Sixty Years of Quantum Physics

Minutes

Sixty Years of Quantum Physics By Edward U. Condon Washington University, St. Louis, Missouri [Read before the Society December 2, 1960] I was invited to speak on the occasion of the 1500th Regular Meeting of the Society, and of course am delighted to be able to come and do it. But those who conveyed the invitation could not refrain from reminding me that I owed the Society a retiring presidential address. I was President, in 1951, and it was in the fall of that year that I departed hastily to go to Corning Glass Works to be Director of Research. That was a very interesting experience, and I am still connected with the glass business, though I am also doing professing. I started my career in experimental physics and lasted one day. When I started work on a doctoral thesis at the University of California in 1925, I had to set up a vacuum system. All experimental physicists in those days had to get a Cenco pump on the floor and glass tubing up to something that was on the table. I started out like all the rest but broke so much glass the first day that they suggested I go into theoretical physics. I told this story at Corning after I became their Director of Research. Mr. Amory Houghton, Chairman of the Board, who is now our Ambassador to France, said, "Isn't it good that at last you are in a place where you can't possibly break enough glass to make any difference." Looking back over the various possibilities of things that might be suitable to talk about this evening, I thought it would be interesting to review the historical development of what I now would like to call quantum physics, rather than quantum mechanics, because it has grown and expanded in such a way that it permeates all of modern physics. In fact it is extremely difficult to think of any actively cultivated part of physics that is not directly involved with Planck's quantum constant "h". The basic discovery by Planck was made within a week or two of exactly 60 years ago, so I thought it might be interesting to discuss this subject. The subject of quantum physics started with the statistical theory of the distribution of energy in the black-body spectrum. The spectrum of radiated energy in equilibrium with matter in an enclosure is commonly called black-body radiation because it is the kind of radiation that would be emitted by a perfect absorber. The active problem in 1900 was the explanation of the distribution of energy in the spectrum. It is interesting to realize that the subject has quite an ancient history. The first application of thermodynamics to black-body radiation goes back to 1859 when Kirchhoff first developed the ideas of radiative exchanges, and the connections between emission and absorption, rules according to which a good emitter is a good absorber, and a poor emitter is a poor absorber. In 1884 the discovery had been made of what we now call the Stefan-Boltzmann law, that the total radiation goes up as the fourth power of the absolute temperature. It was discovered by Stefan experimentally and interpreted theoretically by Boltzmann, making one of the earliest applications of thermodynamics to radiation after those first ideas of Kirchhoff's. In 1894 came the discovery by Wien of the displacement law, which tells how the distribution of energy over various wavelengths changes with the absolute temperature. The big problem at that time was to try to understand the reason for this distribution. Contrary to the general belief, which has become true in the last 30 years or so, that all physics is really done by young men in their 20's, the discovery of Planck was done when he was at the advanced age of 42. In 1900 he had already put a part of his career of research work behind him and was a professor in the University of Berlin, so that his work on quantum physics was done 21 years after he had received his doctorate for a thesis on the second law of thermodynamics. His thesis, it is interesting to note, was done under Kirchhoff and Helmholtz at Berlin. In his autobiography he says that he is quite confident neither of them ever read it. Thermodynamics was Planck's first love, his principal love throughout physics. In fact there are many indications that he was rather annoyed with his discovery of the Planck constant of action and did his best for about 15 years or so, on up to about 1915, to find ways of evading his own discovery and reconciling the theory that he had discovered with classical theory. This resembles somewhat the story that I used to hear from Professor Ladenburg at Princeton, about Roentgen. Everybody knows about the great consequences of Roentgen's discovery of the Roentgen rays, or x rays. Ladenburg was a student of Roentgen. He said that Roentgen was annoyed with his x rays because he did not understand what they were and much preferred classical subjects. So the upshot of it was that Ladenburg did a doctoral thesis under Roentgen just a few years after Roentgen had discovered x rays, on the subject of the correction to Stokes' law for a body falling through a viscous medium in a cylindrical tube, allowing for the finite diameter of the tube and the wall effect. They had a long pipe filled with castor oil, which is the traditional viscous material. It reached from the top floor of the laboratory to the basement. He said nothing ever gave Roentgen quite as much pleasure as to see the steel ball arrive down at the basement just when the calculation said it ought to. You can tell by a great deal of Planck's writings and readings that he felt much the same way about classical physics in relation to the modern