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Anamorphosis of Bohr-Rosenfeld

Stefano Furlan, Sub History and Philosophy of Science, History of Science

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

In 1933, Bohr and Rosenfeld published a famous article, “On the question of the measurability of electromagnetic field quantities”, which by many accounts became a milestone. Historiography, though, does not seem to have really grasped its impact. In this brief paper I will highlight how the work by Bohr and Rosenfeld had an important reception story also outside of QED, more specifically in quantum gravity attempts: in the USSR, at the hands of Bronstein (mid-1930s), and in the US, at the hands of Wheeler (mid-1950s).

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An historical account is given of the circumstances whereby the uncertainty relations were introduced into physics by Heisenberg. The criticisms of QED on measurement-theoretical grounds by Landau and Peierls are then discussed, as well as the response to them by Bohr and Rosenfeld. Finally, some examples are given of how the new freedom to advance radical proposals, in part the result of the revolution brought about by 'uncertainty,' was implemented in dealing with the new phenomena encountered in elementary particle physics in the 1930's.

•Jan 1, 1993•0 citations
In 1933, Bohr and Rosenfeld published a famous article, “On the question of the measurability of electromagnetic field quantities”, which by many accounts became a milestone. Historiography, though, does not seem to have really grasped its impact. In this brief paper I will highlight how the work by Bohr and Rosenfeld had an important reception story also outside of QED, more specifically in quantum gravity attempts: in the USSR, at the hands of Bronstein (mid-1930s), and in the US, at the hands of Wheeler (mid-1950s).
In the 1933 Bohr and Rosenfeld’s famous article on electromagnetic field measurements they did not consider the measurement of a magnetic component in a given space‐time region, nor the measurement of two parallel magnetic components, nor the measurement of two non‐parallel magnetic components, nor the parallel measurement of one magnetic and one electric component, nor the non‐parallel measurement of one electric and one magnetic component, nor the non‐parallel measurement of one magnetic and one electric component in two different space‐time regions. This article covers the first one of these pending matters.
In 1933, Bohr and Rosenfeld published a seminal paper in which they claimed to solve the measurement problem of the free quantum electromagnetic field. In 1951, however, Corinaldesi discovered, in the analysis of the above-mentioned authors, an error in the order of magnitude of a certain critical field. This paper shows, through a comparative analysis between the results of Bohr and Rosenfeld and Corinaldesi, that the error discovered by the latter does not affect the conclusions of the former. It is also possible to consider as a deficiency of their work the fact that Bohr and Rosenfeld never responded to the mistake found by Corinaldesi. It will be shown here that in fact Bohr and Rosenfeld studied a measurement situation, the problem of which was equal to the one that would be originated if the correction of Corinaldesi were taken into account.
Bohr and Rosenfeld showed in 1933 that the order of magnitude of precision, in the measurement of the free quantum electromagnetic components imposed by their uncertainty relations, could be estimated with thought experiments. The ingenious article by Bohr and Rosenfeld describes the complicated measuring devices that would be needed, but does not include a graphic representation of these. Neither does it show the measurement of a magnetic component in a given space-time region, nor the measurement of two parallel magnetic components, nor the measurement of two non-parallel magnetic components, nor the parallel measurement of one magnetic and one electric component, nor the non-parallel measurement of one electric and one magnetic component, nor the non-parallel measurement of one magnetic and one electric component in two different space-time regions. This article covers these pending matters and the graphics of cases studied by them.
Meanwhile, on 18 September 1931, Heisenberg wrote to Bohr that ‘my work seems to be somewhat gray on gray’ (Pauli, 1985). By 1931 the bright future for quantum physics that seemed just over the horizon in the fall of 1927 paled with the formulation of relativistic quantum mechanics. Besides the as yet uninterpreted negative energy states, there was the electron's divergent self-energy and the continuous energy spectrum of β-particles in the supposedly two-body final state of nuclear β-decay, which implied that energy was not conserved in nuclear reactions (Bohr, 1932) and that perhaps quantum mechanics was not valid within the nucleus (to be discussed in Chapter 5). Measurement problems in a quantum theory of the electromagnetic field At the 20–25 October 1930 Solvay Conference, Bohr, Dirac, Heisenberg and Pauli concurred that fundamental difficulties in quantum electrodynamics might be clarified by investigating measurability of electromagnetic field quantities. Upon his return to Copenhagen from Brussels, Bohr continued discussing field measurements with Lev Landau, who happened to be visiting at Bohr's institute. In December 1930 Landau went on to Zürich, where he interested Pauli's assistant Rudolf Peierls in field measurements. Their deliberations led to a joint 1931 publication entitled ‘Extension of the uncertainty principle to relativistic quantum theory’ (Landau and Peierls, 1931). Measurement of an electric field can be accomplished through measuring the change in momentum of a charged test body placed in the field.
An historical account is given of the circumstances whereby the uncertainty relations were introduced into physics by Heisenberg. The criticisms of QED on measurement-theoretical grounds by Landau and Peierls are then discussed, as well as the response to them by Bohr and Rosenfeld. Finally, some examples are given of how the new freedom to advance radical proposals, in part the result of the revolution brought about by 'uncertainty,' was implemented in dealing with the new phenomena encountered in elementary particle physics in the 1930's.