Quantum Theory in 1929

Recollections from the first Copenhagen conference

L. Rosenfeld

Although in the historical perspective the first Copenhagen conference in 1929 rather marks the completion of a heroic period in the life of the Institute than the initiation of its activity fifty years ago, the celebration of the jubilee may be a fitting occasion for calling up recollections of an elating week when the Copenhagen spirit hovered over the troubled waters from which quantum theory had just emerged. The circumstances of this gathering loom large in my own memory: I was then a mere tiro, and the pictures I have kept of the events has all he vividness of the first glimpse into a wonderful world; I have therefore no scruple to revive it, as a testimony of the mood in which a new generation was then taking the cue from the pioneers to carry on the unending quest. In fact, I have once before written down some of my impressions of this famous week under the title "My initiation", which conveys this mood. It was a lighthearted, but truthful tale, which had the honour of publication in the 1945 issue of the Journal of Jocular Physics; I do not want the present account to be much more solemn, and I shall take the liberty of quoting occasionally from the previous one.

As most good things in the world, the idea of this conference was due to chance. In Bohr's own words: Der Plan zu dieser Konferenz ist dadurch entstanden, dass mehrere Physiker, die früher hier gearbeitet haben, besuche in Kopenhagen in den Osterferien angemeldet haben. Da wir unter anderen auf die Anwesenheit von Kramers und Pauli rechnen, wird es wohl zu lebhaften und lehrreichen Diskussionen Anlass geben könen ... [1] It was quite in line with Bohr's paternal attitude that this fortuitous conjunction of visits should have prompted him to summon a full-scale family reunion. Not all could manage to be there, but a good twenty of them from all over Europe responded to the call: from Cambridge, Bohr's old friend from the Manchester time, Darwin; from Leiden another near friend, one of the great masters from the classical era, Ehrenfest, accompanied by one of his youngest students, Casimir; from Utrecht, Bohr's first collaborator, Kramers, who had left Copenhagen three years before to take up the Utrecht chair; from Zürich came Pauli, who with his acutely critical mind, was already then, as Bohr used to put it, "the conscience of the physicists"; further from Holland, Germany and Scandinavia a number of those who, each in his domain of predilection, had shared in the edification of the atomic theory: Goudsmit and Kronig, Hückel, Fues, Jordan, Heitler and Nordheim, Rosseland, Holtsmark and Waller. My own good luck was due to the circumstance that I had some time before written to Bohr to enquire whether I could come to work under his guidance; he generously counted me as a disciple in spe. At the time, four foreign visitors were staying in Copenhagen; they added their disctintive features to a variegated assembly: Mott's Cantabrigian elegance, Trumpy's Norse cheerfulness, the quiet composure of the Chinese Chou were overshadowed by the whimsical fantasy that Gamow had brought to the West from the lively group of young Soviet physicists. As to the Institute's staff, it consisted of two experimenters, S. Werner and J.C. Jacobsen, and of Bohr's closest collaborator, Oskar Klein, who had succeeded Kramers and Heisemberg in this position of trust. Among the handful of Danish students who attended the proceedings, we find the familiar names of Christian Møller, Bengt Strömgren, Mogens Pihl and the regretted Ebbe Rasmussen.

The conference was due to start on Monday the 8th of April, and a number of the pilgrims travelled on the preceding Sunday. They all met inevitably on the deck of the ferry from Warnemünde to Gedser. There was much handshaking, exchange of news and shop talk. This was my maiden trip, and a propitious day for a first view of the Danish scenery, in the timid budding of spring, with flags daily flying in front of every thatch roofed farmhouse (not, as I learned from my more experienced companions, in honour of the conference, but just as a weekly manifestation of homely content). The old-fashioned look of the ferries and railway carriages, the queer funnels of the locomotives, the easy-going demeanour of the railway people and of the local passengers at the cosy red-brick stations where the train unhurriedly lingered, all concurred to build up the impression of a simple-minded, un demanding peasant community, happily confined to its own well protected little world. Tourist agents had not yet discovered how idyllic a country it was, how wonderful its capital.
The pleasant feeling of old-time hospitality conveyed by the Danish countryside came to a climax on our arrival at Copenhagen. Niels Bohr himself was awaiting us on the platform, together with his brother Harald, his lieutenant Klein and a few boys of various sizes, obviously his sons. I recognized Harald, whose lectures on almost periodic functions I ha attended in Göttingen, and I shook hands with Niels for the first time. He received me with a broad, benevolent smile; I was struck by the cordial simplicity with which he greeted old friends and newcomers alike. Fro the station I strolled to the boarding house I had been assigned, on the Vester Boulevard, then a spacious promenade lined with stately elms, which formed a worthy setting for the little trumpeter's eternally unavailing last call. At dinner, I had occasion to experience how the Danes could sometimes overdo their hospitable attentions. They subjected me to the ordeal of pronouncing rødgrød med fløde, and adding insult to injury, expected me to find the stuff delicious.