developments. Lord Rayleigh had published a theory that was based on the equipartition of energy doctrine, that goes back to Maxwell, Waterston, and Boltzmann, whereby every degree of freedom in the radiation field should have had the energy kT. He knew it did not, because that would have given an infinite or divergent result. But nevertheless that was where the theoretical thinking of that time led, and this served to point up the importance of the quantum modifications that had to be made. One of the things that I found interesting in looking back in the history of this theory is that it has always been referred to as the Rayleigh-Jeans law, and I had supposed that Rayleigh and Jeans had worked together on it. In point of fact Rayleigh derived it and made a mistake by a factor of 8 and Jeans corrected that in a letter to Nature, so that dividing the original Rayleigh formula by 8 was Jeans' contribution. It was an essential contribution because it is a mistake that we all might make very readily. In counting up the degrees of freedom in the radiation field that are associated with frequencies between n and n + dn one has to calculate how many integers there are whose squares add up to a certain value, and it is natural to take the volume of a sphere of a certain radius. But in fact only one takes an octant out of this sphere because the integers, all three of them, have to be positive, and that is where Rayleigh went wrong. The radiation measurements that served to inspire Planck were being made at the Physikalische-Technische Reichsanstalt by some of the great names of early days of radiation measurement work: Lummer, Pringsheim, and Rubens. So that the problem of distribution of energy in the spectrum was very much to the fore and very good measurements were being made. It was on October 19, 1900, that Planck presented his radiation formula to the German Physical Society at a meeting in Berlin, strictly as an empirical interpolation formula between the Rayleigh-Jeans law, which is valid at long wavelengths, and the Wien law, which is valid at short wavelengths. By interpolating in between he had been able to find a simple formula that extended across the whole regime. But at that time he had no theoretical basis for it whatever. That night Rubens took the data to which he had access and made a very careful comparison with Planck's formula—a more careful one than Planck himself had made at that time—and found that it represented the data with extraordinary accuracy, much better than an empirical formula usually does. He called on Planck the next morning with a strong conviction that there was some real fundamental truth in the formula and not just an accidental agreement. Planck then set to work to find a theoretical basis for this formula and worked very hard for quite a while. In his biography he speaks of this as the most difficult period of his whole life. Then, just within less than two months, on December 14, 1900—so we are just 12 days ahead of the 60th Anniversary—he presented a paper to the Physical Society of Berlin in which he took the decisive step. By applying the Boltzmann principle for the connection of entropy with probability—which up to that time had hardly been used at all—he was able to work out the spectral distribution of energy that would be in equilibrium with a system of electrical oscillators. In order to get the desired result he had to suppose that the energy of each oscillator was built up in finite steps of energy, whereas in all of physics hitherto energy had been a continuous variable. To agree with the Wien displacement law he then had to assume that the finite size of these steps was proportional to the frequency, and so the energy quanta were hn. In that way he arrived at the famous formula Un = 8phn3 / c3 (ehn/kT - 1) for the density of the energy in the spectral frequency range between n and n + dn in black-body radiation at absolute temperature T. As is readily seen, in the limit of hn/kT small compared with 1 this formula transforms into the Jeans formula, and in the limit of hn large compared with kT it becomes the Wien formula and represents the data with great accuracy in between. Additional measurements of the same sort were later made with great precision at the National Bureau of Standards by W. W. Coblentz. One of the most extraordinary things about this is the accuracy with which Planck was able to get these fundamental constants. At that time there was no good value available for Avogadro's number, or for the charge on the electron; and the values that Planck was able to get out of his work were much closer than is usually appreciated. When he first represented the data, in order to obtain a fit with the old black-body data he had to assume that h was 6.885×10-27 erg/sec, and k, which we now call the Boltzmann constant, 1.429×10-16 erg/°K. The present best value for the first number is 6.6252×10-27 instead of 6.885×10-27 and for the second number, 1.3804×10-16 instead of 1.429×10-16. At that very first time Planck got Planck's constant only about 4.4 percent too high, and Boltzmann's constant about 3.5 percent too high relative to the best modern values. This was actually the first time that the Boltzmann constant had been evaluated. Let me just remind you of its relation with the other basic constants that have so much importance. The gas constant, R, as we ordinarily know it, per gram mole, is equal to the Avogadro number, N, times k; and the Faraday, F, the amount of charge needed to plate out a gram mole of univalent ions, is equal to Avogadro's constant times the charge of the electron. That is R = Nk and