‘The quantum theory of radiation,’ pp. 785-802 in Philosophical Magazine, Sixth Series, Vol. 47, No. 281, May 1924.

London: Taylor & Francis, [1924].

First edition, very rare offprint, inscribed by one of Bohr’s closest friends and collaborators, of this celebrated paper. “Its idea of modeling atomic behaviour under incident electromagnetic radiation using ‘virtual oscillators’ led Born and Heisenberg to explore mathematics that strongly inspired the subsequent development of matrix mechanics. The most striking feature of this remarkable paper, ‘The Quantum Theory of Radiation,’ was the renunciation of the classical form of causality in favor of a purely statistical description. Even the distribution of energy and momentum between the radiation field and the ‘virtual oscillators’ constituting the atomic systems was assumed to be statistical, the conservation laws being fulfilled only on the average” (DSB, under Bohr). “Although this idea was not substantiated by subsequent experimental and theoretical work, the paper had a profound influence” (DSB, under Kramers). In spite of its success in explaining the photoelectric and Compton effects, Bohr could not accept the light-quantum hypothesis, writing in his Nobel lecture in December 1922, “In spite of its heuristic value … the hypothesis of light-quanta, which is quite irreconcilable with so-called interference phenomena, is not able to throw light on the nature of radiation.” But when the young American physicist John Slater arrived in Copenhagen just before Christmas 1923, and explained his new ideas on radiation theory, Bohr saw a way to explain the Compton effect without invoking light quanta. “BKS begin by recalling that ‘the exchange of energy and momentum between matter and radiation claims essentially discontinuous features. These have even [!!] led to the introduction of light-quanta…’ They abandon light-quanta in their own paper, replacing this concept by a new one ‘due to Slater … the atom, even before the process of transition between stationary states takes place is capable of communicating with distant atoms through a virtual radiation field’, a field distinct from the conventional, real radiation field. This virtual field, carried by the atom in a given stationary state, was supposed to know and carry all the possible transition frequencies to lower states, one might say, to release one of these frequencies. Emission of light in an atomic transition is, BKS posited, not spontaneous but rather induced by the virtual fields ‘by probability laws analogous to those which in Einstein’s theory hold for induced transitions’. Accordingly, ‘the atom is under no necessity of knowing what transition it is going to make ahead of time’” (Pais, Niels Bohr’s Times, pp. 236-7). “The paper was hardly in print before A. H. Compton and A. W. Simon had established by direct experiment the strict conservation of energy and momentum in an individual process of interaction between atom and radiation. Nevertheless, this short-lived attempt exerted a profound influence on the course of events; what remained after its failure was the conviction that the classical mode of description of the atomic processes had to be entirely relinquished” (DSB, under Bohr, p. 247). 

Provenance: Fritz Kalckar (1910-38), Danish physicist (signature on front wrapper, marginal annotations in text). Kalckar was one of Niels Bohr’s closest collaborators in Copenhagen after Bohr turned the main attention of the Institute for Theoretical Physics to nuclear physics in the 1930s. In 1937, the year before his death from a cerebral haemorrhage at the age of 27, Kalckar published with Bohr ‘On the Transmutation of Atomic Nuclei by Impact of Material Particles’, in which they introduced the famous ‘liquid drop’ model of nuclear structure.

“It was the position of most theoretical physicists during the first decades of the quantum era that the conventional continuous description of the free radiation field should be protected at all cost and that the quantum puzzles concerning radiation should eventually be resolved by a revision of the properties of interaction between radiation and matter. The BKS proposal represents the extreme example of this position. Its authors suggested that radiative processes have highly unconventional properties ‘the cause of [which] we shall not seek in any departure from the electrodynamic theory of light as regards the laws of propagation in free space, but in the peculiarities of the interaction between the virtual field of radiation and the illuminated atoms’. Before describing these properties I should point out that the BKS paper represents a program rather than a detailed research report. It contains no formalism whatsoever. This program was not to be the right way out of the difficulties of the old quantum theory, yet the paper had a lasting impact in that it stimulated important experimental developments. Let us discuss next the two main paradoxes which BKS addressed.

