes, Snell had experimentally dis covered the ratio of the angles in refraction; but it is to Descartes that the credit belongs for having been the first to state in exact terms the system of laws of reflection and refraction, to which, at any rate in France, we attach his name. To interpret these laws Descartes adopted the corpuscular conception of Light, and assumed that these corpuscles meet with a resistance which deflects their trajectory, whenever they enter Matter which is dense in the optical sense.
Rather earlier in the seventeenth century Pierre de Fermat, a magistrate and a geometrician, had shown that Descartes' laws could be deduced from a Principle of Minimum Time, to which he attributed a teleological significance. According to this well-known Principle, the path of a ray of light passing through two given points A and B is always such that the time taken by the ray in passing from A to B is less than that which would correspond to any other path, however closely similar to that of the ray.
About the same time experiments met with new successes. While Hooke and Grimaldi observed the colours of thin metallic films without making any attempt at interpreting them, Newton discovered in 1666 the spectral decomposition of Light by the prism, and the Danish astronomer Roemer, observing the occultations of the satellites of Jupiter, inferred in 1676 that the velocity of Light in empty space must have a finite value. Pursuing a different method, Bartholin discovered double refraction in spar crystals. All these experimental discoveries provided a powerful impulse to theoretical speculation. Christian Huyghens (as I have already remarked) first of all advanced the Wave Theory in a definite form by assuming that there is an ether in which light waves can move. With the help of the Principle which today bears his name, he showed that the Wave Theory can explain the phenomena of reflection and refraction, and also succeeded in finding an explanation for double refraction. But, admirable as were his labours, they did not command universal assent. They suffered, moreover, from a serious lack: they offered no explanation for the fundamental fact that Light travels in a straight line. Newton for his part adopted the corpuscular view, and showed the advantages it possessed for a dynamic interpretation of the propagation of Light in a straight line, of reflection and of refraction. At the same time he was already acquainted with certain interference phenomena (Newton's rings) and accordingly, by a bold stroke of intuition, tried to establish an association between waves and corpuscles—the motion of a projectile and the propagation of a periodicity. But this theory of "Fits of easy reflection and easy transmission" was too far ahead of his time; it remained embryonic and underwent no further development.
The majority of eighteenth-century scientists followed Newton and adopted the corpuscular theory. At the same time there were some notable exceptions, among whom Euler may be mentioned.
We have seen that at the beginning of the nineteenth century there came some fresh experimental discoveries to add an impetus to the more sedate pace of the development of optics. In 1801 Young made some accurate observations of interference phenomena, and enunciated their ruling principle; but his work was rather of an empirical nature, and at first little notice was taken of it. About the same time Malus observed certain polarization phenomena, but without entirely clearing up their obscurities. In this manner, however, the way had been prepared for a new advance in theory, an advance due to the genius of Augustin Fresnel (1788-1827), who rejected the corpuscular Theory which at this stage was still being defended with talent and authority by Laplace and Biot. As I have previously observed, Fresnel reverted to Huyghens Wave Theory, which he completed by adding an interpretation of the motion of Light in a straight line, and gave an account of interference and diffraction phenomena of which he also made an extensive experimental investigation. The opposition school, led by Poisson, was worsted when demonstration came to prove the correctness of even the most paradoxical predictions of the Wave Theory. Some time later Fresnel adopted a suggestion made by Young and introduced the principle of the transversality and the polarization of light-waves, being in this way enabled to develop his brilliant theory of the intensity of reflection and of refraction. The period following Fresnel’s death was characterized by the gradual triumph of his ideas. Fizeau’s and Foucault’s experiments (1850), which showed by direct measurement that the velocity of Light in water is less than in empty space, seemed to provide a crucial proof of the Wave Theory's correctness.
