2026-10-09 PubMed Central: Vickers 2018

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Peter Vickers, "Disarming the Ultimate Historical Challenge to Scientific Realism", Brit. J. Phil. Sci. 71(3), 987-1012 (2020; online 2018), doi:10.1093/bjps/axy035, open access, https://pmc.ncbi.nlm.nih.gov/articles/PMC7418904/ [web]. - Abstract: "Probably the most dramatic historical challenge to scientific realism concerns Arnold Sommerfeld's ([1916]) derivation of the fine structure energy levels of hydrogen. Not only were his predictions good, he derived exactly the same formula that would later drop out of Dirac's 1928 treatment (something not possible using 1925 Schrödinger-Heisenberg quantum mechanics). And yet the most central elements of Sommerfeld's theory were not even approximately true: his derivation leans heavily on a classical approach to elliptical orbits, including the necessary adjustments to these orbits demanded by relativity. Even physicists call Sommerfeld's success a 'miracle'..." - In the physics literature "the case is known as 'The Sommerfeld puzzle'"; Heisenberg suggested a project to explain why the old theory "leads already to this formula" (1968, p.534); Lawrence Biedenharn (1982-83) claimed to "resolve" it through "an underlying symmetry of the problem" and wrote "Sommerfeld's success is not at all a matter of blind luck" (Biedenharn 1983, p.14) [web]. - Vickers's earlier paper "Historical Magic in Old Quantum Theory?" (Eur. J. Phil. Sci., Durham repository) cites Robotti (1986) on the hydrogen fine-structure measurements; the Durham copy was blocked (Cloudflare). - Bears on claims 1 and 2: the success of the energy formula is not in doubt in this literature; what is debated is why a theory with the wrong mechanism produced the right formula. Priority 2/3.