BOHR, Niels.

The Quantum Postulate and the Recent Development of Atomic Theory. Offprint from: Atti del Congresso Internazionale dei Fisichi Como, Septembre 1927. [Offered with:] The Quantum Postulate and the Recent Development of Atomic Theory. Offprint from Nature, vol. 121, no. 3050, April 14, 1928.

Bologna; Edinburgh: Nicola Zanichelli; R. & R. Clarke, 1928; 1929.

First edition, extremely rare offprints, of the two quite distinct versions of this fundamental paper introducing Bohr’s statement of his ‘complementarity’ principle, the basis of what became known as the ‘Copenhagen interpretation’ of quantum mechanics. Bohr “defined the complementarity principle as ‘a new mode of description … in the sense that any given application of classical concepts precludes the simultaneous use of other classical concepts which in a different connection are equally necessary for the elucidation of phenomena’ … The wave description and the particle description are complementary and thus in conflict. But Bohr argued that the physicist is still able to account unambiguously for his experiments, for it is he who chooses what to measure and thereby destroys the possibility of the realization of the conflicting aspect … The complementarity principle became the cornerstone of what was later referred to as the Copenhagen interpretation of quantum mechanics. Pauli even stated that quantum mechanics might be called ‘complementarity theory’, in an analogy with ‘relativity theory’. And Peierls later claimed that ‘when you refer to the Copenhagen interpretation of the mechanics what you really mean is quantum mechanics’ … by the mid-1930s Bohr had been remarkably successful in establishing the Copenhagen view as the dominant philosophy of quantum mechanics” (Kragh, Quantum Generations, 1999, pp. 209-210).

“From the epistemological point of view, the discovery of the new type of logical relationship that complementarity represents is a major advance that radically changes our whole view of the role and meaning of science. In contrast with the nineteenth-century ideal of a description of the phenomena from which every reference to their observation would be eliminated, we have the much wider and truer prospect of an account of the phenomena in which due regard is paid to the conditions under which they can actually be observed – thereby securing the full objectivity of the description” (DSB). Bohr presented his complementarity principle on 16 September 1927 at the meeting held in Como on the occasion of the centenary of the death of Alessandro Volta – the first offprint is the text of this lecture. Following the conference, Bohr spent a week at Lake Como discussing his new ideas with Wolfgang Pauli, which resulted in a rewriting of the article for publication in Nature. “In December 1927 Bohr wrote to the editor of Nature: 'I have found it most expedient to rewrite the whole article … I am much ashamed for all the trouble I am giving you.’ After more writing back and forth the editor received Bohr’s final version in the first days of March 1928. It appeared in Nature on 14 April” (Pais, Bohr’s Times (1991), p. 316). The differences between the two versions of Bohr’s paper are very substantial and a comparison between these two articles vividly illustrates the evolution of Bohr’s understanding of the interpretation of quantum mechanics in 1927/28. A brief summary of only the major changes occupies two pages in Bohr’s Collected Works (Vol. 6, pp. 111-112). OCLC lists only the Dibner copy of the Nature offprint at the Smithsonian, and no copy of the Como offprint.

The concept of complementarity started to develop in Bohr’s mind during discussions with Heisenberg in Copenhagen early in 1927, when Heisenberg was preparing for publication his famous paper on the uncertainty principle. In fact, the published version of Heisenberg’s paper contains a note added in proof which mentions ‘recent investigations by Bohr [that] have led to points of view that permit an essential deepening and refinement of the analysis of the quantum mechanical relationship attempted in this work’. Heisenberg’s “influence was crucially important for the evolution of Bohr’s own ideas in 1927. He must of course have reflected on his prior discussions with Heisenberg as, all by himself, he spent at least four weeks skiing in the Norwegian mountains around Guldbrandsdalen. It was there (as he often told) that the complementarity argument first dawned on him. Heisenberg remembered: ‘When I discussed [my work] with Bohr after his return, we were unable to find at once the same language for the interpretation of the theory because in the meantime Bohr had developed the concept of complementarity.’ The result was ‘a fresh round of difficult discussions’. [Oskar] Klein has recalled: ‘Both the results and the failures in Heisenberg’s work became a source of inspiration to [Bohr], and from then on he worked almost day and night on these questions’ …

