CHAPTER XTHE NATURE OF RADIANT ENERGY
The problems thus far discussed have all been in the domain of molecular physics, but the discovery and measurement of the electron have also exerted a powerful influence upon recent developments in the domain of ether physics. These developments are of extraordinary interest and suggestiveness, but they lead into regions in which the physicist sees as yet but dimly—indeed even more dimly than he thought he saw twenty years ago.
But while the beauty of a problem solved excites the admiration and yields a certain sort of satisfaction, it is after all the unsolved problem, the quest of the unknown, the struggle for the unattained, which is of most universal and most thrilling interest. I make no apologies, therefore, for introducing in this chapter one of the great unsolved problems of modern physics, nor for leaving it with but the vaguest of suggestions toward a solution.
I. THE CORPUSCULAR AND THE ETHER THEORIES OF RADIATION
The newest of the problems of physics is at the same time the oldest. For nothing is earlier in the experiences either of the child or of the race than the sensation of receiving light and heat from the sun. But how does light get to us from the sun and the stars through the empty interstellar spaces? The Greeks answered this query very simply and very satisfactorily from the standpoint of people who were content with plausible explanations but had not yet learned perpetually to questionnature experimentally as to the validity or invalidity of a conclusion. They said that the sun and all radiators of light and heat must shoot off minute corpuscles whose impact upon the eye or skin produces the sensations of light and warmth.
This corpuscular theory was the generally accepted one up to 1800 A.D. It was challenged, it is true, about 1680 by the Dutch physicist Huygens, who, starting with the observed phenomena of the transmission of water waves over the surface of a pond or of sound waves through the air, argued that light might be some vibratory disturbance transmitted by some medium which fills all interstellar space. He postulated the existence of such a medium, which was called the luminiferous or light-bearing ether.
Partly no doubt because of Newton’s espousal of the corpuscular theory, the ether or wave theory gained few adherents until some facts of interference began to appear about 1800 which baffled explanation from the standpoint of the corpuscular theory, but which were easily handled by its rival. During the nineteenth century the evidence became stronger and stronger, until by its close the corpuscular theory I had been completely eliminated for four different reasons: (1) The facts of interference were not only found inexplicable in terms of it, but they were completely predicted by the wave theory. (2) The fact that the speed of propagation of light was experimentally found to be greater in air than in water was in accord with the demands of the ether theory, but directly contrary to the demands of the corpuscular theory. (3) Wireless waves had appeared and had been shown to be justlike light waves save for wave-length, and they had been found to pass over continuously, with increasing wave-length, into static electrical fields such as could not apparently be explained from a corpuscular point of view. (4) The speed of light had been shown to be independent of the speed of the source as demanded by the ether theory and denied by the corpuscular theory.
By 1900, then, the ether theory had become apparently impregnably intrenched. A couple of years later it met with some opposition of a rather ill-considered sort, as it seems to me, from a group of extreme advocates of the relativity theory, but this theory is now commonly regarded, I think, as having no bearing whatever upon the question of the existence or non-existence of a luminiferous ether. For such an ether was called into being solely for the sake of furnishing a carrier for electromagnetic waves, and it obviously stands or falls with the existence of such wavesin vacuo, and this has never been questioned by anyone so far as I am aware.
II. DIFFICULTIES CONFRONTING THE WAVE THEORY
Up to 1903, then, the theory which looked upon an electromagnetic wave as a disturbance which originated at some point in the ether at which an electric charge was undergoing a change in speed, and was propagated from that point outward as a spherical wave or pulse, the total energy of the disturbance being always spread uniformly over the wave front, had met with no serious question from any source. Indeed, it had been extraordinarily successful, not only in accounting for all the known facts, but in more than one instance in predicting new ones. The first difficulty appeared after the discovery of the electron andin connection with the relations of the electron to the absorption or emission of such electromagnetic waves. It was first pointed out in 1903 by Sir J. J. Thomson in his Silliman lectures at Yale. It may be stated thus:
X-rays unquestionably pass over all but an exceedingly minute fraction, say one in a thousand billion, of the atoms contained in the space traversed without spending any energy upon them or influencing them in any observable way. But here and there they find an atom from which, as is shown in the photographs oppositep. 192, they hurl a negative electron with enormous speed. This is the most interesting and most significant characteristic of X-rays, and one which distinguishes them from the- and-rays just as sharply as does the property of non-deviability in a magnetic field; for Figs.14and15and the plate oppositep. 190show that neither- nor-rays ever eject electrons from the atoms through which they pass, with speeds comparable with those produced by X-rays, else there would be new long zigzag lines branching out from points all along the paths of the- and-particles shown in these photographs.