F = Ne. These molar quantities, R and F, were well known, and good values for them were available in those days, but what was not known was the Avogadro number N. However, if you know any one of these quantities you can get the other. So that as it turns out, the getting of the Boltzmann constant, k, enabled one to get N by the first equation, and then, using that N in combination with the knowledge of the Faraday, F, one was able to get the charge on the electron. The electron had only been recognized about three years earlier by J. J. Thomson, and while the ratio of its charge to mass was known, its charge by itself was not well known. You will find in the literature of that time values published for e, the charge on the electron, ranging all the way from 1.29×10-10 electrostatic units, on up to 6.5×10-10 electrostatic units, which was given by J. J. Thomson, and a little while later revised back down to 3.4×10-10. In other words, at that time one only knew the charge on the electron to a factor of about 5 or 6. On the other hand if you take the value of the Faraday and the value of k and solve for N from the gas constant and then solve for e, you find, surprisingly enough, that e equals 4.69×10-10 electrostatic units, which is only 2.3 percent below the presently recognized value. Thus in the space of just a month or two Planck first found an empirical formula which to this day gives the most accurate representation of the spectral distribution of the radiant energy; second, he found a derivation of that formula. In order to get the derivation he had to introduce the extraordinary idea of energy quantization into physics. Third, he obtained an excellent value for the charge on the electron, which everybody was trying to do at that time. You might expect that this would cause a great deal of excitement among physicists at that time, but it did not. If you search through the journals you find that practically nothing is said about Planck in the years 1900 through 1904. I was very much intrigued, therefore, when just before this meeting Mr. Marton recalled that a search of the records of this Society indicated that in 1902 Arthur L. Day gave a report on Planck's work. Thus The Philosophical Society of Washington was one of the earliest to pay attention to it. The first real extension of Planck's work came with Einstein's famous paper of 1905, the paper for which he got the Nobel prize. (It is important to realize that Einstein did not get the Nobel prize for the theory of relativity. They might give it to him now if he were around, but they did not in those days.) Planck wrote only one other paper on the subject in that period between 1900 and 1905 and this was mainly an expository paper. There is one brief mention by Burbury, another paper by van der Waals, Jr., and that is all. In those days Planck was almost completely ignored. In Planck's own autobiography he tells of his own attitude toward the Planck constant, and I thought it would be interesting to read his own words on that, of course translated into English. He said: While the significance of the quantum of action for the interrelation between entropy and probability was thus conclusively established, the great part played by this new constant in the uniform regular occurrence of physical processes still remained an open question. I therefore tried immediately to weld the elementary quantum of action, h, somehow into the framework of classical theory. But in the face of all such attempts the constant showed itself to be obdurate. So long as it could be regarded as infinitesimally small, i.e., dealing with higher energies and longer periods of time, everything was in perfect order. But in the general case difficulties would arise at one point or another, difficulties which became more noticeable as higher frequencies were taken into consideration. The failure of every attempt to bridge that obstacle soon made it evident that the elementary quantum of action plays a fundamental part in atomic physics and that its introduction opened up a new era in natural science, for it heralded the advent of something entirely unprecedented and was destined to remodel basically the physical outlook and thinking of man which, ever since Leibniz and Newton laid the ground work for infinitesimal calculus, were founded on the assumption that all causal interactions are continuous. He goes on in a more personal vein to say: My futile attempts to fit the elementary quantum of action somehow into the classical theory continued for a number of years [actually until 1915] and they cost me a great deal of effort. Many of my colleagues saw in this something bordering on a tragedy. But I feel differently about it, for the thorough enlightenment I thus received was all the more valuable. I now knew for a fact that the elementary quantum of action played a far more significant part in physics than I had originally been inclined to suspect, and this recognition made me see clearly the need for the introduction of totally new methods of analysis and reasoning in the treatment of atomic problems. In spite of Jeans' intimate association with this problem, you find no reference whatever to the Planck black-body law in the first edition of his Dynamical Theory of Gases, which was published in 1904, four years after Planck's work. In the Landolt-Bornstein Tables, published in 1905, we find an extraordinary thing, namely, that it gives widely different values for what is often called the Loschmidt number, the number of molecules in one cubic centimeter of various gases under standard conditions. Of course this value should be the