“The task of assisting Bohr in composing a paper on his new ideas fell to Klein. ‘Bohr began eagerly … in April [1927], and then we went to Tisvilde … and Bohr dictated and the next day all he had dictated was discarded and we began anew. And so it went all summer … and then Bohr had to go to the Como meeting and then, under strong pressure by his brother Harald, he really tried to get an article written down’ … The manuscript of his [Como] lecture appears to be lost but many drafts of his paper have been preserved in the Niels Bohr Archives. These give us a good picture of Bohr’s struggles with the formulation of his ideas … The term ‘complementarity’ appears for the first time in a draft from 10 July 1927 … It is possible that Bohr decided to use that word during a sailing trip with friends. ‘Ole Chievitz [Bohr’s friend since his high school days] and Bohr had long discussions about whether ‘complementarity’ was the correct designation for the relation between the wave and the particle picture . . . and we flattered ourselves with the belief that the decision to use the word ‘complementarity’ took place on one of our sailing trips’ …

“One of the prettiest points in the Como paper is Bohr’s own derivation of the uncertainty relations, which goes like this. Consider a wave packet of either light or material waves, an object with finite extension. Introduce the following definitions: Δt, the time interval during which the bulk of the wave packet passes some fixed point; Δv, the frequency interval in which the bulk of the participating frequencies lie; Δ(1/λ), the similar interval for inverse wave lengths; Δx, the spatial extension of the packet. Then

ΔtΔv ≥ 1, ΔxΔ(1/λ) ≥ 1.

These are classical relations, known from the theory of the resolving power of optical instruments. Now use the Einstein-de Broglie relations

E = hv, p = h/λ,

and there you are [i.e., the position-momentum and energy-time uncertainty relations ΔpΔx ≥ h and ΔEΔt ≥ h, where h is Planck’s constant]. The beauty of this argument lies in its avoidance of all quantum mechanical technology.

“A second main point first made by Bohr concerns the meaning of the conservation laws of energy and momentum in quantum mechanics. Does the appearance of ΔE’s and Δp’s mean that these laws are not precisely satisfied? No, he explains, one should rather put it as follows. They can only be sharply verified, hence sharply applied, under circumstances in which E and p are sharply measurable – at a loss of sharp information on ‘space-time coordination’ (to use Bohr’s terminology). Under other circumstances one should not say that the conservation laws are not valid, but rather that their validity cannot be verified.

“That reasoning brings us to the heart of Bohr’s concepts. In the very first sentence ever written on quantum mechanics, the abstract of Heisenberg’s July 1925 paper, it was stated that ‘quantum mechanics should be founded exclusively upon relationships between quantities that are in principle observable’. By his uncertainty relations Heisenberg had shown that there exist limitations of principle on the precision of what is observable in the region where quantum effects are important … he had concluded from this that, to some extent, we have to abandon the concepts of particles and waves and that our classical words do not any longer fit in the quantum region.

“At this point Bohr went beyond Heisenberg in taking the opposite view: ‘Our interpretation of the experimental material rests essentially upon the classical concepts.’ One may say that with the elaboration of that statement the logic of quantum mechanics reached its closure …

“Bohr’s expertise in classical physics made him ideally suited for the delicate and far from trivial ‘interpretation of the experimental material’, as he showed at Como by his improved discussion of Heisenberg’s γ-ray microscope. [In his paper on the uncertainty principle, Heisenberg considered the orbit of an electron in the ground state of hydrogen which is supposed to have a radius of about 10^–8 cm. In order to ‘see’ the electron’s position (at a given time) one has to illuminate it with light with a wavelength small compared to this radius, hence also small compared to the wavelengths of visible light: one has to observe the electron under a ‘γ-ray microscope’. Illumination of that kind will scatter the electron (by the Compton effect) and knock it out of the orbit which one hoped to determine. In other words, Heisenberg said, when we look at the electron, we disturb its momentum, and so lose the possibility of measuring its momentum precisely.] In Heisenberg’s example, Bohr noted, one can calculate the change of the momentum of the electron kicked out of its orbit and therefore we can correct for that effect. Nevertheless there is an uncertainty in the determination of the electron’s position. We observe that position by scattering a γ-ray off the electron, then sending that ray through a microscope and observing its momentum direction. The precision with which we can do this is limited, however. In order to observe that direction as well as possible one focuses the γ-ray beam by passing it through a lens, a familiar procedure for any kind of microscope. According to classical optics that lens diffracts the beam, hence makes its direction imprecise, hence makes the electron’s position imprecise. A quantitative analysis of this imprecision shows that it is exactly in accord with the uncertainty relations.