But this property of X-rays introduces a serious difficulty into the ether theory. For if the electric intensity in the wave front of the X-ray is sufficient thus to hurl a corpuscle with huge energy from one particular atom, why does it not at least detach corpuscles from all of the atoms over which it passes?
Again when ultra-violet light falls on a metal it, too, like X-rays, is found to eject negative electrons. This phenomenon of the emission of electrons under the influence of light is called the photo-electriceffect. Lenard[165]first made the astonishing discovery that the energy of ejection of the electron is altogether independent of the intensity of the light which causes the ejection, no matter whether this intensity is varied by varying the distance of the light or by introducing absorbing screens. I have myself[166]subjected this relation to a very precise test and found it to hold accurately. Furthermore, this sort of independence has also been established for the negative electrons emitted by both X- and-rays.
Facts of this sort are evidently difficult to account for on any sort of a spreading-wave theory. But it wall be seen that they lend themselves to easy interpretation in terms of a corpuscular theory, for if the energy of an escaping electron comes from the absorption of a light-corpuscle, then the energy of emission of the ejected electron ought to be independent of the distance of the source, as it is found to be, and furthermore corpuscular rays would hit but a very minute fraction of the atoms contained in the space traversed by them. This would explain, then, both the independence of the energy of emission upon intensity and the smallness of the number of atoms ionized.
In view, however, of the four sets of facts mentioned above, Thomson found it altogether impossible to go back to the old and exploded form of corpuscular theory for an explanation of the new facts as to the emission of electrons under the influence of ether waves. He accordingly attempted to reconcile these troublesome new facts with the wave theory by assuming a fibrous structure in the ether and picturing all electromagnetic energy as traveling along Faraday lines of forceconceived of as actual strings extending through all space. Although this concept, which we shall call the ether-string theory, is like the corpuscular theory in that the energy, after it leaves the emitting body, remains localized in space, and, when absorbed, is absorbed as a whole, yet it is after all essentially an ether theory. For in it the speed of propagation is determined by the properties of the medium—or of space, if one prefers a mere change in name;—and has nothing to do with the nature or condition of the source. Thus the last three of the fatal objections to a corpuscular theory are not here encountered. As to the first one, no one has yet shown that Thomson’s suggestion is reconcilable with the facts of interference, though so far as I know neither has its irreconcilability been as yet absolutely demonstrated.
But interference aside, all is not simple and easy for Thomson’s theory. For one encounters serious difficulties when he attempts to visualize the universe as an infinite cobweb whose threads never become tangled or broken however swiftly the electrical charges to which they are attached may be flying about.
III. EINSTEIN’S QUANTUM THEORY OF RADIATION
Yet the boldness and the difficulties of Thomson’s “ether-string” theory did not deter Einstein[167]in 1905 from making it even more radical. In order to connect it up with some results to which Planck of Berlin had been led in studying the facts of black-body radiation, Einstein assumed that the energy emitted by any radiator not only kept together in bunches or quanta as it traveled through space, as Thomsonhad assumed it to do, but that a given source could emit and absorb radiant energy only in units which are all exactly equal to,being the natural frequency of the emitter anda constant which is the same for all emitters.
I shall not attempt to present the basis for such an assumption, for, as a matter of fact, it had almost none at the time. But whatever its basis, it enabled Einstein to predict at once that the energy of emission of electrons under the influence of light would be governed by the equationin whichis tine energy absorbed by the electron from the light wave or light quantum, for, according to the assumption it was the whole energy contained in that quantum,is the work necessary to get the electron out of the metal, andis the energy with which it leaves the surface—an energy evidently measured by the product of its chargeby the potential differenceagainst which it is just able to drive itself before being brought to rest.
