Conservation Laws and Space-Time Description

First of all, from Einstein's proof that the conservation of energy-momentum in radiation processes implied their directed character, Bohr concluded that conservation laws were violated during a quantum jump. To him there was no milder escape from absurdity, for as Lorentz had argued in 1910, light quanta seemed incompatible with interference phenomena. This private opinion of Bohr was expressed, for instance, in an early draft of "On the quantum theory of line spectra" (but withdrawn from the final version):

Reversing the line of argument in Einstein's paper, it might be said that Einstein's result combined with interference phenomena would seem to prove that conservation of momentum cannot hold for a single process of radiation .... It would seem that any theory capable of an explanation of the photoelectric effect as well as the interference phenomena must involve a departure from the ordinary theorem of conservation of energy as regards the interaction between radiation and matter.^[216]

Bohr publicized this opinion in the context of a broader discussion of radiation phenomena published in 1923 in "The fundamental postulates," under the heading "On the formal nature of the quantum theory." In his

[214] Sommerfeld 1919, 3d ed. (1922), 311-312; Einstein to Ehrenfest, 15 March [1921], AHQP; Pauli 1923b. On the empirical studies of high-frequency radiation, see Wheaton 1983; on Einstein's "Gespensterfeld" see Lorentz 1927, pars. 50-53; Hendry 1984, 16-19; Klein 1970a.

[215] See above, pp. 140-142. Bohr expressed a similar opinion in a never-sent letter to Darwin of 1919, BCW 5: [15]-[16].

[216] BMSS, partly quoted in BCW 5: [15].

quantum theory there were already principles, but, he admitted, there was "no consistent picture of radiation phenomena with which these principles [could] be brought into conformity." This is why he spoke of the "formal nature" of the quantum theory (in the same sense as he earlier spoke of the formal nature of electronic orbits). With his usual optimism, Bohr hoped that the future and the correspondence principle would bring the lacking "picture," in the broadest sense of the word, that is, a "description," as he would soon prefer to say. However, he very much doubted that a picture in the narrow spatiotemporal meaning of the word would ever be attainable:

The satisfactory manner in which the [light-quantum] hypothesis reproduces certain aspects of the phenomena is rather suited for supporting the view, which has been advocated from various sides, that, in contrast to the description of natural phenomena in classical physics in which it is always a question only of statistical results of a great number of individual processes, a description of atomic processes in space and time cannot be carried through in a manner free from contradiction by the use of conceptions borrowed from classical electrodynamics, which up to this time have been our only means of formulating the principles which form the basis of the actual applications of the quantum theory.^[217]

Here, Bohr was still careful: he did not quite exclude the possibility of a space-time description that was based on a theory deviating from classical electrodynamics. However, he was more radical in private, for instance in a letter to Harald Høffding written in September 1922:

It is my personal opinion that these difficulties [in the atomic theory] are of such a nature that they hardly allow us to hope that we shall be able, within the world of the atom, to carry through a description in space and time that corresponds to our customary sensory images.^[218]

A few months later, after the light-quantum interpretation of the Compton effect was established, and after conversations with Pauli, he also wrote:

It is . . . probable that the chasm appearing between these two different conceptions of the nature of light [corpuscular and wavelike] is an evidence of unavoidable difficulties of giving a detailed description of atomic processes

[217] Bohr 1923b, trans., 34, 35. As noted in Bohr, Kramers, and Slater 1924, 190n, in 1916 O. W. Richardson had written: "At the present there seems no obvious escape from the conclusion that the ordinary formulation of the geometrical propagation involves a logical contradiction and it may be that it is impossible consistently to describe the spatial distribution of radiation in terms of three-dimensional geometry" (Richardson 1916, 507-508).

[218] Bohr to Høffding, 22 Sept. 1922, AHQP.

without departing essentially from the causal description in space-time that is characteristic of the classical mechanical description of nature.^[219]

To avoid a common misinterpretation of the latter statement, I will recall that Bohr's rejection of any space-time description of radiation processes in late 1922 did not concern his previous use of space-time pictures for electronic motion and freely waving electromagnetic fields. In his opinion these pictures remained the necessary basis for the application of the correspondence principle; but their validity was to be limited to the approximation where the interaction between the two entities in question, the radiation field and the electronic orbits, could be neglected; and they were of a purely formal nature, since the "correspondence" between the electronic orbits and the emitted radiation could not be deduced from a causal mechanism occurring in space and time.

In fact the correspondence principle, with its limited recourse to classical pictures, and the adiabatic principle, in its updated version as a principle of permanence, were the only general principles that could guide the future elaboration of the quantum theory, as Bohr concluded in his "Fundamental postulates": they were true principles of the quantum theory, whereas the energy principle and the implicit principle of visualizability were only principles of the classical theory—which were likely to collapse along with the classical theory. As we shall presently see, the BKS theory allowed for violation of the energy principle, while maintaining the space-time picture of radiation to a degree somewhat higher than originally expected by Bohr.^[220]