“I next enlarge on Bohr’s general statement on the classical interpretation of experimental data. In the classical era one verified the validity of theories by comparing them with experimental observations made with balances, thermometers, voltmeters, etc. The theories have been modified in the quantum era but – and this was Bohr’s point – their validity continues to be verified by the same readings of a balance’s equilibrium position, a thermometer’s mercury column, a voltmeter’s needle, etc. The phenomena may be novel, their modes of detection may have been modernized, but detectors should be treated as classical objects; their readings continue to be described in classical terms.

“‘The situation thus created is of a peculiar nature,’ Bohr remarked. Consider for example the question: Can I not ask for the quantum mechanical properties of a detector, say a voltmeter? The answer is yes, I can. Next question: But should I then not abandon the limited description of the voltmeter as a classical object, and rather treat it quantum mechanically? The answer is yes, I must. But in order to register the voltmeter’s quantum properties I need another piece of apparatus with which I again make classical readings. In Bohr’s own rather cryptic words: ‘The concept of observation is in so far arbitrary as it depends upon which objects are included in the system to be observed.’

“The language of science, more generally the ways in which we communicate – these were the themes on which Bohr focused in the Como lecture and for the rest of his life. Thus, he said (I paraphrase): The question of whether an electron is a particle or a wave is a sensible question in the classical context, where the relation between object of study and detector either needs no specification or else is a controllable relation. In quantum mechanics that question is meaningless, however. There one should rather ask: Does the electron (or any other object) behave like a particle or like a wave? That question is answerable, but only if one specifies the experimental arrangement by means of which ‘one looks’ at the electron …

“To summarize, Bohr stressed that only by insisting on the description of observations in classical terms can one avoid the logical paradoxes apparently posed by the duality of particles and waves, two terms themselves defined classically. Wave and particle behavior mutually exclude each other. The classical physicist would say: if two descriptions are mutually exclusive, then at least one of them must be wrong. The quantum physicist will say: whether an object behaves as a particle or as a wave depends on your choice of experimental arrangement for looking at it. He will not deny that particle and wave behavior are mutually exclusive but will assert that both are necessary for the full understanding of the object’s properties. Bohr coined the term complementarity for describing this new situation: ‘The very nature of the quantum theory … forces us to regard the space-time coordination [meaning: particle behavior] and the claim of causality [meaning: wave behavior], the union of which characterizes the classical theories, as complementary but exclusive features of the description … complementary pictures of the phenomena … only together offer a natural generalization of the classical mode of description …

“I have related earlier how all through the summer of 1927 Bohr struggled with committing his thoughts to paper. That was only the beginning. On 7 September, before Como, Bohr had sent a short article to Nature. After Como he wrote to the Editor of Nature: ‘I regret that I have not yet returned the proof of my article … [I was] led to rewrite the whole article, and I hope that in its present form it will be better suited to promote the mutual understanding of the advocators of the conflicting views.’ That new version was almost certainly the one on which Bohr and Pauli had worked during the week they spent together at Lake Como, after the Volta meeting” (Pais, pp. 310-316).

“After the Volta Meeting in Como, Bohr spent a week together with Pauli at Lake Como in order to prepare the publication of an extended version of his lecture. Back in Copenhagen a manuscript entitled ‘Das Quantenpostulat und die neuere Entwicklung der Atomistik’ was completed and sent to the Naturwissenschaften on October 11, although it was never published in this form … From the last sentence of the manuscript it is clear that Bohr thought of this article as being different from the Como Lecture: ‘A more detailed elaboration of this point of view in its application to a number of simple examples was recently given by the author in a lecture at the Volta congress in Como and will soon appear in the transactions of this congress’ …

“The further work on the proofs dragged on well into 1928, in spite of Pauli’s assistance. At the beginning of January, Bohr had to confess to Pauli that he had prepared an entirely new manuscript and proposed to visit Hamburg in order that he and Pauli could go through it together. Pauli answered on January 13: ‘… We are all looking forward to your arrival … I am really quite happy that you have altered the manuscript. Indeed, after some time I did not particularly like the old one, especially as it seemed to me that ‘the complementarity of causal and space-time description’ requires still further elucidation, and the statistical interpretation of the results of theoretical computation seemed to me to be introduced too abruptly’ … Bohr was much relieved to receive Pauli’s positive reaction and answered promptly: ‘… I hope that you will find that the paper has been improved. Or, to express myself more modestly I should say that I believe that I understand various essential points better than when we last met’ … Finally, on April 13, the paper was published in German in Naturwissenschaften, and the following day the English version appeared in Nature. These two versions are essentially identical, but represent a substantial expansion in comparison with the text printed in the transactions from the Como Conference … On May 14, Bohr sent Pauli a reprint of the published paper together with his sincere thanks for Pauli’s faithful and friendly help. He had earlier sent a reprint to Schrödinger …

