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SOME RECENT SPECULATIONS ON
THE NATURE OF LIGHT1

FOUR weeks, one day and four hours ago I was sitting on a sofa in the Cosmos Club, Washington, chatting with your distinguished director during a brief interval between long committee meetings. That was when, but I know not just how or why, I was caught by that wily hunter for this particular repast. This time he was not after big game-merely angling for a poor fish.

There is no need to import any outsider into the Jefferson Physical Laboratory to talk about light. Here you have Pierce with his wave lengths in hundreds of meters and Duane with them in fractions angstroms, a range of 1014. Here the celebrated Lyman region was found and explored. You have in Saunders one who has followed series spectra from Ritz to Bohr and beyond. Then there is infra-red Kemble and band-spectra Mulliken, and for recent speculations on the nature of light why look further than Slater? The whole range of factual and deductive and speculative optics is here, and nowhere else in greater variety or completeness or perfection. If Count Rumford were alive he would perhaps feel that you were all out for the Marathon that leads to his medal and premium-and all likely to win.

The count spoke of light and heat. To-day light and heat and electricity have come together. Therein lies our difficulty and thence issue our speculations. While light stood alone we had reached a satisfactory theory of its nature as a wave motion in a medium. When it passed to heat and we became interested not in the transparent but in the black body we were in trouble at the short end of the spectrum and that trouble has been confirmed and accentuated by photoelectric phenomena. A score of years ago Ritz2 in a masterly critique of electromagnetic theory suggested strongly that the time had come when it might be no longer useful and might perhaps even be harmful to consider energy as localized. We have proceeded, in the most contrary way, to emphasize more and more the localization of energy, especially radiant energy, and to endow this energy with momentum, angular momentum, with mass, inertia and weight. The quantum theory and the Bohr orbit have certainly been 1 An address before the Physical Colloquium, Jefferson Physical Laboratory, May 24, 1926.

2 W. Ritz, "Gesammelte Werke."'

increasingly with us, and are likely to remain for some time.

Perplexing as our situation is, we should be happy in it. For it is wholesome, healthy and young. We have become again as little children to whom everything is new and wonderful, and we are learning facts so fast that their systematization is not to be expected. In due time we shall come again to a period of senility in which we shall understand and no longer learn. It will be some precocious, maybe I had better say some prematurely senile young man from whom will issue this virus of sclerosis.

AN INTERPRETATION

Let

Light came into the world on the first day, and it was good. Sight is our best sense. To see is a synonym, not even colloquial, for to understand. A dog would say, "Do you smell that?" Optics is one of our oldest sciences. For long times there was dispute as to whether light issued from the perceived object into the eye or emanated from the eye to the object seen. It has remained till the year 1925 and to G. N. Lewis3 to suggest that the eye and the object are in contact and that the relation is mutual. us examine this speculation of Lewis's. Einstein interpreted the Lorentz transportation as relativity, not the relativity of Newton nor of the later Einstein, but the special relativity of electromagnetic theory. Minkowski gave an elegant mathematical formulation of this relativity which Lewis and I elaborated in 19101912 and printed in the latter year in the Proceedings of the American Academy. One may say that fundamentally neither space nor time are of separate physical significance, they are individually anthropomorphic, if not conceited, conceptions based on the notion that the individual observer is at rest, probably at the center of the universe, and everything else in motion. Physically the important thing is the local time, the Eigenzeit, dt = V c2dt2 - ds2, a fusion of space and time. Along the path of light dt = 0, and there is no lapse of space-time; a particle moving with velocity less than that of light has a past and future defined by its space-time path, but not so for light itself. Hence, says Lewis, we make the interpretation that there is contact between the perceiving eye and the object perceived and more generally between any two objects in radiative interchange. To some this sounds bizarre if not impish.

Let us for a moment consider what is the function of mathematical physics. In a certain sense we get out of mathematical physics only what we put in. This is a purely mathematical implication and means

3 G. N. Lewis, Silliman Lectures, Yale University and Proc. Nat. Acad Sci., 12, p. 22.

merely that if our mathematics is water-tight every conclusion must follow deductively from the premises. But in another and more physical sense we may and we ordinarily do hold that when we interpret our mathematical conclusion as a fact of nature we get new physics. In this way Hamilton got conical refraction, and it was a sound way to get it provided that observation verified deduction. Suppose observation had belied deduction. Then we should have been forced to conclude not that the demonstration was in error but that the premises on which it was based were inadequate for, or contained elements extraneous to the theory of light, or were contradictory within themselves; i.e., they were logically inconsistent or inconsistent with nature. Many other instances of obtaining from mathematics new physics could be adduced, and also many, perhaps more, instances of obtaining too much or too little. It is the interpretations that determine the value of mathematical physics and that make it as Darwin pointed out in 1912 a more exacting science than pure mathematics. Now Lewis has made an interpretation. It is a reasonable interpretation of the mathematics fundamental to relativity. Without prejudicing the mutuality of the relationship of contact, I may be permitted to say anthropomorphically that the interpretation can not fail to throw light upon the subject.