But though triumphant in the experimental sphere, this Theory met the greatest difficulties in the theoretical domain when it sought to become a full and complete mechanical theory of ether vibrations. Despite the efforts made by many able theorists — Poisson, Green, MacCullagh, F. Neumann and, later, Lord Kelvin, Carl Neumann, Lord Raylegh and Kirchhoff — it remained impossible to establish definitely a coherent theory of ether vibrations. It was under a wholly different form, and one implying a much more far-reaching surrender of any kind of visual representation, that the Wave Theory was developed about the year 1870, about which time Clerk Maxwell created the electromagnetic Theory, a more exact form of ideas originally due to Faraday. Maxwell's Theory is based entirely on the rather abstract concept of the electromagnetic field; and all attempts to reduce this concept to that of a certain state of a hypothetical medium (the electromagnetic ether) have had to be finally abandoned. Maxwell showed that Light can be embraced within the general category of electromagnetic disturbances—a brilliant conception by which he was enabled to subsume the whole of optics under the electromagnetic Theory. From this new point of view—a more formal one than that of Fresnel—the fact that Light is of the nature of a wave finds expression in the fact that the electromagnetic fields of the light wave are certain periodic functions of the co-ordinates of Time and Space.
Any really complete theory of optical phenomena, however, assumes a knowledge of the laws of interaction between Light and Matter, since it is impossible to study Light otherwise than through the effects it produces on Matter. A comprehensive theory of this kind had been the goal pursued by the champions of an elastic ether; but it did not become a reality until H. A. Lorentz developed his electron Theory. By introducing the concept of the electron, and the Law of the interaction between the electromagnetic field and electrons, Lorentz and his rivals were enabled to investigate the different ways in which Matter reacts when an electromagnetic light-wave passes through it. The electron Theory, by stating in more precise terms the meaning, and by substantially extending the scope, of the fragmentary results reached by earlier theories, succeeded in finding a place for the formulae of dispersion, the law of the absorption of Light by absorbing bodies, those of the various magneto-optic and electro-optic effects, etc. Its success in interpreting, too, the normal Zeeman effect is familiar. But fruitful as was this attempt to analyse the interactions between Matter and radiation, it encountered totally unforeseen difficulties when it came to the details of these phenomena. On entering the atomic domain, the electromagnetic Theory, together with Lorentz's complementary electron Theory, encountered the quanta: the result was that the very nature of Light once more became matter of debate.
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The electromagnetic Theory, still further, and the electron theory of the interactions between Matter and radiation, lead to incorrect results regarding thermal equilibrium. For they yield a law of spectral distribution of the energy of radiation in thermal equilibrium (Rayleigh's Law) which contradicts the experimental results for high frequencies and which, in a sense, is absurd, since it leads to an infinite value for the total density of energy. These perplexing consequences of the classical Theory were avoided by Planck through the introduction of the entirely novel idea that the only way in which Matter can emit radiant energy is by quanta equal to hν where ν is the frequency emitted and h a new universal constant. It followed from Planck's hypothesis that Matter could lose energy only in finite quantities. This did not necessarily mean that a ray, once given out, must have a discontinuous structure, for energy only in finite quantities. This did not necessarily mean that a ray, once given out, must have a discontinuous structure, for it was possible to develop the theory in two different ways as far as the absorption of radiation by Matter was concerned. The first point of view—a more straightforward one, which eventually proved the more acceptable—consisted in assuming that the elementary constituents of Matter can only assume certain quantized states of energy, whence it follows that in absorption, as well as in emission, the exchange of energy between Matter and radiation occurs in quanta.
1. A Survey of the History of Optics
But this necessarily implied that radiation has a discontinuous structure. Shrinking from this disturbing consequence of his own ideas, however, Planck persisted in making every effort to work out a different and less radical form of Quantum Theory, in which emission alone would be discontinuous, while absorption would remain continuous. Matter would then be capable of accumulating continuously part of the radiant energy falling on it, but it would be able to emit it only discontinuously and in finite quantities.
The aim of Planck's efforts is readily seen: he wished to preserve the continuity of radiation, because this principle alone seemed compatible with the Wave Theory which was supported by so many successes. But despite all the ingenuity brought by Planck to the development of this second version of the Quantum Theory, the latter was disproved by the eventual advance of our knowledge. An essential stage in this advance was the discovery of the photo-electric effect, and its interpretation by Einstein. The facts have been outlined already; and Einstein showed that they can be explained only by a certain reversion to the corpuscular view of Light, in which any ray of frequency ν is considered as being formed of corpuscles containing energy equivalent to hν. This is the theory of light-quanta or photons. Supported first of all by investigation of the photo-electric effect, and later by various ideas developed by Lorentz and Einstein—the statistical equilibrium between the molecules of a gas and the surrounding radiation in thermal equilibrium, fluctuations of energy in black body radiation —this view demonstrated the need for accepting the Quantum Theory in its first and more radical form.