At the time at which it was made this prediction was as bold as the hypothesis which suggested it, for at that time there were available no experiments whatever for determining anything about how the positive potentialnecessary to apply to the illuminated electrode to stop the discharge of negative electrons from it under the influence of monochromatic light varied with the frequencyof the light, or whether the quantityto which Planck had already assigned a numerical value appeared at all in connection with photo-electric discharge. We are confronted, however, by the astonishing situationthat after ten years of work at the Ryerson Laboratory (1904-15) and elsewhere upon the discharge of electrons by light this equation of Einstein’s was found to predict accurately all of the facts which had been observed.
IV. THE TESTING OF EINSTEIN’S EQUATION
The method which was adopted in the Ryerson Laboratory for testing the correctness of Einstein’s equation involved the performance of so many operations upon the highly inflammable alkali metals in a vessel which was freed from the presence of all gases that it is not inappropriate to describe the experimental arrangement as a machine-shopin vacuo.Fig. 32shows a photograph of the apparatus, andFig. 33is a drawing of a section which should make the necessary operations intelligible.
One of the most vital assertions made in Einstein’s theory is that the kinetic energy with which monochromatic light ejects electrons from any metal is proportional to the frequency of the light, i.e., if violet light is of half the wave-length of red light, then the violet light should throw out the electron with twice the energy imparted to it by the red light. In order to test whether any such linear relation exists between the energy of the escaping electron and the light which throws it out it was necessary to use as wide a range of frequencies as possible. This made it necessary to use the alkali metals, sodium, potassium, and lithium, for electrons are thrown from the ordinary metals only by ultra-violet light, while the alkali metals respond in this way to any waves shorter than those of the red, that is, theyrespond throughout practically the whole visible spectrum as well as the ultra-violet spectrum. Cast cylinders of these metals were therefore placed on the wheel(Fig. 33) and fresh clean surfaces were obtained by cutting shavings from each metal in an excellent vacuum with the aid of the knife,which was operated by an electromagnetoutside the tube.
i032Fig. 32
Fig. 32
Fig. 32
After this the freshly cut surface was turned around by another electromagnet until it was opposite the pointofFig. 33and a beam of monochromatic light from a spectrometer was let in throughand allowed to fall on the new surface. The energy of the electrons ejected by it was measured by applying to the surface a positive potential just strong enough to prevent any of the discharged electrons from reaching the gauze cylinder opposite (shown in dottedlines) and thus communicating an observable negative charge to the quadrant electrometer which was attached to this gauze cylinder.
i033Fig. 33
Fig. 33
Fig. 33
For a complete test of the equation it was necessary also to measure the contact-electromotive force between the new surface and atest plate.This was done by another electromagnetic device shown inFig. 32, but for further details the original paper may be consulted.[168]Suffice it here to say that Einstein’s equation demands a linear relation between the applied positive volts and the frequency of the light, and it also demands that the slope of this line should be exactly equal to.Hence from this slope, sinceis known, it should be possible to obtain.How perfect a linear relation is found may be seen fromFig. 34, which also shows that from the slope of this lineis found to be,which is as close to the value obtained by Planck from the radiation laws as is to be expected from the accuracy with which the experiments in radiation can be made. The most reliable value ofobtained from a consideration of the whole of this work isIn the original paper will be found other tests of the Einstein equation, but the net result of all this work is to confirm in a very complete way the equation which Einstein first set up on the basis of his semi-corpuscular theory of radiant energy. And if this equation is of general validity it must certainly be regarded as one of the most fundamental and far-reaching of the equations of physics, and one which is destined to play in the future a scarcely less important rôle than Maxwell’s equations have played in the past, for it must govern the transformation of all short-wave-length electromagnetic energy into heat energy.
i034Fig. 34
Fig. 34
Fig. 34
V. HISTORY OF EINSTEIN’S EQUATION
The whole of this chapter up to this point has been left practically as it was written for the first edition of this book in 1916. Now the altogether overwhelming proof that Einstein’s equation is an exact equation of very general validity is perhaps the most conspicuous achievement of experimental physics during the past decade. Its history is briefly as follows.
As early as 1900 Planck[169]had been led from theoretical considerations to the conclusion that atoms radiated energy discontinuously in units which were equal to, or multiples of,,in whichis the natural frequency of the radiator, anda universal constant which is now called Planck’s.He adopted the view that the seat of the discontinuity wasin the radiator, not in the radiation after it had left the radiator, and in the second edition of his book modified the formulation of his theory so as to make this appear without any ambiguity.