“An amusing footnote to the story of the birth of this, Bohr’s first and decisive paper on the foundations of modern quantum theory, is the ‘introduction’ with which the editors of Nature found it appropriate to embellish Bohr’s article. On this rigmarole Pauli comments tersely and to the point: ‘… Honestly, I have not laughed so much for a long time as when reading the ludicrous comment with which the editors of Nature have prefaced your article. After a superfluous historical survey, in short sentences, of the development of quantum theory in recent years, in which the name of de Broglie is not mentioned, there follows an obscure paraphrase of the following mood: ‘We British physicists would be awfully pleased if in the future the points of view advocated in the following paper should turn out not to be true. Since, however, Mr. Bohr is a nice man, such a pleasure would not be kind. Since moreover he is a famous physicist and more often right than wrong, there remains only a slight chance that our hopes will be fulfilled.’ In any case, this is how I read the Nature commentary, and I thought to myself, ‘Sancta simplicitas!’” (Complete Works, 6, pp. 30-53).

The Nature article represents a substantial revision and expansion of the Como lecture. Sections have been rearranged and titles added. Some of the most important textual additions are as follows: p. 581: The last two sentences of the first paragraph, on the complementary aspects of light; p. 582: The last three sentences of the first paragraph, concerning the analogy with optics and the role of conservation laws, and the last three sentences of the last paragraph of Section 2, concerning the role of the electric charge; p. 583: The first two sentences of the fourth paragraph, concerning the irrelevance of the time of observation, and the fourth sentence, on the concept of velocity; pp. 583-4: Two whole paragraphs, and the first two sentences of the following paragraph, dealing with the definition of a coordinate system by solid bodies and imperturbable clocks; p. 584: The last three sentences of the third paragraph, on the interaction between object and measuring instrument; p. 584: The last two paragraphs, on the connection to classical physics and the correspondence principle, have been considerably expanded; p. 585: The second paragraph, on Heisenberg’s paper, has been considerably expanded, and in the third paragraph the sentence on the transformation theory, and that on the possibilities of definition and observation, have been added; p. 586: The second paragraph is considerably expanded, and formula (5) is added; p. 587: The first four sentences of the second paragraph, concerning the impossibility of defining electron orbits in a stationary state, and the last paragraph of section 5, dealing with the transformation theory; p. 588: One sentence in the first paragraph, on collision time and energy conservation, and the last two lines; pp. 589-590: The section on the Kaluza-Klein theory; p. 590: This page represents a considerable revision and expansion of the last paragraph in the Como lecture.

The Como lecture was published only once, except for its reprint in the Collected Works. The later revised version was published almost simultaneously in English, as here, and in German (Die Naturwissenschaften, Bd. 16, pp. 245-257); it appeared in French, “Le Postulat des Quanta et le nouveau Développement de l’Atomistique,’ in the proceedings of the fifth Solvay Congress, Électrons et Photons. Rapports et Discussions du Cinquieme Conseil de Physique tenu a Bruxelles du 24 au 29 Octobre 1927 sous les Auspices de L'Institut International de Physique de Solvay (Paris: Gauthier Villars, 1928), pp. 215-247 – this was, “according to the author’s footnote [p. 215], a translation of the paper in the Naturwissenschaften and therefore is of a later date” (Collected Works, 6, p. 35); and in the following year a Danish translation was published in Atomteori og Naturbeskrivelse, Festskrift udgivet af Københavns Universitet i Anledning af Universitetets Aarsfest November 1929 (Copenhagen: Bianco Lunos, 1929), pp. 40-68.

I. 8vo (240 x 157 mm), pp. [1], 2-24. Original pale green printed wrappers (wrappers a bit creased with two small chips from outer corners, rear wrapper with two small closed tears). II. Large 8vo (266 x 192 mm), pp. [1], 580-590. Original brown printed wrappers (some very light scuffing and one short closed tear to upper margin). Very good copies of these two extremely rare offprints.

Item #5039

Price: $15,000.00