Actually it was the Quantum Theory in its first version which prevailed with the triumph of Bohr's Atomic Theory.—According to Bohr an atom possesses certain "stationary states" in which it emits no radiation. When it passes from one stationary state to another (the quantum transition), its energy suddenly varies by a finite quantity. If the transition is accompanied by a diminution of energy, the atom emits a finite quantity of energy in the form of a quantum hν, such that the frequency of the ray emitted is equal to the quotient of the diminution of the atom's energy, when the transition occurs, by Planck's constant, h. This is Bohr's Frequency Law. But under the influence of a ray of frequency ν the atom can also undergo the reverse change, and pass from one stationary state to another such state having a higher energy the result of absorbing a quantum hν provided that the difference between the energies of the respective stationary states is exactly equal to hν.
Such a view of the emission and absorption of radiation by Matter is obviously in complete contradiction with the electromagnetic Theory evolved by Maxwell and Lorentz. According to the latter a planetary atom, as envisaged by Rutherford and Bohr, ought to be emitting radiation continually, its frequency being continuously variable. Like classical Mechanics, classical electromagnetism also is proved to be incorrect in the microscopic sphere, though there should be a certain compromise on passing from the microscopic to the macroscopic—as is the case with Mechanics. Such was the idea clearly formulated by Bohr in 1916— a few years after the development of his atomic Theory—in the form of his “Correspondence Principle.” Bohr begins by pointing out that there are very many quantum numbers for which the difference between the energies of the consecutive stationary-states tends to become infinitely small, so that there is a tendency for continuity to reappear. The frequencies predicted by the Quantum Theory in such cases accordingly tend to agree with those of the classical Theory. He accordingly assumes that the intensities of emission and of polarization, as calculated by the classical Theory, should remain correct also for the Quantum Theory in this sphere; then, by a bold extrapolation, he assumes that even for the smaller quantum numbers the indications furnished by the classical Theory may be used to a certain extent. Bohr's Correspondence Principle proved extremely useful some fifteen years ago in enabling intensities and polarizations to be predicted within the sphere of the Quantum Theory as it was then formulated. More particularly, it enabled selection rules to be stated, indicating which among the spectral lines predicted by Bohr's "Frequency Law have an intensity above zero, and therefore are really capable of observation.
During recent years, as I have repeatedly observed, there has been a development of Wave Mechanics. We now regard radiation from two points of view—as corpuscular and also as undulatory; and this view has helped in the formulation of the new Mechanics, whose essential idea is to assume that Matter also has the same double wave-corpuscle character. Optics has thus served as a guide in the erection of the structure of Wave Mechanics. A very curious thing, however, has happened: Wave Mechanics—at least in its non-relativistic form—very soon reached a high degree of perfection, while the dual Theory of Light—the photon Theory and the Fresnel wave Theory—lagged far behind. The chief reason for this is that any theory of Light must necessarily be relativistic, because the corrections which Relativity introduces in the dynamics of a corpuscle increase in importance as the velocity of the corpuscle approximates to that of Light. The theories advanced during recent years in order to quantize the electromagnetic field, so as to find in it a place for photons (Dirac's Theory and the Quantum Theory of the Field enunciated by Heisenberg and Pauli), are not wholly satisfactory and seem to be rather provisional. To grapple with the problems connected with the interactions between Matter and Light, physicists were usually content to employ an extension of the Correspondence Principle; and indeed the new Mechanics lends itself to a more precise statement of this Principle than those sanctioned by the older Quantum Theory. To reach this end a combination is effected between the ideas of classical electro-magnetism and the magnitudes of Wave Mechanics. It is certainly a somewhat awkward method: it does not account for the dual character of radiation, and it leaves the concept of the photon rather obscure. At the same time it has proved possible in this way to obtain interesting results and to form a theoretical schema of a certain number of the phenomena connected with the inter action between Matter and Light—a schema which, if probably provisional, is undoubtedly of practical use.