same for all gases. But they solemnly give you a table with 2.1×1019 for air, 4.2×1019 for nitrogen, 7.3×1019 for hydrogen, and so on. Apparently Landolt and Bornstein did not believe in the Avogadro number. Planck got 2.76×1019 for this number, which as we have seen is a good value. Josiah Willard Gibbs was America's first great theoretical physicist. He was elected, I find, to membership in the Washington Academy of Sciences in 1900. He died in 1903 at the age of 64. There is no indication in any of his publications or notes that he left behind that he paid any attention to Planck's work. He had puzzled over the problem of the specific heat of polyatomic gases, which everybody was puzzled about at that time, because it has too low a value to correspond with the equipartition law. There is some indication that he found these difficulties with the equipartition law revealed in the specific heat of gases somewhat depressing, and I find an indication of that perhaps in an interesting paragraph from the preface to his famous work on statistical mechanics, published in 1902, a year before Gibbs' death: In the present state of science it seems hardly possible to frame a dynamic theory of molecular action which shall embrace the phenomena of thermodynamics, of radiation and of the electrical rnanifestations which accompany the union of atoms. Yet any theory is obviously inadequate that does not take account of all these phenomena. [There is a wonderful sentence at the end of this paragraph which I think we all ought to realize was written by Gibbs in 1902.] Certainly one is building on an insecure foundation who rests his work on hypotheses concerning the constitution of matter. Lord Kelvin's Baltimore lectures, which were delivered at The Johns Hopkins University in 1884, but were not published until 1904, had a great deal of revision up to that time. The preface to these is very interesting to those who have anything to do with editing or getting things through the press. He admits that he had been working on the revision for all of the 19 years. I can well imagine he was a popular fellow around the print shop. That work includes as its appendix B, the famous lecture to which I am sure you have all heard allusions, "Nineteenth Century Clouds over the Dynamical Theory of Heat and Light." That lecture was delivered in April 1900, some months before Planck's work, and then it was published originally in the Philosophical Magazine of July 1901. It makes no reference to the black-body radiation or to Planck's work, although cloud 2—he had his clouds numbered—was this same concern about the failure of equipartition of energy as evidenced by the specific heats of gases, the same problem that was troubling Gibbs. Lord Rayleigh's publication of what we now call the Rayleigh-Jeans law was in the Philosophical Magazine in 1900. He did not return to the subject again until 1905 when he wrote several notes in Nature in which he concedes or agrees with the comment that Jeans had made about being wrong by a factor of 8. It is interesting in that he says that he "has not succeeded in following Planck's reasoning." That is how Planck's work was received by Lord Rayleigh, one of the greatest British physicists. Rayleigh actually published papers actively through 1919, but he seems to have had no more to say on black-body radiation than what he said in that one 1905 paper. Search through his published papers reveals two more items relating to modern quantum physics. In the 1906 Philosophical Magazine he comments on the classical radiative properties of the atom models that resemble J. J. Thomson's. However, he goes beyond them in that he regards the negative charge as distributed more like a continuous fluid and studies it as a normal mode of vibration problem. In an editorial note that he adds in his collected papers, written in 1911, he refers back to some old work of an 1897 paper. An interesting thing to me appears in this note when he comments that all kinds of models of normal modes of vibrations of continuous systems always come up with formulas in which the square of the frequency is written additively as the sum of contributions coming from the different degrees of freedom—from what we would now call the different quantum numbers. Rayleigh was wedded to a classical vibration theory model where the squares of the frequencies get in because of the second derivative with regard to the time based on Newton's law of mechanics. Nowadays when we lecture on quantum mechanics we just quietly make the Schrödinger equation contain the first time derivative so we will not have this trouble. That is the advantage of making up your equations as you go along as compared with getting them from Newton or somebody like that. Steeped in acoustics as he was, Rayleigh does say: "A partial escape from these difficulties might be found in regarding the actual spectrum lines as due to difference tones from primaries of much higher pitch." That is a well-known device that gives physicists license to pass from a square term to a linear term. That is to say, a small change in the square is linear. There is still something else in the 1906 paper which intrigues me. Rayleigh devotes a paragraph to the problem of the sharpness of spectral lines despite the random character of the conditions of excitation and concludes with a paragraph that sounds very modern. I will quote that: It is possible, however, that the conditions of stability or of exemption from radiation may, after all, demand this definiteness, notwithstanding that in the comparatively simple cases treated by Thomson, the angular