AN ADAPTATION

For a long time there was a dispute as to whether light moved faster in the optically denser medium or more slowly. On the corpuscular theory it was believed that the potential energy was constant in each uniform isotopic medium but changed in the interface, i.e., that the normal component of the velocity of light changed across the interface but the horizontal component remained the same. This led to the view that the velocity was greater in the denser mediumfor such an interpretation is forced by the law of refraction. Moreover, this theory may be supported by the law of stationary or varying action. It is only necessary to take the law in the form 8 fvds=0 with v=nc, where c is the velocity of light and n is the index of refraction, to obtain the proper relation 8 f n ds = 0 of geometrical optics. On the other hand the wave theory leads to the conclusion that the velocity is less in the denser medium, and this view was early urged by Fermat in connection with his principle of least time. Here we have 8f ds/v=0, but v = c/n and hence again 8 fn ds = 0. The question of velocity as a physical fact was settled experimen

4 W. R. Hamilton, Trans. Irish Acad., 15 (1924), p. 69. See also H. A. Lorentz on Light, Encyc. Brit., Vol. 16, p. 618.

tally by Foucault and would in any case have been assumed as settled by the triumph of the wave theory even if the experiment had not been forthcoming at a time proper to the support of the theory. The equation 8 fn ds = 0 remains and the principle of least action must be adapted thereto with the condition vc/n instead of v=nc.

As is usual in such cases the adaptation may be made in a number of ways. The most recent and perhaps the neatest is that due in 1925 to Cox and Hubbard. They assume that a beam of light is made up of quanta hv, that the number of these quanta in the incident beam is equal to the sum of the numbers in the reflected and refracted beams, which is equivalent to assuming the constancy of energy. The momentum in vacuo associated with a quantum hv is hv/c and the authors assume that in a medium of index n = c/v the momentum will be hv/v, so that a quantum has a greater momentum in the denser medium where it has the smaller velocity. This checks with our notions on the basis of the wave theory. If we define the element of action for the quantum as the product of the momentum hv/v by the element of distance ds we have in the equation 8 f (hv/v.ds) = 0 the principle of least action so adapted as to give the correct equation 8 fn ds = 0 from which the laws of reflection and refraction flow. It should be remarked that in this theory we are dealing with large numbers of quanta. It would seem as though individual quanta must be either refracted whole or reflected whole. The constitution of the medium must therefore determine, and through its index of refraction specify, what fraction of a large number of quanta, i.e., what is the chance that any one quantum, incident at a given angle, shall be refracted or reflected.

AN ABSTRACTION

6

Maxwell gave us an electromagnetic wave theory of light. Gibbs gave us an electrical theory. These amount to the same thing if all magnetism is generated by the motion of electricity. But the method of Gibbs is totally different from the method of Maxwell; it is a real contribution, and though scarcely recent seems never to have made an impression on optics and hence is worth mentioning. He likened a transparent body to an area of marine piling and light to a ground-swell moving towards and through it. The piles will not affect the groundswell much as a whole, there will still advancing periodic motion of the original frequency though of diminished wave length. But superposed upon that will be an irregular motion.

be an

Cox and Hubbard, Proc. Nat. Acad. Sci., 11, p. 498. J. W. Gibbs, "Scientific Papers," Vol. 2.

Gibbs set himself the problem of calculating the part of the energy that would be found in the regular and the part that would be found in the irregular motion -not of course for the two-dimensional analogon of the area of piling, but for the transparent body and the light. On these very general assumptions of a fine-grained structure for his medium, of some general properties of simple harmonic waves and of a few basic principles of electrodynamic action he was able to explain the behavior of transparent bodies, including those optically active, and by a familiar analytical device using complex numbers further to extend the equations to absorbing media. I would emphasize the uselessness of special hypothesis for so much of optical theory as is derivable from abstract generalities. How this work would be adapted to the theory of quanta is not easy to see; before we get quanta fully adapted to the type of optical phenomena with which he and the older physicists were concerned such difficulties may be resolvable.

A PICTURE

Maxwell built his theory of electromagnetism on the work of Faraday with a good training, which Faraday did not have, in the work of Green and Stokes and other workers with continuous media. It is not easy to understand Maxwell in all places, one may even doubt if he fully understood himself. Kelvin never completely went over to him. Perhaps Heaviside was our only complete Maxwellian, more complete than his original. Presumably Maxwell attributed little physical reality to the Faraday lines of force; it would be unnatural for a student steeped in hydromechanics and the theory of elasticity to do So. J. J. Thomson has tended to return to Faraday and treat the lines or tubes of force as real and atomic. Writing in 1903 he said:"

This view of light as due to the tremors in tightly stretched Faraday tubes . . . discrete threads embedded in a continuous ether, giving to the latter a fibrous structure ... ..." on this view, then a wave of light itself must have structure, and the front of the wave instead of being, as it were, uniformly illuminated, will be represented by a series of bright specks on a dark ground, the bright specks corresponding to the places where the Faraday tubes cut the wave front.

