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The quantum theory of the electromagnetic field was regarded as an important component of the relativistic quantum theory, but not the sole one. In that pre-neutron epoch, nuclei were believed to be composed of protons and 'intranuclear' electrons. The uncertainty relation and the small size of the nucleus suggested a high relativistic speed of 'intranuclear' electrons.

At the same time, before the positron was discovered, Dirac's ch- equation was considered to be burdened with a most serious 'plus-minus' problem. Therefore, theorists hoped that the coming relativistic quantum theory would solve a cluster of puzzling problems, such as infinities, nuclear spins, and continuous spectra of beta-decay.

They awaited the revolutionary reconstruction of physics comparable with relativistic and quantum physics. Niels Bohr, the chief inspirer of the revolutionary mood, was even prepared to sacrifice the law of conservation of energy for the sake of successful reconstruction. This attitude was shared by Landau, who had met Bohr in and at once adopted him as his sole teacher. Landau soon made a step from general hope to specific calculations. In January , he and R. Peierls arrived at a revolutionary conclusion, which is that the most natural problem of the 'relativistic quanta theory' — the quantum theory of the electromagnetic field — is unsolvable because of the defectiveness of the basic notion 'field at a point'.

It was the beginning of the story, the development of which should have been discussed by the four theorists gathered at the round table in Kharkov in May Quantum mechanics and its uncertainty principle brought some limitations on the applicability of concepts inherited from classical physics. This gave reason to apply these variables in the h- theory. Soon after the meaning of h -limitations was understood, the question arose as to the character of quantum constraints imposed when relativity was taken into account as well, or ch- limitations.

Thought experiments such as the 'Heisenberg microscope' provided arbitrarily accurate results only if the c -theory was ignored. However, a most important physical subject, the electromagnetic field, was relativistic even before the theory of relativity was created, since Maxwell equations contained the constant c. An article published by Landau and Peierls in was entitled "Extension of the uncertainty principle to the relativistic quantum theory".

In this case, however, the recoil momentum of the test charge produced an additional electromagnetic field that distorted the field being measured. Hence, the conclusion that the notion of 'field at a point' is undefinable.


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This paper written in Zurich in January manifested the great influence of Bohr by referring to his articles and oral discussions in Copenhagen. Evidently, the authors were sure they were developing Bohr's ideas in particular by theoretically substantiating his hypothesis about energy non-conservation in ch -physics.

However, when Landau and Peierls came to Copenhagen to see Bohr in February , he rejected their conclusion. The situation is depicted in a drawing by G Gamow and in recollections by Leon Rosenfeld, then Bohr's assistant:. As I asked him about the news, he replied in his own picturesque way by showing me a neat pen drawing he had just made. It represented Landau, tightly bound to a chair and gagged, while Bohr, standing before him with upraised forefinger, was saying 'Bitte, bitte. Landau, muss ich nur ein Wort sagen! Landau stayed for a few weeks longer, and I had the opportunity of ascertaining that Gamow's representation of the situation was only exaggerated to the extent usually conceded to artistic fantasy.

Landau and Bohr discussing measurability of field, Nevertheless, Landau held to his opinion and the article was published.

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Quantum metrology for gravitational wave astronomy

Bronstein saw it this way. Considerations of observability and measurability played an important role in the analysis of the simultaneity notion in the theory of relativity. Meanwhile, Bohr worked together with Rosenfeld to transform his oral objections to Landau into a well-grounded text to defend quantum uncertainty from the 'relativistic threat'.

General Relativity

The work took two years to complete and resulted in a lengthy article, "famously obscure and difficult" in the words of the well-known physicist and historian of science S Schweber [31]. Indeed, this super-theoretical article is frightening both in its volume more than 60 pages and the abundance of laboratory terminology used to describe thought experiments, such as test bodies of arbitrary mass and charge able to penetrate each other, countless small mirrors at every part of the test body, rigid bindings to a hard frame, flexible magnetic threads, etc.

But the notion of the point-like charge is illegitimate in classical field theory. On the other hand, classical physics allows measuring an average field in a finite space region with any desired accuracy.