velocity is open to variation. According to this view, the frequencies observed in the spectrum may not be frequencies of disturbance or of oscillation in the ordinary sense at all, but rather form an essential part of the original constitution of the atom as determined by conditions of stability. Maybe one reads into that one's present knowledge of the later developments of quantum theory, but I found that very interesting as a foreshadowing of the way we look at it now. Even as late as 1911 we find Lord Rayleigh worrying about Kelvin's cloud 2, the specific heat difficulty, although Einstein had really put that difficulty away in 1907. In 1911 Rayleigh wrote to Walter Nernst to express his concern: If we begin by supposing an elastic body to be rather stiff, the vibrations have their full share of kinetic energy [that is the equipartition law] and this share cannot be diminished by increasing the stiffness…. We all know that increasing the stiffness makes the interval between the vibration quantum levels greater, so that they do not take part practically in the equipartition law simply because they cannot get enough energy to be even excited to the first state. However, Rayleigh goes on: Perhaps this failure might be invoked in support of the views of Planck and his school that the laws of dynamics as hitherto understood cannot be applied to the smallest parts of the bodies. But I must confess that I do not like this solution of the puzzle . . . I have a difficulty in accepting it as a picture of what actually takes place. We do well I think to concentrate attention on the diatomic gaseous molecule. Under the influence of collisions the molecule freely and rapidly acquires rotation. [He knows this from the specific heat.] Why does it not also acquire vibration along the line joining the two atoms? If I rightly understand, the answer of Planck is that in consideration of the stiffness of the union, the amount of energy that should be acquired at each collision falls below the minimum possible and that therefore none at all is acquired [this is of course exactly what we know] an argument which certainly sounds paradoxical. This is the end of it for Rayleigh. So we can see that the acceptance of these ideas was something that came very, very slowly. The examples I have chosen illustrate that very little was stated about the subject at all from 1900 to 1905, and even after that you find the great men of the period hesitant and unwilling to build it into their thinking. Let us now turn to Einstein's famous 1905 paper, which I must confess I had not read until I got to thinking over the preparation for this lecture. It is one of the papers we all hear about in school and worship, but do not read. One of the odd things about this paper is that "h" is not in it, believe it or not. In the paper Einstein denotes by the letter b what we now would call h/k, and then he writes R/N for what we call k, and thus you find in that paper that the energy of a light quantum is not hn at all. It is Rbn/N, which certainly takes a bit of getting used to. The title of his paper is an interesting one: "Heuristic Viewpoint Concerning the Emission and Transformation of Light," indicating I think that he meant that there is something in the paper, but he does not quite know what. At least that is what I mean when I say "heuristic." Einstein might, of course, have meant something else. He says: The energy of a ponderable body cannot be divided into indefinitely many indefinitely small parts, whereas the energy emitted by a point light source is regarded on the Maxwell theory or more generally according to every wave theory as continuously spread over a continuously increasing volume. Such wave theories of light have given a good representation of purely optical phenomena and will surely not be replaced by any other theory. [He was right in that. They have not been replaced.] He Continues: It is to be remembered, however, that the optical observations referred to time mean values, not to instantaneous values, and it is quite conceivable that, in spite of complete success in dealing with diffraction, reflection, refraction, dispersion, et cetera, such a theory of continuous fields could lead to contradictions with experience when applied to phenomena of light emission and absorption. After a little more discussion he makes the key declaration which played such a decisive role in all subsequent developments in which in one sentence he says: According to the supposition here considered, the energy in the light propagated from rays from a point is not smeared out continuously over larger and larger volumes, but rather consists of a finite number of energy quanta localized at space points, which move without breaking up and which can be absorbed or emitted only as wholes. Oddly enough, though everybody quotes this paper purely for the photoelectric effect in the discussion nowadays, the photoelectric effect is only one section, paragraph 8, of the whole paper. The first six paragraphs are concerned entirely with another way of looking at the details of the statistical distribution of the black-body radiation law, and the entropy of radiation along the lines of the quantized wave theory. Finally paragraph 7 is an interpretation of the Stokes' rules for photoluminescence. In ordinary fluorescence and phosphorescence, Stokes' law, which goes way back to 1860, says that the wavelength of the fluorescent light is always greater than the wavelength of the exciting light, or nearly so. There is some radiation, that is called anti-Stokes radiation, for which the wavelength is a little shorter. That