‘At the present state of science it does not seem possible to avoid the formal character of the quantum theory which is shown by the fact that the interpretation of atomic phenomena does not involve a description of the mechanism of the discontinuous processes […]. On the correspondence principle it seems nevertheless possible to […] arrive at a consistent description of optical phenomena by connecting the discontinuous effects occurring in atoms with the continuous radiation field […]’. This announced a turning point in atomic physics research; for the first time there were reasons to assert that discontinuity was not in itself incompatible with the theory's descriptive content, and rational solutions were provided that related a whole set of phenomena dependent on the radiation properties of matter to the continuous picture of the radiation field. This was the conclusion arrived at in a new paper by Bohr which took up and developed the hypothesis put forward by the American physicist John Slater that ‘the atom, even before a process of transition between two stationary states takes place, is capable of communication with distant atoms through a virtual radiation field’ was taken up and developed. The article, ‘The Quantum Theory of Radiation’, signed by Bohr, Kramers and Slater, was published in the Philosophical Magazine in January 1924. Slater had arrived in Copenhagen at the end of the preceding year with the idea that his hypothesis might lead to very different theoretical results.
‘At the present state of science it does not seem possible to avoid the formal character of the quantum theory which is shown by the fact that the interpretation of atomic phenomena does not involve a description of the mechanism of the discontinuous processes […]. On the correspondence principle it seems nevertheless possible to […] arrive at a consistent description of optical phenomena by connecting the discontinuous effects occurring in atoms with the continuous radiation field […]’. This announced a turning point in atomic physics research; for the first time there were reasons to assert that discontinuity was not in itself incompatible with the theory's descriptive content, and rational solutions were provided that related a whole set of phenomena dependent on the radiation properties of matter to the continuous picture of the radiation field. This was the conclusion arrived at in a new paper by Bohr which took up and developed the hypothesis put forward by the American physicist John Slater that ‘the atom, even before a process of transition between two stationary states takes place, is capable of communication with distant atoms through a virtual radiation field’ was taken up and developed. The article, ‘The Quantum Theory of Radiation’, signed by Bohr, Kramers and Slater, was published in the Philosophical Magazine in January 1924. Slater had arrived in Copenhagen at the end of the preceding year with the idea that his hypothesis might lead to very different theoretical results.
An attempt is made to present a consistent detailed theory of optical phenomena, based on the suggestion recently made by the author in collaboration with Bohr and Kramers. This suggestion is that atoms are radiating or absorbing continuously, during their stationary states, and that transitions influence radiation only in terminating the radiation characteristic of the old state, and substituting that of the new. The atoms, on the other hand, are supposed not to change their energy while radiating, but to change it discontinuously on transition. This necessitates giving up the detailed application of the conservation of energy in interaction between atoms and radiation. In the present paper, an additional suggestion is made, namely that resonance radiation is to be identified with the radiation carried out by the spherical wavelets which, by their interference with the external field, also produce absorption. This is practically a return to the classical picture of resonance radiation. Statement of the theory consists formally of two parts: the description of the behavior of atoms, and of radiation, when the two interact. The first involves the statement of the probabilities of transition of atoms, and is taken without change from Einstein. The probability of interruption of coherent vibrations is also discussed. The second requires the specification of the fields emitted by atoms in any steady state under the influence of any external field. These consist of spherical wavelets of the frequencies of the various quantum lines which the atom can emit or absorb in the stationary state in which it is. For emission frequencies, wavelets are emitted even in the absence of an external field; for absorption frequencies, external fields induce wavelets, similar to the wavelets of linearly bound electrons in electron theory, which on the one hand interfere with the external field to produce the phenomena of dispersion, etc., and on the other carry out the resonance radiation in all directions. Detailed descriptions of these fields are given. In a discussion of the theory, it is first shown that the assumptions which have been made about the field satisfy the correspondence principle, in that for large quantum numbers the field aproaches that which would be emitted classically on account of the interaction of an external field and a multiply periodic atom. On the other hand, it is shown that the field has a character essentially like that of classical electron theory, which is known to be in general agreement with experiments. Next, the energy and momentum relations at interaction of atoms and light are investigated, and it is shown that, although these quantities are not precisely conserved, still the assumptions as to atomic and radiation processes have been so made that they are conserved on an average over a great number of atomic processes. Finally the spectral resolution of emitted and absorbed radiation is considered; the theory gives a minimum breadth for the lines, depending on the finite length of wave trains resulting from the finite life in stationary states, and it is shown that Kirchhoff's law is obeyed, the emission and absorption lines being of the same breadth. By way of illustration, specific application of the theory is made to the simple examples of emission of light by bombardment of electrons at the resonance potential, resonance radiation, its quenching by presence of foreign gases, absorption, scattering, and disperison.
Abstract This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT.
