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Grete Hermann

Grete Hermann (2 March 1901 – 15 April 1984)[1] was a German mathematician and philosopher noted for her work in mathematics, physics, philosophy and education. She is noted for her early philosophical work on the foundations of quantum mechanics, and is now known most of all for an early, but long-ignored critique of the no hidden variables proof by John von Neumann.

Grete Hermann
Born(1901-03-02)2 March 1901
Bremen, German Empire
Died15 April 1984(1984-04-15) (aged 83)
Bremen, West Germany
EducationUniversity of Göttingen (PhD)
Known forPrimary decomposition
Scientific career
FieldsMathematics
Philosophy
InstitutionsPädagogische Hochschule Bremen [de]
Thesis Die Frage der endlich vielen Schritte in der Theorie der Polynomideale  (1926)
Doctoral advisorEmmy Noether
Edmund Landau

Mathematics

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Hermann studied mathematics at Göttingen under Emmy Noether and Edmund Landau,[2] where she achieved her PhD in 1926. Her doctoral thesis, The Question of Finitely Many Steps in Polynomial Ideal Theory (German: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale), published in Mathematische Annalen, is the foundational paper for modern computer algebra. It first established the existence of algorithms (including complexity bounds) for many of the basic problems of abstract algebra, such as ideal membership for polynomial rings. Hermann's algorithm for primary decomposition is still in contemporary use.[3]

Assistant to Leonard Nelson

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From 1925 to 1927, Hermann worked as assistant for Leonard Nelson.[1] Together with Minna Specht, she posthumously published Nelson's work System der philosophischen Ethik und Pädagogik,[4] while continuing her own research.

Quantum mechanics

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As a philosopher, Hermann had a particular interest in the foundations of physics. In 1934, she went to Leipzig "for the express purpose of reconciling a neo-Kantian conception of causality with the new quantum mechanics".[5] In Leipzig, many exchanges of thoughts took place among Hermann, Carl Friedrich von Weizsäcker, and Werner Heisenberg.[5] The contents of her work in this time, including a focus on a distinction of predictability and causality, are known from three of her own publications,[1] and from later description of their discussions by von Weizsäcker,[6] and the discussion of Hermann's work in chapter ten of Heisenberg's Physics and Beyond. From Denmark, she published her work The foundations of quantum mechanics in the philosophy of nature (German: Die naturphilosophischen Grundlagen der Quantenmechanik). This work has been referred to as "one of the earliest and best philosophical treatments of the new quantum mechanics".[7] In this work, she concludes:

The theory of quantum mechanics forces us […] to drop the assumption of the absolute character of knowledge about nature, and to deal with the principle of causality independently of this assumption. Quantum mechanics has therefore not contradicted the law of causality at all, but has clarified it and has removed from it other principles which are not necessarily connected to it.

— Grete Hermann, The foundations of quantum mechanics in the philosophy of nature[8]

In June 1936, Hermann was awarded the Richard Avenarius prize together with Eduard May and Th. Vogel.[9][10]

Hidden variables

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Based on her views on quantum causality, Hermann concluded that there was no way to explain quantum mechanics in terms of a hidden variable theory. However, she published a critique of John von Neumann's 1932 proof from his book Mathematical Foundations of Quantum Mechanics, that was widely claimed to show that such a theory was impossible. Hermann's work on this subject went unnoticed by the physics community until it was independently discovered and published by John Stewart Bell in 1966, and her earlier discovery was pointed out by Max Jammer in 1974.[11][12] Some have posited that had her critique not remained nearly unknown for decades, her ideas would have put in question the unequivocal acceptance of the Copenhagen interpretation of quantum mechanics, by providing a credible basis for the further development of nonlocal hidden variable theories, which would have changed the historical development of quantum mechanics.[1]

Political activism

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As Adolf Hitler came to power in Germany, Hermann participated in the underground movement against the Nazis. She was a member of the Internationaler Sozialistischer Kampfbund (ISK).[13]

Emigration and later years

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By 1936, Hermann left Germany for Denmark and later France and England.[13] In London, in order to avoid standing out on account of her German provenance, she married a man called Edward Henry early in 1938.[14] Her prescience was justified by events: two years later the British government invoked its hitherto obscure 1939 Defence Regulation 18B, identifying several thousand refugees who had fled Germany for reasons of politics or race as enemy aliens and placing them in internment camps.[15]

After World War II ended in 1945, she was able to combine her interests in physics and mathematics with political philosophy. She rejoined the Social Democratic Party (SPD) on returning in 1946 to what would become, in 1949, the German Federal Republic (West Germany).[16] Starting in 1947 she was one of those contributing behind the scenes to the Bad Godesberg Programme, prepared under the leadership of her longstanding ISK comrade Willi Eichler, and issued in 1959, which provided a detailed modernising platform that carried the party into government in the 1960s.[16]

She was nominated professor for philosophy and physics at the Pädagogische Hochschule Bremen [de] and played a relevant role in the Education and Science Workers' Union. From 1961 to 1978, she presided over the Philosophisch-Politische Akademie [de], an organisation founded by Nelson in 1922, oriented towards education, social justice, responsible political action and its philosophical basis.[13][17]