2. Old ways and new perspectives in the theory of light
The story of the different theories of Light is one of the most exciting parts of the history of Physics. It is here, more clearly than perhaps anywhere else, that the century-old struggle between the corpuscular and the undulatory conceptions of Light has shown how contradictory hypotheses, both based on experimental facts, can both contain a part of the truth, and how the advance of Science has on many occasions been effected through the synthesis of opposed points of view. Nor has the long story yet come to an end; for at the present moment the Theory of Light, which at one time played so large a part in inspiring the modern dualist theories of Matter, is lagging behind these theories, and the future no doubt holds further shocks and further developments in store for it.
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The corpuscular Theory of Light was based on certain simple facts familiar practically throughout history: the propagation of Light in a straight line, and reflection. The interpretation given by this Theory is direct and appeals to the eye, and many of the greatest scientists, headed by Newton himself, have supported it during the course of centuries.
Nevertheless, since Newton's time the corpuscular Theory has always been faced by a severe obstacle in the shape of the phenomena of interference and diffraction. Newton himself had dis covered the phenomenon of the coloured rings which are named after him, and to interpret it had developed his theory of "Fits of easy reflection and easy transmission" which, regarded for long as a complicated and hybrid conception, would today be considered rather as the anticipation by a man of genius of current theories. Actually, the experimental research on diffraction and interference at the beginning of last century by Fresnel and Young had to be carried out, and the theoretical labours to which we have already found the name of the former to be attached had to be completed, before the Wave Theory triumphed over its rival— a state of affairs which was destined to endure for a long period. Fresnel (to repeat) reverted to and perfected the arguments previously outlined as having been used by Christian Huyghens, the seventeenth-century champion of the Wave Theory; and as has already been observed, he succeeded in showing that this theory explains the propagation of Light in a straight line, reflection, refraction in its various forms, diffraction and the interference phenomena. It is true that for the first two the Wave Theory gives a less simple and direct account than does the corpuscular; but when we come to refraction the former has the better of it, and for interference and diffraction it is the only theory to provide an adequate interpretation. But Fresnel—a brilliant physicist— gave us additional knowledge of the utmost value about Light in the phenomena of polarization, and thus revealed an aspect of fundamental symmetry appertaining to light-waves. For a light wave must be defined, not only by a scalar "light variable," but also by an oscillating vector, which in the simple case of a plane monochromatic wave in a vacuum, or in an isotropic medium, is in the wave-front normal to the direction of propagation. On the basis of the polarization of Light Fresnel constructed the theory of the intensity of reflection at the surface of separation of two substances and also that of the propagation of Light in anisotropic media. Experiments have brilliantly confirmed the theory, and it is to be found with hardly a change in every modern work.
In elaborating his Wave Theory Fresnel—to repeat my earlier observations—had made use of the idea of an elastic ether of such a kind as to be able to transmit only transverse vibrations. In this way it was possible to obtain results completely agreeing with experiment over a wide field. But there were also difficulties and contradictions; still further, there was no apparent connection between luminous phenomena and those of electromagnetism, in which research was at the time advancing rapidly. Faraday's discovery in 1850 of the first magneto-optic phenomenon, however— the rotation of the plane of polarization of Light passing through a substance in which a uniform magnetic field prevails—drew attention to one necessary connection between these two groups of phenomena. Next came Clerk Maxwell, who formulated that admirable synthesis, the Electromagnetic Theory of Light. Here the luminous vibration is represented by the oscillating electric vector propagated in waves. This vector is accompanied by a second, the magnetic vector, which also oscillates, and which in the simple case of a plane monochromatic wave in empty space is equal and perpendicular to the first, both being in the wave-front normal to the direction of propagation. The velocity of propagation in a vacuum is equal to the constant c in Maxwell's equations, i.e. to the ratio of the electromagnetic unit of charge to the electro static unit. All this is familiar and agrees with experiment. In this way Maxwell has given to Light an electromagnetic structure which it is impossible to neglect.