‘The new wave mechanics gave rise to the hope that an account of atomic phenomena might be obtained which would not differ essentially from that afforded by the classical theories of electricity and magnetism. Unfortunately, Bohr's statement in the following communication of the principles underlying the description of atomic phenomena gives little, if any, encouragement in this direction.’ This comment is to be found in the brief note prefaced by the editors of the British journal Nature to Niels Bohr's paper ‘The Quantum Postulate and the Recent Development of Atomic Theory’ in the supplement of 14 April 1928. The article in question is the famous paper which first introduced and defined the concept of ‘complementarity’ and outlined the basic points of what was to become known as the Copenhagen interpretation of quantum mechanics. In the paper, Bohr returned to the arguments contained in the paper discussed at the International Congress of Physicists held at Como in September 1927 to mark the centenary of the death of Alessandro Volta and published in the proceedings of the same congress. It was probably his conviction that the new viewpoint adopted in the description of nature fully expressed the theoretical and cognitive content of quantum physics coupled with his enthusiasm at having achieved ‘after many years of struggling in the dark […] the fulfilment of the old hopes’ that induced him to give his work broader and more prestigious circulation.
Abstract It is well known that the experimental facts of atomic physics necessitate a departure from the classical theory of electrodynamics in the description of atomic phenomena. This departure takes the form, in Bohr’s theory, of the special assumptions of the existence of stationary states of an atom, in which it does not radiate, and of certain rules, called quantum conditions, which fix the stationary states and the frequencies of the radiation emitted during transitions between them. These assumptions are quite foreign to the classical theory, but have been very successful in the interpretation of a restricted region of atomic phenomena. The only way in which the classical theory is used is through the assumption that the classical laws hold for the description of the motion in the stationary states, although they fail completely during transitions, and the assumption, called the Correspondence Principle, that the classical theory gives the right results in the limiting case when the action per cycle of the system is large compared to Planck’s constant h, and in certain other special cases. In a recent paper Heisenberg puts forward a new theory, which suggests that it is not the equations of classical mechanics that are in any way at fault, but that the mathematical operations by which physical results are deduced from them require modification. All the information supplied by the classical theory can thus be made use of in the new theory.
It is shown that, assuming conservation of energy and momentum in individuai transitions, radiation must be regarded as propagated by linearly directed quanta. Evidence is brought forward in favour of the view that these quanta are spatially localised longitudinally as well as laterally. As these conclusions seem unavoidable, an attempt is made to see if there is any possibility of accounting for interference effects in terms of quants possessing periodic properties. The idea that a single quantum can produce interference effects is untenable. The conception of the phase of a quant is introduced, and it is supposed that atoms may absorb a quant in a given phase provided they are in a “state” corresponding to that phase. Considering radiation emanating from a point, it is shown that a tentative explanation of interference may be obtained if the quants have a constant phase at emission, and if they give atoms at any point an impulse towards the state corresponding to their phase at the point. According as these impulses reinforce or oppose each other, bright or dark parts of a fringe System are obtained. Practically the whole nomenclature and method of the wave theory may be taken over and applied to the quant phase field surrounding an emitting source. Essentially, on this view, an explanation of interference is sought in terms of different quants, and the dark and bright parte of a fringe system are to be explained, not in terms of different numbers of quante arriving at them, but in different phase relations of quante which do arrive. Quante are characterised by a magnetic and electric vector, whose magnitudes and directions define the state of polarisation and the phase. Electron orbite may also be regarded as characterised by two vectors in terms of which it seems as if the “state” may be specified. The relation between transition character and type of radiation emitted is finally considered and it is shown that the evidence so far available renders plausible an explanation of interference of the kind put forward. Much further experimental work, particularly in connection with the Stark and Zeeman effects, is, however, necessary, before sufficient precision can be given to the views put forward to make them satisfying. On the other hand, it seems premature to suppose that only a formal treatment is possible of the physical phenomena involved.
Introduction Quantum mechanics is based on the intuition that the essential difference between atomic physics and classical physics is the occurrence of discontinuities (see in particular [1,4,58–63]). Quantum mechanics should thus be considered a direct continuation of the quantum theory founded by Planck, Einstein and Bohr. Bohr in particular stressed repeatedly, already before the birth of quantum mechanics, that the discontinuities must lead to the introduction of new kinematical and mechanical concepts, so that indeed classical mechanics and its corresponding conceptual scheme should be abandoned [1,4]. Quantum mechanics tries to introduce the new concepts through a precise analysis of what is ‘observable in principle’. In fact, this does not mean setting up the principle that a sharp division between ‘observable’ and ‘unobservable’ quantities is possible and necessary. As soon as a conceptual scheme is given, one can infer from the observations to other facts that are actually not observable directly, and the boundary between ‘observable’ and ‘unobservable’ quantities becomes altogether indeterminate. But if the conceptual scheme itself is still unknown, it will be expedient to enquire only about the observations themselves, without drawing conclusions from them, because otherwise wrong concepts and prejudices taken over from before will block the way to recognising the physical relationships [Zusammenhänge].