And he went on to use this picture to explain the small amount of ionization produced by light. As a Faraday tube must start and end on electric charges, these charges must be separated by the wave front. This implies a separation of charge for which I have J. J. Thomson, Silliman Lectures, Yale University, published as "Electricity and Matter," p. 62.

never seen any physical evidence, unless we get around the difficulty by assuming that the Faraday tubes are in pairs, about one half running from negative electricity behind the wave to positive ahead of it, the other half from positive behind to negative ahead. If we can get around the difficulty of charge, there is a remarkable similarity between Thomson's suggestion of 1903 and Lewis's of 1925-the emitter and recipient electrons are in connection via a Faraday tube which is a light-path and from the viewpoint of relativity may be said to be in contact.

Similar as the two suggestions are, I can not see that Thomson's of 1903 has any similarity to Thomson's of 1924, and I must confess to having had that difficulty before with some of Thomson's papers separated by an interval much shorter than twenty-one years. At any rate he appears to consider that there is some continuity between the papers because we find in that of 1924 a brief extract in quotation marks from the earlier paper. The Faraday tube is of course still with us, but so far as I can determine the tightly stretched strings whose tremors constitute light and which cut the wave front in the bright specks have quite disappeared. What the Faraday tube now does is to stay in the atom, but occasionally to get snarled up and throw off the snarls as light corpuscles. Let us quote Thomson: "The mutual potential energy of an electron E and a positive charge

P is located in the tube of force stretching between E and P. If the electron falls from E to E' this potential energy is diminished by the energy in the portion EE' of this tube of force. During the approach of E to P the tube may be thrown in a loop, the closed part of the loop gets detached and goes off as a closed ring which rapidly becomes circular and travels with the velocity of light in a direction at right angles to its plane like a circular vortex ring." The process of absorption is the reverse-one of these rings gets foul of the Faraday tube in an atom in such a peculiar way that it reunites with the tube and pushes the electron out to a more distant orbit.

PSYCHICS

It appears as though the Faraday tube were a very obliging if not changeable fellow. To his tension, at one time, is due the tendency of positive and negative charge to get together, but now the electron under some circumstances can move in so fast that his tube can not follow and gets looped. And though in the process of getting looped a tube must apparently travel largely in its own plane, once it snaps off its loop the latter moves perpendicular to its plane and with the velocity of light despite the fact that

8 J. J. Thomson, Phil. Mag., 48, p. 737; 50, p. 1181.

previously it had not been able to keep up with an electron. The leopard has changed his spots. We need not insist upon sense in such matters. Bohr has written that an electron does not know it is in a stationary state until it has been around the orbit a few times. This is humanly intelligible, it is sound be haviorism. All we need now is to have some physicist who has read up the new psychology as a minor tell us that the Faraday tube that draws the negative and positive electricity together is but a gross materialization of the real fundamental force of nature, the sex instinct, and our molecules have become as inhumanly lewd as we are alleged to be! There must always be mystery forces and mystical structures at the basis of physics, we can not explain except from unexplained postulates or define except in terms of the

℗ N. Bohr, D. Kgl. Danske Vid. Sels Skrift, Nat. Math., Afd. 8, IV, Pt. I. German Translation by Hertz (pp. 28-29): Die Antwort . . . ob ein gegebener Zustand stationär ist . . . kann nicht gegeben werden, ehe die Teilchen nicht durch einen völlstandigen Zyklus von Zuständen hindurch gegangen sind und sozusagen Kenntnis vom ganzen Kraftfeld und desen Wirkung auf die Bewegung genommen haben. . . . It may be remarked that the quantum theory originated with Planck in connection with an empirical equation for black body radiation and that in the first edition of his Wärme

strahlung he proves the formula from the Maxwell theory

and classical mechanics. Later Poincaré showed that the conclusions were inconsistent with the premises and in subsequent editions of his book Planck suppressed the proof in question and substituted a quasi-axiomatic pro

cedure. Bohr's work and its elaboration into an astounding detail by him and others was based on a combination between dynamics of a particle (central forces) and the quantum conditions. Lapsing into a psychological mode of expression is no retraction of accomplishments but an indication of perplexity as to the future; it is only in the most recent months that we are learning from Born and Heisenberg how to set up the quantum theory on its own feet independent of classical mechanics or electromagnetics and in a way which if successful may lead, as implied in the text, to a redefinition of fundamental concepts in terms of it.

[Note added in proof. Another hopeful formulation of the quantum theory on its own feet, which was appear ing as this lecture was in preparation, is Schrödinger's undulatory theory of mechanics, now available in Physical Review, Vol. 28, 1926, pp. 1049–1070, and apparently largely transformable into the system of Born and Heisenberg, but inspired by the contributions of de Broglie mentioned in the final paragraph and by the optical investigations of Hamilton cited above, ref. 4. The Bohr orbits seem to have gone and to be superseded by structure represented by vibrational types in a distributed charge, a suggestion which in different mathematical guise was put forward long ago, I think by J. J. Thomson.]