puzzled me, why so little stress in Einstein's paper on the photoelectric effect compared with these other things. Then comes section 8 which deals with the photoelectric effect. So I asked Professor A. L. Hughes, one of the pioneers of photoelectric work, who is at our place—he is emeritus professor in Washington University in St. Louis—how that could be. He told me how very primitive the knowledge of photoelectric effect was at that time. No vacuum work on photoelectricity had been done, and even that which had been done was done with very poor vacuums, under very poor conditions. In point of fact no effort to find out the retarding potential required to stop the photocurrent in a definite circuit had been made. What had been observed was that if you insulate a metal object and shine light on it, it will build up to a certain potential and then stay at that potential. That is, it builds up its own retarding potential and finally prevents the escape of further electrons just out in the air. Different metals differed in regard to what potential would be built up by certain light, and it was found that as one went to more and more violet light one got a higher potential. But there were only very crude measurements indeed, so crude that one would hardly think that there was any possibility of a fundamental understanding being involved there. That perhaps is the reason why the photoelectric effect was so little stressed in that paper. The Stokes' law argument was a much more direct experimental one and, conversely, it seems rather odd to me as I think about it, that Stokes' law is not more stressed today in teaching the subject. It was in 1907 that the specific heat work of Einstein clarified the problem of low-temperature specific heat. It is fascinating to look up some of the historical information that is available in the literature. I do not mean that one has to go to ancient history, just the history of the last century. For example, in 1904, when the great St. Louis World's Fair was held, various distinguished visitors were giving lectures. Lord Kelvin gave a speech there that was rather suggestive of a sort of inverse neutrino theory. The thing that was bothering him at that time was—this is a little off the subject of quantum theory, but I think it is interesting—the measurement just made by the Curies of the amount of energy being given off by radium per unit time. They had not measured the half life and the energy given off did not show any signs of weakening, and you know that physicists are great on extrapolation. They said that radium gives off energy perpetually—that was the word, perpetually. So the question was, how could anything radiate perpetually at this tremendous rate, unheard of when expressed in terms of energies of usual chemical reactions. Kelvin had an idea which he propounded at this talk, that perhaps there was some kind of energy that we were not able to detect—like the neutrinos—that was floating around in space, and that radium had the property of absorbing it in that form and then reconverting it, like a fountain, and shooting it out, and that is what we observe. Even in those days people were perfectly willing to balance the books on conservation of energy in ways like that. The next major historical event was the development of the Bohr atom model in 1913. At this point, since we are just talking a little bit of anecdotal material about the history of our subject, I will tell a story that I learned from George Gamow. The young Bohr—he was about 26 at that time—came to England from Copenhagen to work in the Cavendish Laboratory. The great J. J. Thomson was at the height of his powers. Bohr came to the great center to study fundamental atomic physics; but within a few months he left the Cavendish Laboratory and went up to Manchester to work under a relatively unknown fellow named Rutherford. The question is why did he do that? According to Gamow, Bohr had gotten into trouble with "J. J." because he was a little critical of the Thomson atom model, and "J. J." had politely indicated to him that it might be nice if he left Cambridge and went to work with Rutherford. That is how Bohr went to work for Rutherford, which was advantageous, I think, for all. It was not so good for the Thomson model but it was fine for the future development of physics. To bring this story up to date, Gamow told me that in 1928, when he worked on the alpha particle tunneling paper, the basic work which Gurney and I did simultaneously in Princeton, Rutherford sent Gamow to see Bohr and to tell him about this exciting new development. He also wrote him a letter—which Gamow said he still has a copy of—saying, "Please pay attention to this fellow; there is something in it. It isn't cockeyed. You remember how it was with you when you went to 'J. J.' and he wouldn't listen; so now you listen to Gamow." I do not know whether there is any truth in that or not, but at any rate Bohr did listen to Gamow. Of course, the most exciting immediate experimental consequence of Bohr's work was, besides the direct interpretation of the spectrum of hydrogen that was well known at that time—I mean the facts of the Balmer series, which went way back into the 19th century—was the interpretation of spectroscopic term values as being energy levels with the associated implication that controlled electron impact would produce controlled excitation of atoms and molecules. This was the work that was immediately followed up by James Franck and Gustav Hertz, and for which they received the Nobel prize in physics in 1926. That work was very quickly taken up here in Washington, in