2026-10-09 Il Nuovo Saggiatore (Italian Physical Society magazine)

Found via Google query Paschen 1916 He+ 4686 fine structure reanalysis spin Dirac agreement Sommerfeld "wrong reasons". Fetched by script.

Helge Kragh, "From Sommerfeld to Dirac: quantum theory and relativity", Il Nuovo Saggiatore 41 (2025) no. 1-2, https://www.ilnuovosaggiatore.sif.it/article/402 [web]. Kragh also wrote the standard history of the controversy, "The fine structure of hydrogen and the gross structure of the physics community, 1916-26", Hist. Stud. Phys. Sci. 15(2) (1985) 67-125, JSTOR https://doi.org/10.2307/27757550 (paywalled; not obtained). - Quotes Paschen to Sommerfeld, May 1916: "My measurements are now finished and they agree everywhere most beautifully with your fine spectrum". Then: "In fact, the agreement was far from perfect and questioned by a minority of physicists who disliked either Bohr's quantum atom or Einstein's relativity theory, or both. The controversy that followed is of historical and sociological interest, but it did not affect the consensus view of mainstream physicists, namely that the fine-structure problem was no longer a problem." [web] - "As seen in retrospect, Sommerfeld's theory played a dogmatic role in keeping life in a research program which since about 1923 increasingly showed signs of degeneration. ... Sommerfeld's celebrated fine-structure formula was correct for the wrong reasons. Or phrased differently, whereas the theory was wrong the energy formula deduced from it was not." [web] (Kragh's characterisation; he is a historian, no stake.) - Heisenberg and Jordan (March 1926) found that reproducing Sommerfeld's formula in the new mechanics needed both relativity and electron spin; the Lamb-Retherford experiment (1947) showed that two levels degenerate in Dirac's theory are separated by about 0.033 cm^-1 (the Lamb shift) [web]. - Bears on claims 2 and 6. The dissent Kragh mentions (Gehrcke, Lau, Lenard; see the archive.org and Sommerfeld-Projekt notes) concerned the measured size of the hydrogen doublet, which the book prints as 0.27-0.33 against 0.365. The record shows (a) the measured shortfall, (b) the anti-relativists' use of it, (c) Sommerfeld's private 1924 doubt about 0.365, (d) the later finding that part of the hydrogen line structure is the Lamb shift, unknown in 1923. How much of (a) is due to (d), to unresolved components and discharge conditions, or to the theory, is a question for the reviewers; the 1930s measurements (Houston [1937, memory high]; Williams, "The fine structure of H alpha and D alpha under varying discharge conditions", Phys. Rev. 54, 558 (1938) [web, Univ. Washington course PDF snippet]; Pasternack [1938, memory high]), cited by Lamb and Retherford 1950 as "rather probable discrepancies between theory and experiment", are the records that would connect them (not obtained; scripted fetches of Lamb 1950 returned HTML).