Unhappily, the fine synthesis effected by Maxwell was challenged by the sudden discovery of phenomena where a structure of Light differing completely from that of the electromagnetic wave seemed to manifest itself. The first of these was the photo-electric effect. Its essential characteristic is that Light of frequency ν seems able to transfer its energy to Matter only in finite quantities proportional to the frequency. We recall that by a brilliant intuition Einstein realized (1905 and onwards) that this experimental fact meant the necessity of reverting, to some extent, to the corpuscular Theory of Light. He assumed that Light of frequency ν is divided into corpuscles of energy W = hν and he was thus led immediately to the experimental law of the photo-electric effect, which establishes a connection between the kinetic energy of the electrons photo-electrically expelled, and the frequency of the incident radiation.
What does this new corpuscular Theory, considered apart from any idea of a wave, give us? It obviously yields an immediate and quasi-visual interpretation of the rectilinear propagation of Light and of reflection, and it can be developed a little further if we apply Relativity dynamics to the photon—which is clearly necessary for a corpuscle moving with velocity c. Actually, if we apply Relativity dynamics to the photon we obtain a satisfactory explanation of radiation pressure and of the various kinds of Doppler effect. Finally, the new corpuscular Theory won a brilliant success on the day when the Compton effect was discovered. This consists of a lowering of frequency by the scattering of X-rays by Matter, a change in frequency which is easily interpreted by the assumption that the incident photon is scattered by its encounter with an electron originally at rest. By this encounter energy and momentum are transferred from the photon to the electron, with the result that the energy 'and hence the frequency of the photon is lowered, provided that we assume that W = hν. Thus the theory, based on the idea of the photon, accounts quantitatively for the observed effects.
Yet despite the success of the theory of photons in the interpretation of a considerable number of phenomena, a radically corpuscular theory of radiation cannot be maintained, because it cannot account for the numerous and exactly observed experiments where we find diffraction and interference phenomena. The entire body of research carried out by Fresnel and his followers prevents us from returning to a pure "theory of emission."
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Such was the deadlock reached by the Theory of Light when Wave Mechanics arose; and its fundamental idea can be represented in a whimsical form as follows: the Theory of Light was suffering from a strange disease, which manifested itself in the rival dualistic forms of Fresnel's and Maxwell's waves on the one hand and of photons on the other! To alleviate the situation, then, the desperate remedy might be tried of inoculating the Theory of Matter, immune thus far, with the same disease! Actually, however, there was a substantial reason for such a course; for the fact was that the Theory of Matter too had been manifesting alarming symptoms for a number of years. The fact that it had proved necessary to quantize the motion of particles of Matter, which had first become evident in the theory of black body radiation— a method which had achieved a striking success in Bohr's theory of the atom—showed that the existence of the quantum of action prevented us from extending the concepts and equations of classical Mechanics to the atomic field. The presence of integers in quantum formulae endowed the latter with a certain similarity to the formulae of interference in the Wave Theory; and the analogy between the Principle of Least Action—the keystone of classical Mechanics—and Fermat's Principle—the keystone of geometrical optics—suggested that classical Mechanics might be an approximate form of a more general Wave Mechanics, standing with regard to the latter in the same relation as that in which geometrical optics stands to wave optics. In this way arose the notion of extending to Matter the dualism of corpuscles and waves which had proved necessary in the case of Light. In Wave Mechanics, accordingly, it was assumed that a complete description of the material units could not be effected by operating with corpuscles alone, and that this idea had to be supplemented by that of waves, the correspondence between the dynamic description of the corpuscle in uniform motion and the frequency and wave-length of the associated wave being based on the fundamental relations which include the theory of photons as one particular case. In this way a satis factory synthesis became apparent, in which the corpuscular and the wave aspect—two aspects interconnected by the same general relations—must be taken into account simultaneously, both for Light and for Matter. So satisfactory is this synthesis, and so completely does it form the foundation of Wave Mechanics, that it must be maintained at all costs. We shall., however, shortly see the difficulties met with as soon as we try to express in exact terms the affiliation between the photon and the ultimate constituents of Matter; but I am none the less convinced that it would be an aberration to attempt the erection of a fresh barrier between the Theory of Matter and that of Light.