the pioneer work of Paul Foote and F. L. Mohler. At the National Bureau of Standards the accountants were rather stuffy, and had rather sharp lines about appropriations and budgets, so that all the work on critical potentials for which the Bureau of Standards became famous was carried on under a budget number which had something to do with improving pyrometric methods. I am not quite sure whether this work helped much pyrometry but it certainly was a great addition to the development of fundamental science. The period of the second decade of our subject was also characterized by the very first extension of the idea of quantized energy levels to the interpretation of band spectra, rotation and vibration spectra, and infrared. A curious thing about the atom model work of Bohr, prior to 1923 or 1924, was that if you look at the current papers you get the impression that everybody in the world was terrifically excited about the Bohr model and believed in it hook, line, and sinker, including the atom orbits as they are used in the ads for the atomic age nowadays. Bohr on the other hand was constantly making remarks, speeches, and admonitions to the effect that this is temporary and we ought to be looking for a way to do it right. The great breakthrough, as the saying goes nowadays, came about 1924,1925, and 1926, when the idea of waves of accompanying electrons was first published by Prince Louis de Broglie as a doctor's thesis, and was again ignored. I do know anybody who read that paper until a year or two later. Erwin Schrödinger then founded the great discoveries of wave mechanics on de Broglie's work which were published in the spring of 1926 in a series of papers in the Annalen der Physik. Just before Schrödinger's work in late 1925, Born, Jordan, and Heisenberg had developed the matrix mechanics methods. For about a year they were thought of as two rival and distinct theories, until Schrödinger and Carl Eckart, a young physicist in Chicago, who is now in La Jolla, recognized the mathematical identity of the two theories. I had the good fortune to get my doctorate in the summer of 1926 when all these things were at their highest peak of excitement, and went to Göttingen to work with Born. There was a young graduate student there named Robert Oppenheimer whom I got acquainted with at that time. This was an extremely difficult period because the rate of advance was so great, and the whole subject was so obscure to all of us that it was an extremely difficult thing to keep up with matters. I remember that that fall David Hilbert was lecturing on quantum theory, although he was in very poor health at the time. He had anemia, and liver extract was not available at that time and he was eating a vast quantity of liver every day and saying he would rather not live than eat that much liver. His life was saved by the fact that the liver extract was discovered just about that time. But that is not the point of my story. What I was going to say is that Hilbert was having a great laugh on Born and Heisenberg and the Göttingen theoretical physicists because when they first discovered matrix mechanics they were having, of course, the same kind of trouble that everybody else had trying to solve problems and manipulate and really do things with matrices. So they went to Hilbert for help, and Hilbert said the only times that he had ever had anything to do with matrices was when they came up as a sort of by-product of the eigenvalues of the boundary value problem of a differential equation. So if you look for the differential equation which has these matrices you can probably do more with that. They thought that was a goofy idea, and that Hilbert did not know what he was talking about. So he was having a lot of fun pointing out to them that they could have found out Schrödinger's wave mechanics six months earlier if they had paid a little more attention to him. I mention some of the things that were occurring during those years because I do not believe that anybody who did not live through that period has quite an appreciation of what a tremendous number of new discoveries were made at that time that are still of fundamental importance, and have blossomed out into whole new areas of physics that are subjects for courses in themselves. In 1926 we had the whole wave mechanics as we know it, and the whole matrix mechanics formulated. And just a little before that, we had the discovery of the electron spin and of the Pauli exclusion principle. In 1927 came the whole theory of the chemical valence bond as a perturbation problem in quantum mechanics with correlations over electron pairs with their spins antiparallel. Then came almost simultaneously with that the whole development of Fermi-Dirac statistics and its clarification of the problems of metal theory. A few months after that, came the Dirac papers on the quantization of the electromagnetic field which explained at last the difference between spontaneous and induced emission and put the two together in a unified theory. Soon after that came the whole Dirac relativistic theory of the electron which later led to the prediction of the positron. It was a little after that, in 1928, that the interpretation of natural alpha radioactivity came as a consequence of the barrier leakage idea, also an essential element of quantum mechanics and an essential element of its statistical or probability interpretation. I think it is fair to say that the barrier leakage idea was the opening of the modern period of the application of quantum mechanics to nuclear physics. Nuclear physics, in terms of real specific models, has never had a