The first Paradox. Consider an atom which emits radiation in a transition from a higher to a lower state. BKS assume that in this process ‘energy [is] of two kinds, the continuously changing energy of the field and the discontinuously changing atomic energy’. But how can there be conservation of an energy which consists of two parts, one changing discontinuously, the other continuously? The BKS answer: ‘As regards the occurrence of transitions, which is the essential feature of the quantum theory, we abandon … a direct application of the principles of conservation of energy and momentum.’ Energy and momentum conservation, they suggested, does not hold true for individual elementary processes but should only hold statistically, as an average over many such processes. The idea of energy non-conservation had already been on Bohr’s mind a few years prior to the time of the BKS proposal. However, it was not Bohr but Einstein who had first raised—and rejected—this possibility. In 1910 Einstein wrote to a friend: ‘At present I have high hopes for solving the radiation problem and that without light-quanta. I am enormously curious how it will work out. One must renounce the energy principle in its present form.’ A few days later he was disenchanted: ‘Once again the solution of the radiation problem is getting nowhere. The devil has played a rotten trick on me’. He raised the issue one more time at the 1911 Solvay meeting, noting that his formula for the energy fluctuations of black-body radiation could be interpreted in two ways: ‘One can choose between the [quantum] structure of radiation and the negation of an absolute validity of the energy conservation law.’ He rejected the second alternative. ‘Who would have the courage to make a decision of this kind … We will agree that the energy principle should be retained.’ But others were apparently not as convinced. In 1916 the suggestion of statistical energy conservation was taken up by Nernst. Not later than January 1922 Sommerfeld remarked that the ‘mildest cure’ for reconciling the wave theory of light with quantum phenomena would be to relinquish energy conservation. Thus the BKS proposal must be regarded as an attempt to face the consequences of an idea that had been debated for quite some time.

“In order to understand Bohr’s position in 1924 it is important above all to realize that the correspondence principle was to him the principal reliable bridge between classical and quantum physics. But the correspondence principle is of course no help in understanding light-quanta: the controversial issue of photons versus waves lies beyond this principle. To repeat, the photon-wave duality was the earliest known instance of what was later to be called a complementary situation. The BKS theory, with its rejection of photons and its insistence on the continuous picture of light at the price of non-conservation, historically represents the last stand of the old quantum theory. For very good reasons this proposal was characterized some years later by one of the principal architects of quantum mechanics [Heisenberg] as representing the height of the crisis in the old quantum theory. Nor was non-conservation of energy and momentum in individual processes the only radical proposal made by BKS.

The second paradox. This one concerns a question which had troubled Einstein since 1917: How does an electron know when to emit radiation in making a spontaneous transition?

“In its general form the BKS answer to this question was: there is no truly spontaneous emission. They associated with an atom in a given state a ‘virtual radiation field’ which contains all the possible transition frequencies to other stationary states and assumed that ‘the transitions which in [the Einstein theory of 1917] are designated as spontaneous are, on our view, induced by the virtual field.’ According to BKS, the spontaneous transition to a specific final state is connected with the virtual field mechanism ‘by probability laws which are analogous to those which in Einstein’s theory hold for induced transitions. ‘In this way the atom is under no necessity of knowing what transition it is going to make ahead of time’. Thus spontaneous emission is ascribed to the action of the virtual field, but this action is non-causal …

“ … at the time of the BKS proposal there did not exist any direct experimental proof of energy-momentum conservation nor of causality in any individual process. This is one of the reasons why the objections to BKS (held by many, perhaps the majority of physicists) were initially expressed in a somewhat muted fashion. Thus Pauli (1924) wrote to Bohr that he did not believe in his theory but that ‘one cannot prove anything logically and also the available data are not sufficient to decide for or against your view.’ All this was to change soon.

“There was a second reason, I believe, for the subdued character of comments by others. The physics community was witness to a rare occurrence. Here were the two leading authorities of the day locked in conflict. (The term ‘conflict’ was used by Einstein himself.) To take sides meant to choose between the two most revered physicists. Ideally, personal considerations of this kind ought to play no role in matters scientific. But this ideal is not always fully realized. Pauli (1924) reflected on this in a letter concerning the BKS issue: ‘Even if it were psychologically possible for me to form a scientific opinion on the grounds of some sort of belief in authority (which is not the case, however, as you know), this would be logically impossible (at least in this case) since here the opinions of two authorities are so very contradictory.’

“Even the interaction between the two protagonists was circumspect during that period. They did not correspond on the BKS issue. Nor (as best I know) were there personal meetings between them in those days even though Bohr had told Pauli repeatedly how much he would like to know Einstein's opinion. Werner Heisenberg wrote (1924) to Pauli that he had met Einstein in Göttingen and that the latter had ‘a hundred objections.’ Sometime later Pauli also met Einstein whereupon he sent Bohr a detailed list of Einstein’s criticisms.

“Einstein of course never cared for BKS. He had given a colloquium on this paper at which he had raised objections. The idea (he wrote Ehrenfest) ‘is an old acquaintance of mine, which I do not hold to be the real fellow however’. At about that time he drew up a list of nine objections which I shall not reproduce here in detail. Samples: ‘what should condition the virtual field which corresponds to the return of a previously free electron to a Bohr orbit? (very questionable) … Abandonment of causality as a matter of principle should only be permitted in the most extreme emergency.’ The causality issue (which had plagued him already for seven years by then) was clearly the one to which he took exception most strongly. He confided to Born that the thought was unbearable to him that an electron could choose freely the moment and direction in which to move. The causality question would continue to nag him long after experiment revealed that the BKS answers to both paradoxes were incorrect.