I must here add the fact that the fundamental idea of Wave Mechanics received complete experimental confirmation by the discovery of the diffraction by crystals, first of electrons, and later of protons and heavy nuclei.
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In revealing the undulatory aspect of the constituents of matter, particularly of electrons, Wave Mechanics undoubtedly brought the two Theories—of Matter and of Light—closer together. The question still remains, however, whether it brought about a complete synthesis—a single Theory applicable to both Matter and radiation. In its original form, certainly, it did not. In the first -place, this form rests on non-relativistic equations. Primitive Wave Mechanics, in other words, is a development of Newtonian Mechanics, not of Einsteinian. It is indubitably applicable only to material particles whose velocity is much lower than c, and hence, with equal certainty, it cannot be applied to the photon. This alone shows that if we wish to find a single Theory to embrace both Matter and Light, we must generalize the original Wave Mechanics in the relativistic sense.
Another difference between the original Wave Mechanics and the Theory of Light is the fact that the former contains no element of symmetry corresponding to polarization. Here again one feels that, to reach a single Theory of Matter and Light, some quantity corresponding to polarization must be introduced, which is absent from the original form of Wave Mechanics.
Finally, I must insist on the unique part played by the photo electric effect in the Theory of Light. Material corpuscles can exchange energy and momentum by interaction; but though they can thus lose their entire kinetic energy, they invariably conserve their mass-energy, and never disappear. In the photo-electric effect, on the other hand, the photon loses its entire energy on coming into contact with Matter, and is annihilated. The interchange of energy and momentum between the photon and Matter in such phenomena as the Compton effect, or reflection by a rotating mirror, is quite similar to the exchanges in collisions between material corpuscles; but the photo-electric effect is wholly different, and the difference cannot be over-emphasized. Now it must be noted that whenever an interference or diffraction phenomenon is observed, the observation is effected through the medium of a photo-electric effect, which takes place in the sensitive layers of the retina in the case of direct observation, or in a film of gelatine in the case of photographic observation. If we wish to interpret these phenomena in terms of the interferences occurring in an electromagnetic field connected with the photon, we must establish a close connection between the transition between states of the photon corresponding to the photo-electric effect—a transition which may be compared to an annihilation of the photon—and the electromagnetic field.
Another obstacle must finally be mentioned which seems to stand in the way of an amalgamation of the theories of Matter and Light. This obstacle consists in the fact that the elementary corpuscles of Matter—electrons, for example—follow Fermi-Dirac statistics when they form a large group, whereas photons, when they form such a group, as in black body radiation, follow Bose-Einstein statistics. The mention of this difficulty, to which I shall revert later, must here suffice.
Unable thus to embrace Matter and Light within one single Theory, what has Wave Mechanics done to deal with the problems of the interaction between Matter and radiation? It has had recourse to a hybrid method, relying on the Correspondence Principle, where the corpuscular nature of Light does not explicitly appear. The method has certainly yielded very interesting results and pro vides a good approximate prediction of the phenomena under investigation; but to my own mind it has one grave fault, that of completely obscuring the symmetry in the structure of Light and Matter respectively. There can be no doubt that Dirac's photon Theory comes nearer the truth; but this Theory can deal only with large groups of photons by the method of second quantization, whereas I think it probable that it should be feasible to deal with individual phenomena without making use of this method.