On the next morning, we all flocked to the Institute lecture room; old acquaintances were reniewed, new ones formed. I happened to be nearby when a beaming Ehrenfest came in and went straight to greet Bohr, followed by a tall, fair-haired, rosy-cheecked youth of rather indolent gait, who did not quite know what to do with his arms. Ich bringe Dir diesen Knaben, he said to Bohr, while he affectionately put his hand on the boy's shoulder. Er kann shon was, aber er braucht noch Prügel. Well, in the course of the week, Casimir was going to show us, unobtrusively, that he indeed could do something. Goudsmit was then applying his extraordinary skill to the classification of hyperfine spectra and was naturally anxious to know what the contribution of the electron spin to the hyperfine structure would look like. As soon as he heard Goudsmit mention the problem, Casimir keenly responded: he asked Goudsmit some brief questions and, lost in meditation, withdrew to a quiet corner; but let us hear the story from himself [2]: At the time of the conference Dirac's theory of the spinning electron was still fairly new ... I had studied the paper and also Weyl's Gruppentheorie und Quantenmechanik and had been much impressed by the beautiful simplicity of the current distribution in the fundamental state of the hydrogen atom. So when Goudsmit asked me whether I could calculate the hyperfine interaction in a S state I realized at once that one had only to calculate the magnetic field of the current. I arrived at the formula

where the nuclear moment is given by . Goudsmit supplied an estimate for for "Tauchbahnen" and we obtained pretty nice results for Na if I remember well. After the conference I wrote a manuscript --a fairly clumsy one I fear-- which I sent to Goudsmit. I got it back, much later but soon afterwards Fermi's manuscript "Ueber die magnetischen Momente der Atomkerne" was received (18. Dec. 1929) by Zs. für Physik and appeared (Z. für Physik 60, 320, 1930). It was quite edifying to watch Casimir's eagerness in working out this problem. One evening we, some of us went to see the pictures, and persuaded him to join us. In those days, they showed one reel of film at the time, and lit the room every time they changed reels; at each recurrence of the light, we could see our friend bending over odd scraps of paper and hastily filling them with formulae.
Commenting on the decisive part of the unravelling of the spectral regularities had played in the development of atomic theory, and mentioning especially Goudsmit's virtuosity in this art, Bohr told us that the latter's talent for tracking hidden order in apparent capriciousness was by no means limited to physics; he also exercised it on classifying the types of representation of sacred scarabs by the ancient Egyptians. On Goudsmit's first visit to Copenhagen in 1926, Bohr had been with him to see the collection of Egyptian sculpture at the Glyptotek; as he started translating the Danish labels for Goudsmit's benefit, the latter quietly told him it was not necessary, as he could read the inscribed hieroglyphs. Bohr had a large stock of such pointed anecdotes, reflecting his warm interest in people, that he was never tired of telling in those conversation with the older and younger physicists clustered around him, during which he freely expressed his thoughts on the prospects of current research as well as the widest implications of science, and displayed the best of his wisdom and deep humanity.