Works

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Articles
  • Grete Hermann: Die naturphilosophischen Grundlagen der Quantenmechanik, Naturwissenschaften, Volume 23, Number 42, 718–721, doi:10.1007/BF01491142 (preview in German language)
  • Grete Hermann: Die Frage der endlich vielen Schritte in der Theorie der Polynomideale. Unter Benutzung nachgelassener Sätze von K. Hentzelt, Mathematische Annalen, Volume 95, Number 1, 736–788, doi:10.1007/BF01206635 (abstract in German language) — The question of finitely many steps in polynomial ideal theory (review and English-language translation)

References

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  1. ^ a b c d Soler, Léna (2009). "The Convergence of Transcendental Philosophy and Quantum Physics: Grete Henry-Hermann's 1935 Pioneering Proposal". In M. Bitbol; P. Kerszberg; J. Petitot (eds.). Constituting Objectivity. The Western Ontario Series in Philosophy of Science. Vol. 74. Springer. pp. 329–344. doi:10.1007/978-1-4020-9510-8_20. ISBN 978-1-4020-9509-2.
  2. ^ "Margarethe Hermann - The Mathematics Genealogy Project". www.genealogy.math.ndsu.nodak.edu. Retrieved 29 May 2019.
  3. ^ Ciliberto, Ciro; Hirzebruch, Friedrich; Miranda, Rick; Teicher, Mina, eds. (2001). Applications of Algebraic Geometry to Coding Theory, Physics and Computation. Nato Science Series II. Dordrecht: Springer Netherlands. ISBN 978-94-010-1011-5.
  4. ^ Minna Specht Archived 3 March 2016 at the Wayback Machine, Philosophisch-Politische Akademie (in German language), doanloaded 22 January 2012
  5. ^ a b Bacciagaluppi, Guido; Crull, Elise (December 2009). "Heisenberg (and Schrödinger, and Pauli) on hidden variables". Studies in History and Philosophy of Science Part B. 40 (4): 374–382. Bibcode:2009SHPMP..40..374B. CiteSeerX 10.1.1.484.3421. doi:10.1016/j.shpsb.2009.08.004. S2CID 13140289. PhilSci:4759.
  6. ^ Carl Friedrich von Weizsäcker, see for example: Jagdish Mehra, Helmut Rechenberg: The Historical Development of Quantum Theory, Volume 6 The Completion of Quantum Mechanics 1926–1941, Part 2, Springer, 2001, ISBN 0-387-95086-9, p. 712 f.
  7. ^ Crull, Elise; Bacciagaluppi, Guido (2021). "Translation of: W. Heisenberg, "Ist eine deterministische Ergänzung der Quantenmechanik möglich?". The Einstein Paradox: The Debate on Nonlocality and Incompleteness in 1935. Cambridge University Press. PhilSci:8590.
  8. ^ Grete Hermann: The foundations of quantum mechanics in the philosophy of nature. Cited after its translation from German with an introduction by Dirk Lumma in The Harvard Review of Philosophy VII (1999), p. 35 ff.
  9. ^ C. F. Freiherr v. Weizsäcker (interviewed), Konrad Lindner: Carl Friedrich von Weizsäcker über sein Studium in Leipzig, NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin, vol. 1, no. 1, pp. 3-18, doi:10.1007/BF02914089, see fulltext
  10. ^ V. F. Lenzen: Die Bedeutung der Modernen Physik für die Theorie der Erkenntnis. Drei mit dem Richard Avenarius-Preis ausgezeichnete Arbeiten von Dr. Grete Hermann, Dr. E. May, Dr. Th. Vogel, In A. P. Ushenko (ed.): The Philosophy of Relativity, Science, vol. 85, no. 2217 (25 June 1937), pp. 606-607
  11. ^ Jammer, Max (1974). The Philosophy of Quantum Mechanics. John Wiley and Sons. pp. 207–209, 265–274. ISBN 0-471-43958-4.
  12. ^ Mermin, N. David; Schack, Rüdiger (September 2018). "Homer Nodded: Von Neumann's Surprising Oversight". Foundations of Physics. 48 (9): 1007–1020. arXiv:1805.10311. Bibcode:2018FoPh...48.1007M. doi:10.1007/s10701-018-0197-5.
  13. ^ a b c Grete Henry-Hermann, Friedrich Ebert Foundation, downloaded 22 January 2012
  14. ^ "Marriage registry index (Marylebone)". FreeBMD. ONS. Retrieved 15 February 2016.
  15. ^ Patricia Shipley; who is "grateful to Fernando Leal, Rene Saran, and Dieter Krohn for their helpful comments in the preparation of this account" (20 November 2012). "Grete Henry - Hermann (1901-1984) (A personal account for the trustees of the SFCP)". {{cite journal}}: Cite journal requires |journal= (help)CS1 maint: multiple names: authors list (link)
  16. ^ a b Andrea Abele; Helmut Neunzert; Renate Tobies (2004). Berufswege promovierter Mathematikerinnen und Mathematiker. Springer Basel AG. pp. 110–111. ISBN 978-3-7643-6749-7. {{cite book}}: |work= ignored (help)
  17. ^ Philosophisch-Politische Akademie (in German language), downloaded 22 January 2012

Further reading

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  • C. Herzenberg: Grete Hermann: Mathematician, Physicist, Philosopher, Bulletin of the American Physical Society, 2008 APS April Meeting and HEDP/HEDLA Meeting, Volume 53, Number 5, 11–15 April 2008 in St. Louis, Missouri (abstract)
  • Vera Venz: Zur Biografie von Grete Hermann, GRIN 2009, First edition 2001, ISBN 978-3640411924 (in German language)
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