It was in 1905, as stated above, that Einstein definitely put the discontinuity into the radiation itself, assuming that light itself consisted of darts of localized energy, “light-quantas,” of amount.He further assumed that one of these light-quantas could transfer its energy undiminished to an electron, so that, in the photo-electric effect, the electron shot out from the metal with the energy,whererepresents the work necessary to get it out of the metal.
In 1913 Bohr, in the development of his theory of spectra, without accepting Einstein’s view as to the seat of the discontinuity, assumed anequationwhich was precisely the inverse of Einstein’s,i.e., he assumed that the energy lost when an electron jumps from one stationary state to another is wholly transformed into monochromatic radiation whose frequency is determined by equating the loss in energyto.In other words,Einstein and Bohr together have set up a reciprocal and reversible relation between electronic and radiant energy.
Up to 1914 no direct experimental proof had appeared for the correctness of this relation. In the photo-electric field discussion was active as to whether any definite maximum velocity of emission of electrons under the influence of monochromatic light existed, and although linear relations between energy and frequency had been reported by Ladenburg, Richardson and Compton, and Hughes, the range of frequencies available had been so small as to leave uncertainties in the minds of reviewers[170]and Planck’shad definitely as yet failed to appear.
The unambiguous experimental proofs of the correctness of the foregoing theoretical relation began with the publication of the accompanying photo-electric results[171]which were reported briefly in 1914, and submittedin extensoin September, 1915. These were in a form to prove the correctness of the Einstein equation; for monochromatic light of known frequencyfell upon a metal and the maximum energy of electronic ejection was found to be exactly determined byas Einstein’s equation required.
A year or two later Duane1[172]and his associates had found unambiguous proof of the inverse effect. A target had been bombarded by electrons of known and constant energyand the maximum frequency of the emitted ether waves (generalradiation) was found to be precisely given by.
D. L. Webster then proved that the characteristic X-ray frequencies of atoms begin to be excited at exactly the potential at which the energy of the stream of electrons which is bombarding the atoms has reached the value given byin whichis now the frequency of an absorption edge.[173]This checks Bohr’s formulation of frequency-energy relations, since it shows that when an electron within an atom receives just enough energy by bombardment to be entirely removed from the atom, the total energy values of the frequencies emitted during its return are equal to the electronic energy of the original bombardment.
De Broglie[174]and Ellis,[175]on the other hand, have measured with great accuracy, by means of the deviability in a magnetic field, the velocities of electrons ejected from different sorts of atoms by monochromatic X-rays, and have completely confirmed by such photo-electric work in the X-ray field my previous results obtained with ultra-violet light. They here verify in great detail and with muchelaboration the Einstein formulationwherenow represents the work necessary to lift the electron out of any particular level in the atom.
Parallel to this very complete establishment of the validity in the X-ray field of the Einstein photo-electric equation, and of its inverse the Bohr equation, has come the rapid working out in the domain of optics of the very large field of ionizing and radiating potentials which has also involved the utilization and verification of the same reciprocal relation. This will be seen at once from the definition of the ionizing potential of an atom as the electronic energy which must be thrown into it by bombardment to just remove from it one of its outer electrons. Through the return of such removed electrons there is in general a whole spectral series emitted. Similarly the radiating potential of an atom is defined as the bombarding energy which must be supplied to it to just lift one of its outer electrons from its normal orbit to the first virtual orbit outside that normal orbit. When this electron drops back there is in general the emission of a single-line spectrum. All this work took its origin in the fundamental experiments of Franck and Hertz[176]on mercury vapor in 1914. From 1916-22 the field was worked out in great detail, especially in America by Foote and Mohler, Wood, McLennan. Davis and Goucher, and others.
Suffice it to say that whether the energy comes in the form of ether waves which through absorption in an atom lift an electron out of a normal orbit, so that the atom passes over to an excited or to an ionized state, or whether the energy enters in the form of a bombarding electron and reappears as a radiated frequency,thereciprocal relation represented in the Einstein-Bohr equationhas been found fulfilled in the most complete manner.
In view of all these methods and experiments the general validity of the Einstein equation, first proved photo-electrically about ten years ago, is now universally conceded.