Bohr as a lecturer is a different matter. It is much glossed, but very little written about. Perhaps the only one who has put his view of it in print so far is Larmor; ina speech (later published [3]) at the Maxwell celebration in Cambridge in 1931, he commented upon Maxwell's reputation of being a poor lecturer and roundly added: So perhaps with our friend Bohr: he might want to instruct us about the correlations of too many things at once ... I was sitting near Bohr when the speech was delivered; as this judgement was expressed, Bohr whispered to me: Imagine, he thinks I am a poor lecturer! Bohr's lectures, composed with tremendous labour, were indeed masterpieces of allusive evocation of a subtle dialectic; the trouble was that the audience was usually unprepared to catch subtle allusions to conceptions and arguments which were anyhow unfamiliar and hard to grasp.
I am not sure whether Bohr's introductory talk at the conference was really worse than the average; perhaps he had not prepared it so thoroughly, since the idea was to have quite informal discussions: no programme had been set up in advance - Bohr took in turn each of the participants aside and asked him what topic he wished to bring up. At any rate, here is the impression this talk has left in my memory, as I described it (with some hindsight) in 1945: He had begun with a few general considerations calculated, no doubt, to convey to the audience the peculiar sensation of having the ground suddenly removed from under their feet, which is so effective in promoting receptiveness for complementary thinking. This preliminary result being readily achieved, he had eagerly hastened to his main subject and stunned us all (except Pauli) with the non-observability of the electron spin. I spent the afternoon with Heitler pondering on the scanty fragments of the hidden wisdom which we had been able to jot down in our note books.
It was comforting to hear from Klein, when I told him some time ago of our failure to understand what Bohr meant by the impossibility of measuring the spin of the electron, that he had the same difficulty when Bohr first discussed the matter with him in the autumn of 1928. Guided by the general correspondence idea, Bohr argued that such a purely quantal concept as the electron spin, vanishing from the theory in the classical limit, could not possibly be brought in direct relation with classical quantities like angular momentum or magnetic moment. It was not immediately clear to Klein, however, how this correspondence argument could be reconciled with the Stern-Gerlach effect, which clearly exhibited a contribution to the magnetic moment of an atom from an electron bound in a 2S state; but what Bohr demonstrated was precisely that with a free electron a Stern-Gerlach experiment could not succeed, because the effect of the Lorentz force would inevitably blur any Stern-Gerlach pattern. This is the point he ineffectually tried to make in his talk. Fortunately, Mott, during his stay at the Institute, had been engaged in the problem of electron polarisation, and in the paper [4] in which he brilliantly showed how this property could in principle be ascertained by a double scattering experiment, he gave a very clear account of the whole situation. He finished writing this paper shortly after the conference (it was sent off by Bohr on the 25th of April) and we were thus soon able to appreciate at leisure the full force of Bohr's famous argument.

The incorporation of the spin into the relativistic quantum theory of the electron had not removed from this theory the riddle of the negative energy states. Klein had just given a striking illustration of the acuteness of the difficulty by showing that electrons impinging upon a sufficiently high and steep potential wall would not only suffer reflexion, but that a sizable fraction of them would penetrate through the wall and undergo a transition to states of negative kinetic energy [5]. At the conference, he submitted, tentatively, a way to escape from this "paradox": it amounted to treating the electrostatic potential as an operator whose eigenvalues would have a finite higher limit. Jordan pointed out that in order to eliminate the paradox, this highest potential value should be of an order of magnitude quite within the range of observation; probably it ought to be something like (m denoting the electron mass). Potential differences of this magnitude are indeed observed between thunderstorm clouds and the earth.
Jordan's remark caught Bohr's imagination: here was a possible test of Klein's assumptions. The limiting potential would presumably entail a limit to the stability of matter: if it did occur in a thunderstorm, a bird flying in the region of highest potential would then be killed. The discussion went on, to and fro, as various consequences of Klein's formalism were either put forth in support of it or found to raise difficulties. Bohr kept musing about the fate of the bird, to Ehrenfest's boundless amusement. Whenever the discussion ebbed out for a moment: Now, Bohr, he would ask with boyish mischief, is the bird still alive?
When we gathered again after lunch, Klein declared that he was now convinced that his proposal would not work and that he withdrew it. This was probably the shortest lifespan ever meted out to any theory. For all his apparent playfulness, Ehrenfest took very much to heart the difficulties in which relativistic quantum theory seemed to be bogged. I got an inkling of this the next day, when, much to my surprise, I was told, shortly after the end of the session, that Bohr wanted me to come to his house (which was adjacent to the Institute and now part of it). I was ushered into his study, where I found him and Ehrenfest installed in comfortable armchairs and, judging by their smiles, engaged in pleasant conversation. Could you tell us, Ehrenfest asked me with his wonted directness, why the relativistic Klein-Gordon theory is unacceptable? - Because, I replied pedantically, the charge-current density is not of definite sign. - Yes, said Ehrenfest, but could you just give us an example in which this property leads to unphysical consequences? I never felt so sheepish in my life. Ehrenfest turned to Bohr: You see, he said, just as I told you! From this remark I surmised with some relief, - and my guess was soon confirmed by the ensuing conversation, - that they did not impute the fiasco to my personal stupidity, but took it as an illustration of a widespread failing of the young generation, prompt to uncritical acceptance of dogmatism. Bohr intervened with a soothing pronouncement about how hard it was to imagine how the behaviour of the electron could be described beyond the limit where correspondence with the classical point-charge picture afforded legitimate guidance; we must here be prepared for further renouncement in the application of classical concepts. How often were we to hear this warning in the following years, until the discoveries of the neutron and the positive electron broke the spell!
In retrospect, one cannot help admiring the penetration and independence of judgment revealed by Ehrenfest's iconoclastic questioning. And yet (as I later learned from Bohr), he was at the same time turning his searching criticism against himself: he realized that progress in such untried regions of thought and imagination as quantum theory had opened, demanded adventurous minds, unhampered by the scruples and doubts that assailed him; he imagined he was losing his grip on physics and - worse still for one always ready to pour out a wealth of affection on the youth - getting out of touch with the coming generation. Of this inner tension there was no outward sign, however: to the last we saw him as cheerful, witty and warmhearted as ever.