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First of all then, and to achieve any real advance in the photon Theory, a relativistic form of the new Mechanics was needed to provide for the corpuscle an element of symmetry of the same kind as polarization. Now this new form had in fact been in existence for a number of years, in the shape of Dirac's Theory of the magnetic electron. Personally, I experienced great satisfaction at the appearance of this Theory of the magnetic electron, for I had always felt that it would contribute greatly towards the formation of a single Theory of Matter and Light. Actually, it offers us on the one hand a Wave Mechanics of the corpuscle which is as relativistic as Quantum Theory permits, given the present state of Science. Thus the first difficulty mentioned above is greatly diminished. Still further, Dirac's Theory automatically introduces a quantity, the spin of the electron, which at first sight has a certain affinity with polarization, whence we can at least hope that we may reduce the difference between material particles and photons resulting from the polarization of Light. For the electron, and more generally for every particle obeying his equations, Dirac assumes the properties of magnetic moment and angular momentum. These intrinsic properties of the electron are in accord with the idea of the magnetic rotating electron suggested at an earlier date by Uhlenbeck and Goudsmit, and they enable us to explain the anomalies of the Zeeman effect and of the fine structure of optical and of Rontgen spectra. It is altogether satisfactory, therefore, to find that these essential properties are automatically contained in Dirac's equations.
I cannot here develop Dirac's Theory, which requires a complicated mathematical apparatus, nor enumerate the many successes with which it has met. I must, however, insist on one peculiarity which was thought at first to constitute a difficulty for his Theory, but which appears since to have turned out to be a support. I allude to the fact (previously mentioned) that Dirac's equations yield solutions corresponding, for the electron, to states of motion having negative energy. Now these states of motion would have properties of a completely paradoxical character (for example, by checking an electron with negative energy we should increase its velocity); and it is certain that motion of this kind has never in fact been found to exist. Thus (to repeat) we are apparently faced by a grave difficulty: in one way, in fact, Dirac's Theory seems to suffer from an embarras de richesse. But I have just referred to my earlier discussion of the ingenious method of removing the obstacle, suggested by Dirac himself, and based on Pauli's Exclusion Principle. From these considerations, therefore, one general idea arises: for any corpuscle obeying Dirac's equations, whatever may be the values of charge and mass, there must be a corresponding anti-corpuscle, which stands to the corpuscle in the same relation as does the positive electron to the negative electron.
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Revenons à nos photons. To obtain a single Theory of Light and Matter, the simplest notion would be to compare the photon to a corpuscle obeying the Dirac equations, but having an electric charge and mass both equivalent to zero, or at any rate quite negligible in comparison with even the mass and charge of the electron. In such a case, the photon would have an appreciable energy that permitted its existence to be manifested experimentally, only when it possessed a velocity equal to, or at any rate indistinguishable from c.
There is, however, a serious a priori objection to any identification of the photon with a Dirac corpuscle, The position is that it is assumed today, for quite good reasons, that an elementary corpuscle, having the properties of a Dirac electron, obeys Fermi statistics in the same way as any other complex particle formed of an odd number of such corpuscles. On the other hand, the complex particle formed of an even number of Dirac corpuscles obeys Bose-Einstein statistics. Now the photons observe these statistics; and it is quite certain that they do so, since otherwise we could not have Planck's Law for black body radiation. Photons must therefore consist of an even number of elementary corpuscles.
To this primary objection, encountered by an attempt to com pare the photon with a Dirac corpuscle, others are added when we try to develop his Theory a little further. I cannot here, however, discuss details, but I may add that a photon constructed in this way would, in a manner, have only half the symmetry needed in order to allow us to associate with it an electromagnetic field of the Maxwellian type. A Dirac corpuscle, in other terms, can only provide us with half a photon.
The idea thus suggests itself that the photon might be considered as consisting of two Dirac corpuscles. But we know that Dirac's Theory, completed by the idea of lacunae already dealt with, makes a positive anti-electron correspond to the negative electron. More generally, we can make an anti-corpuscle correspond to every corpuscle obeying the Dirac equations, the former being defined as a hole or a lacuna within a domain of negative energy. On such a view it becomes tempting to imagine the photon to consist of a corpuscle having a negligible mass and charge and obeying the Dirac equations, associated with an anti-corpuscle of the same kind. It is a hypothesis to which we have been recently led, and it is an attractive one. For it is reasonable to suppose that a photon constituted in this way should be capable of annihilation in the presence of Matter, transferring to it at the same time the whole of its energy—the annihilation corresponding to a quantum transition by which the corpuscle contained in the photon fills up the accompanying lacuna. Actually such a transition, accompanied by annihilation, would constitute the photo-electric effect, whose fundamental importance from the theoretical point of view has already been stressed, while the electromagnetic field associated with the photon would then have to be defined as a function of this transition. Actually it is possible to show that an electromagnetic field, completely analogous to that which in Maxwell's system defines the luminous wave, can be associated with this transition leading to annihilation. In itself this is an encouraging fact; and further, since the photon is now assumed to consist of a corpuscle and an anti-corpuscle both of which are defined by the Dirac equations, the photon ought to follow Bose-Einstein statistics, which experiments show that it actually does follow.