VI. OBJECTIONS TO AN ETHER-STRING THEORY
In spite of the credentials which have just been presented for Einstein’s equation, the essentially corpuscular theory out of which he got it has not yet met with general acceptance even by physicists of Bohr’s type. There seems to be no possibility, at present, of bringing it into harmony with a whole group of well-established facts of physics.
The recent practically complete bridging of the gap between X-rays and light,[177]as well as that between heat waves and wireless waves,[178]with the perfectly continuous passage of the latter over into static electrical fields, appears to demand that, if we attempt to interpret high frequency electromagnetic waves—X-rays and light—in terms of undulatory “darts of light,” we also interpret wireless waves in the same way, and this in turn requires us to use a similar mechanism in the interpretation of static electrical fields. This brings us back to Thomson’s ether-string theory, which seems to be a necessary part of Einstein’s conception, if it is to have any physical basis whatever.
Two very potent objections, however, may be urged against all forms of ether-string theory. The first is that no one has ever yet been able to show that such a theory can predict any one of the facts of interference. The second is that there is direct positive evidence against the view that the ether possesses a fibrous structure. For if a static electrical field has a fibrous structure, as postulated by any form of ether-string theory, “each unit of positive electricity being the origin and each unit of negative electricity the termination of a Faraday tube,”[179]then the force acting on one single electron between the plates of an air condenser cannot possibly vary continuously with the potential difference between the plates. Now in the oil-drop experiments[180]we actually study the behavior in such an electric field of one single, isolated electron and we find, over the widest limits, exact proportionality between the field strength and the force acting on the electron as measured by the velocity with which the oil drop to which it is attached is dragged through the air.
When we maintain the field constant and vary the charge on the drop, the granular structure of electricity is proved by the discontinuous changes in the velocity, but when we maintain the charge constant and vary the field the lack of discontinuous change in the velocity disproves the contention of a fibrous structure in the field, unless the assumption be made that there are an enormous number of ether strings ending in one electron. Such an assumption takes most of the virtue out of an ether-string theory.
Despite, then, the apparently complete success of the Einstein equation, the physical theory of which it was designed to be the symbolic expression is thus far so irreconcilable with a whole group of well-established facts that some of the most penetrating of modern physicists cannot as yet accept it, and we are somewhat in the position of having built a very perfect structure and then knocked out entirely the underpinning without causing the building to fall. It stands complete and apparently well tested, but without any visible means of support. These supports must obviously exist, and the most fascinating problem of modern physics is to find them. Experiment has outrun theory, or, better, guided by unacceptable theory, it has discovered relationships which seem to be of the greatest interest and importance, but the reasons for them are as yet not at all understood.
VII. ATTEMPTS TOWARD A SOLUTION
It is possible, however, to go a certain distance toward a solution and to indicate some conditions which must be satisfied by the solution when it is found. For the energy,with which the electron is found by experiment to escape from the atom, must have come either from the energy stored up inside of the atom or else from the light. There is no third possibility. Now the fact that the energy of emission is the same, whether the body from which it is emitted is held within an inch of the source, where the light is very intense, or a mile away, where it is very weak, would seem to indicate that the light simply pulls a trigger in the atom which itself furnishes all the energy with which the electron escapes, as was originally suggested by Lenardin 1902,[181]or else, if the light furnishes the energy, that light itself must consist of bundles of energy which keep together as they travel through space, as suggested in the Thomson-Einstein theory.
Yet the fact that the energy of emission is directly proportional to the frequencyof the incident light spoils Lenard’s form of trigger theory, since, if the atom furnishes the energy, it ought to make no difference what kind of a wave-length pulls the trigger, while it ought to make a difference what kind of a gun, that is, what kind of an atom, is shot off. But both of these expectations are the exact opposite of the observed facts.The energy of the escaping electron must come, then, in some way or other, from the incident light, or from other light of its frequency, since it is characteristic of that frequency alone.
When, however, we attempt to compute on the basis of a spreading-wave theory how much energy an electron can receive from a given source of light, we find it difficult to find anything more than a very minute fraction of the amount which it actually acquires.