Pauli, so far as I remember, was rather subdued, except on one spectacular occasion. Heitler, by lecturing on the theory of homopolar bond, unexpectedly excited his wrath: for, as it turned out, he had a strong dislike to this theory. Hardly had Heitler finished, that Pauli moved to the blackboard in a state of great agitation; pacing to and fro he angrily started to voice his grievance, while Heitler sat down on a chair at the edge of the Podium. At long distances, Pauli explained, the theory is certainly wrong, since we have there the Van der Waals attraction; at short distances, obviously, it is also entirely wrong. At this point he had reached the end of the podium opposite to that where Heitler was sitting. He turned round and was now walking towards him, threateningly pointing in his direction the piece of chalk he was holding in his hand: Un nun, he exclaimed, gibt es eine an den guten Glauben der Physiker appellierende Aussage, die behauptet, dass diese Näherung, die falsch ist in grossen Abständen und falsch in kleinen Abständen, trotzdem in einem Zwischengebiet qualitativ richtig sein soll! He was now quite near to Heitler. The latter leaned back suddenly, the back of the chair gave way with a great crash, and poor Heitler tumbled backward (luckily without hurting himself too much). Casimir, who also remembers the incident, notes that Gamow was the first to shout: Pauli-effect! And as an afterthought he adds: Sometimes I wonder whether Gamow had not done something to the chair beforehand.

I found Gamow as jolly as I had always known him in Göttingen since the first day I saw him appear at Born's institute and heard of his surprising intention of applying quantum mechanics to alpha-radioactivity. His direct approach to the problem was, of course, most congenial to Bohr, who had supported him wholeheartedly when he had to counter Laue's doubts about the lawfulness of the new type of solution he had introduced [6]. I was then too much indoctrinated with Göttingen lore not to side with Laue in this debate; the more so as Born had just shown us how he wanted to treat the problem by a somewhat hazardous, but very ingenious, extension of hortodox perturbation technique [7]. When remonstrating with Gamow in the library, I went so far as to express doubt whether Gamow wavefunctions, with their infinite norm, could at all be regarded as solutions of a Schrödinger equation. Pauli happened to overhear this rather wild statement: They are certainly solutions, he interjected, but whether they are allowed in quantum mechanics, this is questionable. Gamow looked at us with an expression of wonder in his face: But my solution, he said, just represents a damped resonance process; the exponential increase at large distances has a simple interpretation, and after all I get the decay constant and an improved Geiger-Nuttall law. What else do you want? -- Anyhow, Pauli concluded as he went away, it was great fun to see the flood of papers your theory let loose.
I don't understand what all this fuzz is about, Gamow continued, It is just a solution of a partial differential equation, of the kind we use in mechanics and elasticity. When I showed it to Bohr, he was at once enthusiastic. I was so pleased and proud that I wanted to show him something more. I had noticed that the Schrödinger equation could be written as a classical diffusion equation, - only with a purely imaginary diffusion coefficient. Now, I had better kept that to myself: Bohr's reaction to it was anything but enthusiastic ...