The experimental verdict on causality. The BKS ideas stimulated Walther Bothe and Hans Geiger to develop counter coincidence techniques for the purpose of measuring whether (as causality demands) the secondary photon and the knocked-on electron are produced simultaneously in the Compton effect. Their result (1925): these two particles are both created in a time interval ≤ 10-3 sec. Within the limits of accuracy causality had been established and the randomness (demanded by BKS) of the relative creation times disproved. Since then this time interval has been narrowed down experimentally to ≤ 10-11 sec.

The experimental verdict on energy-momentum conservation. The validity of these conservation laws in individual elementary processes was established for the Compton effect by Compton and Simon … And so the last resistance to the photon came to an end. Einstein’s views had been fully vindicated. The experimental news was generally received with great relief. Bohr took the outcome in good grace and proposed ‘to give our revolutionary efforts as honourable a funeral as possible.’ He was now prepared for an even more drastic resolution of the quantum paradoxes. In July 1925 he wrote: ‘One must be prepared for the fact that the required generalization of the classical electrodynamical theory demands a profound revolution in the concepts on which the description of nature has until now been founded.’ These remarks by Bohr end with references to de Broglie’s thesis and also to Einstein’s work on the quantum gas: the profound revolution had begun” (Pais, Einstein and the quantum theory, pp. 891-3).

The BKS paper was printed simultaneously in German as ‘Über die Quantentheorie der Strahlung’ in Zeitschrift für Physik 24 (1924), pp. 69-87.

Following his early death in January 1938, Bohr wrote this moving tribute to Kalckar:

“The sudden death of Magister Fritz Kalckar [Magister = Master of Science] is a great and painful loss for all who knew him and not least to each of us who worked with him daily at the University Institute for Theoretical Physics.

“Already in his student days, when he rapidly showed his rich talents, he attracted everyone by his fresh and unspoiled human qualities. Immediately upon passing his master's examination with honors, he began his participation in the scientific work at the institute, and already in the course of the first year he completed a theoretical paper on the scattering of electrons on collision with atoms, which explained in the most beautiful manner some experimental results just obtained by Professor Werner, who worked at the institute at that time.

“In the following year, together with Dr Teller, one of the foreign guests at the institute, he carried out an exceedingly interesting investigation of the catalytic effect of paramagnetic gases on the conversion between the so-called orthomodification and paramodification of hydrogen molecules, an investigation whose results allowed—in particular, an accurate calculation of the ratio between the magnetic moments of the heavy and the light hydrogen nucleus. After the completion of this work, Kalckar devoted himself with great energy to the problems of current interest concerning the reactions of atomic nuclei, which in the meantime had become a main topic for the work at the institute, and his valuable participation therein led rapidly to close personal collaboration with Bohr, the first results of which were published only a few months ago [‘On the Transmutation of Atomic Nuclei by Impact of Material Particles’].

“That this collaboration, the continuation of which we had both looked forward to very much, should be interrupted so abruptly is a thought that it is difficult for me to reconcile myself with. Just as all others at the Institute, I shall miss daily his fresh joy in work and the fine understanding of all aspects of human life, which won him friends everywhere. I will also often think of the great help and support he was for me during the trip to America we made together last spring, where, due to his at the same time open and modest personality, he was immediately able to be on close terms with the young physicists with whom we discussed the problems of current interest that occupied us both. For Kalckar, this journey ended with a fruitful period of study in Berkeley and Pasadena, during which he had the opportunity to complete two beautiful papers on problems concerning atomic nuclei in collaboration with Professor Oppenheimer, an outstanding American theoretician, and Dr Serber, one of his pupils.

“In spite of his not quite 28 years, Magister Kalckar had thus already made a name for himself that is respected in wide scientific circles, and he will long be remembered and missed as one of the most sympathetic and promising young Danish scientists.”

Pais, ‘Einstein and the quantum theory,’ Reviews of Modern Physics 51 (1979), pp. 863-914. Bohr, ‘Magister Fritz Kalckar,’ Politiken 12 (1938), pp. 385-386; Translation, pp. 387–388.



8vo (225 x 142 mm), pp. [ii], 785-1056, with two plates numbered VI and VII (small stain in lower margin of a couple of leaves). Original plain wrappers (chipped at fore-edge) with authors and title written on front wrapper.

Item #5156

Price: $3,000.00