Thus, the total luminous energy falling per second from a standard candle on a square centimeter at a distance of 3 m. is 1 erg.[182]Hence the amount falling per second on a body of the size of an atom, i.e., of cross-section,is,but the energywith which an electron is ejected by light of wave-length(millionths millimeter) is,or four thousand times as much. Since not a third of the incident energy is in wave-lengths shorter than,a surface of sodium or lithium which is sensitive up toshould require, even if all tills energy were in one wave-length, which it is not, at least 12,000 seconds or 4 hours of illumination by a candle 3 m. away before any of its atoms could have received, all told, enough energy to discharge an electron. Yet the electron is observed to shoot out the instant the light is turned on. It is true that Lord Rayleigh has shown[183]that an atom may conceivably absorb wave-energy from a region of the order of magnitude of the square of a wave-length of the incident light rather than of the order of its own cross-section. This in no way weakens, however, the cogency of the type of argument just presented, for it is only necessary to apply the same sort of analysis to the case of-rays, the wave-length of which is sometimes as low as a hundredth of an atomic diameter (cm.), and the difficulty is found still more pronounced. Thus Rutherford[184]estimates that the total-ray energy radiated per second by one gram of radium cannot possibly be more than.Hence at a distance of 100 meters, where the-rays from a gram of radium would be easily detectable, the total-ray energy falling per second on a square millimeter of surface, the area of which is ten-thousand billion times greater than that of an atom, would be.This is very close to the energy with which-rays are actually observed to be ejected by these-rays, the velocity of ejection being about nine-tenths that of light. Although, then, it should take ten thousand billion seconds for the atom to gather in this much energy from the-rays, on the basis of classicaltheory, the-ray is observed to be ejected with this energy as soon as the radium is put in place. This shows that if we are going to abandon the Thomson-Einstein hypothesis of localized energy, which is of course competent to satisfy these energy relations, there is no alternative but to assume that at some previous time the electron had absorbed and stored up from light of this wave-length enough energy so that it needed but a minute addition at the time of the experiment to be able to be ejected from the atom with the energy.What sort of an absorbing and energy-storing mechanism an atom might have which would give it the weird property of storing up energy to the value,whereis the frequency of the incident light, and then shooting it all out at once, is terribly difficult to conceive. Or, if the absorption is thought of as due to resonance it is equally difficult to see how there can be, in the atoms of a solid body, electrons having all kinds of natural frequencies so that some are always found to absorb and ultimately be ejected by impressed light of any particular frequency.
However, then, we may interpret the phenomenon of the emission of electrons under the influence of ether waves, whether upon the basis of the Thomson-Einstein assumption of bundles of localized energy traveling through the ether, or upon the basis of a peculiar properly of the inside of an atom which enables it to absorb continuously incident energy and emit only explosively,the observed characteristics of the effect seem to furnish proof that the emission of energy by an atom is a discontinuous or explosive process. This was the fundamental assumption of Planck’s so-called quantum theoryof radiation. The Thomson-Einstein theory makes both the absorption and the emission sudden or discontinuous, while the loading theory first suggested by Planck makes the absorption continuous and only the emission explosive.
The new facts in the field of radiation which have been discovered through the study of the properties of the electron seem, then, to require in any case a very fundamental revision or extension of classical theories of absorption and emission of radiant energy. The Thomson-Einstein theory throws the whole burden of accounting for the new facts upon the unknown nature of the ether, and makes radical assumptions about its structure. The loading theory leaves the ether alone and puts the burden of an explanation upon the unknown conditions and laws which exist inside the atom.
In the first edition of this book, finished in 1917, I expressed the view that the chances were in favor of the ultimate triumph of the second alternative. In 1921, however, I presented at the Third Solvay Congress some new photo-electric experiments[185]which seemed at the time to point strongly the other way.
These experiments consisted in showing with greater certainty than had been possible in earlier years[186]that the stopping potentials of different metals,,,when brought in succession before the same Faraday cylinder(seeFig. 35) and illuminated with a given frequency, were strictly identical. The significance of these results for the theory of quanta lay in the fact that I deducedfrom them the conclusion that in the photo-electric effect, contrary to preceding views including my own, theenergy “” is transferred without loss from the ether-waves to the free, i.e., the conduction electrons of the metal, and not merely to those bound in atoms. This seemed to take the absorbing mechanism out of the atom entirely, and to make the property of imparting the energyto an electron, whether free or bound, an intrinsic property of light itself.