On Gamow's work, which ushered in nuclear physics, there was no debate. Mott, however, presented his analysis of the scattering of alpha-particles by helium [8], which was received with considerable interest. It was a beautifully simple case of an interference effect arising from the identity of the interacting particles, the first concrete example of the intervention of Bose statistics in an individual process. It was also a good lesson in the correct interpretation of a wave-function - an art then so new that Mott's argument was not accepted without some resistance on the part of one or two participants.
Darwin was deeply interested in these problems of interpretation; he did extremely helpful work discussing in great detail, with consummate mathematical skill in the best Cambridge tradition, a variety of idealized experimental devices illustrating typical features of quantum mechanics. The one he submitted at the conference [9] was a rather complicated case of constructive interference of wave-packets producing spontaneously the results which simple intuition would suggest could only be due to particles. The analysis was as brilliant as ever, but unfortunately carried him away, at the end, onto splippery ground. He argued that the seat of an observation could be shifted from the physical receptor to the retina, and thence to somewhere in the brain, where we are absolutely compelled to stop. Right up to the brain the process is non-committal: it is only after our consciousness has animated the proceedings that it is possible to infer back and describe what actually happened in the familiar language of particles. Thus, we have a sub-world described by a wave-function, a dead world, not involving definite events, but instead the potentiality for all possible events. It becomes animated by our consciousness, which so to speak cuts sections of it when it makes observations.
This remarkable anticipation of von Neumann's Schnitt conception struck me as being quite beside the point. It cannot make any difference by how many eyes, or brains, a scintillation on a screen is observed, and there is no reference in the formalism (then my only anchor!) than to the particle producing scintillation: the structure of the eye or the brain, or even that of the screen, is quite irrelevant. These were (as near as I can figure out after so many years) the confused thoughts that crossed my mind as I listened to Darwin. What troubled me mightly, however, was Bohr's failure to react to propositions which seemed to me so alien to the ideas he had expressed in the Como lecture. I was so disturbed by what I mistook for silent acquiescence that, mustering all my courage, I approached Bohr and cautiously started to voice my doubts. Oh! he said, interrupting me, this was all nonsense!
Then he motioned me to a neighbouring room, which had been Hevesy's laboratory: it was lined with cupboards, behind whose glass doors one could see rows of flasks containing brilliantly coloured solutions of rare-earth compounds. In the middle of the room there was a long table, and I stood at one extremity of it. I cannot find better words to tell what happened next than those I wrote in my previous article: Bohr described around the table, "at a rather lively pace, a Keplerian ellipse of large excentricity, of which the place where I was standing was a focus. All the time, he was talking in a soft, low voice, explaining to me the broad outlines of his philosophy. He walked with bent head and knit brows; from time to time he looked up at me and underlined some important point by a sober gesture. As he spoke, the words and the sentences which I read before in his papers suddendly took life and became loaded with meaning. It was one of the few solemn moments that count in an existence, the revelation of a world of dazzling thought, truly an initiation." Bohr was particularly well prepared to comment on the problems Darwin had raised: he was just writing up (in a short essay [10] in honour of the 50th anniversary of Planck's doctorate) his reflexions on the complementary aspects of psychical phenomena. As an example of the shift that can occur in the separation between observing subject and object of observation, he mentioned the case of a cane held in the hand: if it is held firmly, it is an instrument extending the range of tactile perception of the subject, who feels it as a part of himself; if it is held loosely, it ceases to serve as an instrument and becomes an object of observation. He was quite excited about this effect. He insisted that I should try with a pencil that was lying on the table, and he watched me intently during the operation, eager to catch on my face a sign of the joyous wonder I could not fail to experience.

I have not too much to tell about the obligatory three-castle tour, with a stop at Bohr's country house at Tisvilde, a long walk through the wood to Brantebjerg and along the strand to the village. The more enterprising displayed their sportive talents; Bohr was outstanding at ricochet throws of pebbies on the sea, but most spectacular was Jordan's acrobatics (it was rumoured he had lately taken to jiu-jitsu). I would rather recall an afternoon outing of a small group of us, among whom Ehrenfest, to Christianshavn, where Bohr wanted to show us Our Saviour's church. We took the boat at Nyhavn and landed near the famous church, with its queer outer staircase winding up along the steeple. I was thrilled of the thought of seeing this monument, about which I had read as a boy in Jules Verne's Voyage au centre de la terre. From the landing place the steeple looked curiously flat; Ehrenfest had the same impression: It looks as if it had an elliptic cross-section - if this were possible, he said. One ascends to the steeple from inside the church; one first arrives at a kind of platform, on which lies, idle and rusty, a huge clockwork dating, as we ascertained, from the time of Huygens, and Newton. Here was the real goal of the trip. Bohr exulted: This shows us what classical mechanics is about, he exclaimed. Nobody that sees this can doubt that our measuring instruments must be big bodies!
Next time Jauch comes to Copenhagen, I must take him to Our Saviour's church.

References