To construct a photon after the schema outlined above we must assume the existence of a class of corpuscles obeying the Dirac equations and having either no electric charge and mass, or at any rate a charge and mass negligible as compared with those of the electron, minute as the latter are. Now there are in fact certain indications supporting the existence of this new physical entity. When X-rays are emitted by the nucleus of a radioactive substance, the Principle of the Conservation of Energy is not, apparently, satisfied. We may therefore well sacrifice this important Principle of Conservation so far as nuclear phenomena are concerned; and this is the solution supported by Bohr's great authority. Alternatively, we may assume that the phenomenon of the emission of X-rays by radioactive nuclei is accompanied by the emission of a new kind of particle, which it would be hard to detect experimentally because of the slightness of its action on Matter. The energy carried by these particles would thus escape experimental detection, at any rate with such means as we possess today, and on this hypothesis we could retain the Conservation of Energy. This idea was advanced some time ago by Pauli and Fermi, who called the new—and hypothetical—type of corpuscle the neutrino. Certain recent research has rendered the existence of the neutrino more probable, although there is not yet any apparent means of establishing it by direct observation. Francis Perrin and Fermi have shown that if the neutrino does exist, its mass must be zero, or at least negligible compared with that of the electron. At the same time it would be impossible to identify the neutrino with the photon, since it has so far escaped experimental detection, so that its action on Matter must be extremely slight. In other words, it can have no electromagnetic field. This naturally suggests an. identification of the neutrino with that corpuscle having no mass which forms part of the photon, and the neutrino would thus be a kind of semi-photon. In a state of isolation, i.e. when not accompanied by an anti-neutrino, it would have no electromagnetic field, since it could not be annihilated by the photo-electric effect; but when united with an anti-neutrino it would form a photon and would have an electromagnetic field of the Maxwellian type.
It must be admitted that these ideas are still largely hypothetical and raise numbers of difficult questions, and before they can be accepted they must undergo a thorough scrutiny. Yet it does seem probable to me that if some day a satisfactory theory of the nature of the photon is constructed, it will show elements of similarity with the outline I have just drawn.
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The prolonged antagonism between the Corpuscular and the Wave Theories as applied to Light, deriving fresh stimulus from the discovery of the photo-electric effect, had seemed, with the development of Wave Mechanics, to end in a comprehensive synthesis. For Light, as well as for Matter, it seemed that waves and corpuscles were two complementary aspects of a single physical reality. It looked as though a single theory, comprehending both Matter and radiation, and amalgamating waves and corpuscles, were within reach. Actually, however, this comprehensive theory has not yet been formulated. In its application to Matter, Wave Mechanics developed to the accompaniment of striking successes; but it lacked the relativistic aspect and the symmetry necessary to enable it to include Light. Dirac's Theory of the magnetic electron was a most important advance, because it introduced into Wave Mechanics relativistic invariance on the one hand, and on the other those elements of symmetry which recall the polarization of Light. There can be small doubt, therefore, that when a theory to embrace both Matter and radiation is formulated, it will be based on this Theory of Dirac's. Recent discoveries, still further, have introduced us to those new physical entities, positive electrons and neutrons, to which I have had as yet no occasion to refer, and have led us to suspect the existence of others like the neutrino. No doubt it is on such lines that we shall gather the data needed to understand the character of the photon. The Theory of Light, then, has a long and striking history; and a fine career lies before it.
L. de Broglie, Matière et Lumière, 1937, eng. trans. By W.H. Johnston, Matter and Light. The new physics (New York: Norton & Co., 1939), pp. 123-143.