classical past. Nobody tried in those days to develop specific models of the structure of a nucleus. Another big year for discoveries was 1932, the year in which heavy hydrogen was discovered, which from a nuclear point of view means the deuteron, the year in which the first production of an artificial nuclear reaction was accomplished by Cockcroft and Walton, and the year in which the positron was discovered, the antiparticle associated with the electron, as we call it nowadays. In that same decade, a few years later, 1936 saw the development of the Fermi theory of beta decay based on the neutrino hypothesis that had been introduced by Pauli, in almost a joking way, a year or two earlier. I remember in the summer of 1937 when we had a conference on beta decay theory at Cornell University, and a lot of us were having trouble worrying about it, Fermi was in the audience sitting in the back row just smiling and smiling as he usually did. People tried to get him to comment, and he said, "I have always been surprised that people take that theory so seriously." But, of course, as we know, it has turned out to be remarkably correct; that is, the basic formalism which Fermi developed then for accounting for the four-fermion interactions, even in spite of the great crisis it went through in 1957 with the discovery of nonconservation of parity. The basic formalism, as Fermi first introduced it, has beautifully stood the test of time. Of course in the year 1936 you have work which is important to us here because it was done by prominent people in Washington. I refer to the work of Hafstad, Heidenberg, and Tuve in the first real studies of proton-proton scattering, which gave direct evidence of forces between protons other than the Coulomb forces, that is, short-range nuclear forces between protons. The theoretical interpretations of those results was largely done by Gregory Breit and myself up in Princeton, associated with Richard Present, who is now at the University of Tennessee. That gave the first evidence that we had of what is now called the charge independence of nuclear forces, because the additional short-range force that was revealed in this way turned out quantitatively to be very closely the same as the force between a proton and a neutron that is revealed in the normal state of the deuteron. From about 1932 on we have the whole field of nuclear physics coming into being in a big way with deuterons available, with machines available, both cyclotrons and Van de Graaf machines. In the latter part of that decade we began to have the first theories of Bethe and Marshak on the application of specific models of nuclear reactions to finding satisfactory sources of stellar energy. I think perhaps I must give up at this point, because the last two decades have seen such an overwhelmingly rapid and vast amount of progress, spreading out into a great many different fields, that one could not possibly in the short time remaining do more than just mention it. We had, in the decade from 1940 to 1950, the whole development of the modern point of view on quantum electrodynamics. It came rather late in the decade, with the discovery of the Lamb shift and the experimental confirmation of the abnormal magnetic moment of the electron, the fact that it was somewhat off from the original Dirac theory. We had at last the clarification of the puzzling features of the mesons in cosmic rays whereby it turned out that there were the two kinds, the pi mesons and the mu mesons, the pi mesons decaying into the mu mesons. The latter part of the decade represented the beginning of public knowledge of fission, and the engineering and political uses of fission. At the same time, going off in quite another direction, what has turned out to be of equal importance has been the whole wide development of the application of Fermi statistics to electrons in solids, first resulting in the major classification of properties of metals, then of semiconductors, and then finally of really modern tailored effects that led to devices such as transistors and so on. The decade just passed has corresponded to an enormous further development along these same lines. We have the study of nuclear reactions going on up to higher energies of some hundreds of millions of volts, with predominant interest in the study of polarization effects in nuclear reactions as another way of getting at points of detail; the recognition of the nonconservation of parity; the experimental discovery of the neutrino; the recognition that the Fermi interaction that applies in weak interactions is more general than simply the beta decay and also applies to muon decay and other related processes; and the discovery of the strange particles. And then finally, as a roundup of mentioning things that we do not have time to talk about, the extraordinarily fine extensions that have been made in the last five years of the theory of broad, modern, good perturbation theory methods for dealing with the many-body problem. That involved not only the better calculation of nuclear models but also, at last, after many years of effort, is beginning to provide a real understanding of superfluids. In conclusion I should like to emphasize again that all this scientific activity started almost exactly sixty years ago—barring two weeks—on December 14, 1900, when Planck's constant was first introduced into physics. In the sixty years that have intervened it is now almost impossible to find many papers in physics which do not deal directly or indirectly with phenomena that are fully and basically conditioned by the existence of that one universal constant.