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The Origins of Heisenberg’s Program

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Heisenberg’s path of constructing a novel, fundamental theory on the basis of the philosophical principle of reductive monism has its origins in the manifold constraints on scientific research in postwar Germany. In 1941, Heisenberg had become director of the Kaiser Wilhelm (today: Max Planck) Institute for Physics, then located in Berlin.

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  • DOI: 10.1007/978-3-030-20645-1_2
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  1. 1.

    For detailed biographical information on Heisenberg I rely on (Cassidy 1992) throughout.

  2. 2.

    On the history of Heisenberg’s institute see Kant (1996), Rechenberg (1996), Henning and Kazemi (2016).

  3. 3.

    See Cassidy (1981), Blum (2017).

  4. 4.

    See Rechenberg (1989), Blum (2017).

  5. 5.

    For more on how the scientists at Heisenberg’s institute dealt with these restrictions, e.g., by moving into plasma and astrophysics, see an upcoming book on the history of astrophysics within the Max Planck Society by Luisa Bonolis and Juan Andres Leon.

  6. 6.

    As witnessed by an edited volume on cosmic rays presenting the work at the institute (Heisenberg 1953a).

  7. 7.

    On these trips, see Rechenberg (1989). Also see Walker (1992) on how with these trips Heisenberg was (perhaps unwittingly) agreeing to act as a cultural goodwill ambassador for Nazi Germany in order to keep up his scientific collaboration with foreign scholars.

  8. 8.

    Und schließlich wird es noch etwa 2 Jahre dauern, bis wieder genügend junge Physiker mit abgeschlossener Hochschulausbildung, im Alter zwischen 25 und 30 Jahren zur Verfügung stehen, die für den Betrieb eines Forschungsinstituts ebenso notwendig sind, wie die grossen Apparate. Die Geschichte der KWG und MPG 1945–1949, Teil I & II; Festschrift für Otto Hahn (1949). A copy is to be found in AMPG, V. Abt. Vc, Rep. 4.

  9. 9.

    As discussed in Carson (1995, p. 428).

  10. 10.

    Letter to Pauli of 3 February 1950, PSC IV-I.

  11. 11.

    Heisenberg’s father August had taught Classics at secondary school and university, and Pauli, after Heisenberg returned to the atomist narrative in the 1948 lecture to be discussed below, granted: “Heisenberg’s relation with antiquity [is] alive and real. It is quite natural that he returns to this subject time and again” (Heisenbergs Beziehung zur Antike [ist] lebending und echt. Es ist ganz natürlich, dass Heisenberg immer wieder auf dieses Thema zurückkommt.) Letter from Pauli to Markus Fierz of 17 July 1948, PSC III. Heisenberg (1969, p. 7) himself later chose to place his reading of Plato’s Timaeus as a high school student at the beginning of his intellectual autobiography.

  12. 12.

    Einseitigkeit und Überheblichkeit (Heisenberg 1933, p. 30).

  13. 13.

    Which of course strongly rings of the Forman (1971) Thesis.

  14. 14.

    Two years earlier, in 1930, Heisenberg had held a talk in Vienna where he had addressed such concerns, arguing for the epistemologically satisfactory nature of quantum mechanics while avowing that his listeners might “initially regret that the the intuitive and deterministic classical physics has recently been replaced by an unintuitive physics with statistical laws” (Heisenberg 1931, p. 366).

  15. 15.

    Wesen (Heisenberg 1933, p. 31).

  16. 16.

    Die konsequente Verfolgung des vorgeschriebenen wissenschaftlichen Weges führte zu Widersprüchen und der Umstand, dass diese Widersprüche trotz des angestrengten Bemühens der Physiker nicht eliminiert werden konnten, lehrte die Forscher bald, dass sie hier an einen erkenntnistheoretischen Abgrund geraten waren, der die letzten Grundlagen exakt-naturwissenschaftlichen Denkens in Frage stellte. Dies war auch nicht verwunderlich. Denn die Atomhypothese widerspricht dem anschaulichen Denken, das eine unendliche Teilbarkeit der Materie lehrt. Also konnte die Existenz unteilbarer Bausteine der Materie nur unter einem Verzicht auf die anschauliche Deutung verstanden werden.

  17. 17.

    As pointed out by Carson (2010, p. 34). Just like the Greek Classics, the Goethean tradition goes deep with Heisenberg personally. As Yvonne Hütter has pointed out, Goethe’s West-Östlicher Diwan plays a recurring role in Heisenberg’s narrative of his 1925 Helgoland epiphany. See, last accessed 9 May 2018.

  18. 18.

    This was an important event for Heisenberg, signaling his return to the international stage and bringing him together with several old friends whom he had not seen for many years, including most notably Wolfgang Pauli.

  19. 19.

    Dieses Programm konnte jetzt in einem gewissen Sinne vollständig durchgeführt werden (Heisenberg 1934, p. 16).

  20. 20.

    Aber damit, dass wir jetzt drei Grundstoffe, das heisst drei Sorten von Elementarteilchen—Elektronen, Protonen und Neutronen als die Bestandteile aller Materie ansehen, haben wir das Programm der Atomphysik noch nicht ganz zu Ende geführt, und damit komme ich zu dem eigentlichen Anliegen unserer heutigen Atomphysik (Heisenberg 1949, p. 95).

  21. 21.

    The use of this term, I suppose, was meant to conjure up notions of both universality and transformability. It should be noted, however, that in the late 19th Century it was precisely these features of energy that had suggested it as the fundamental concept in a decidedly anti-atomistic worldview, which could remain agnostic about the microscopic constituents of matter. On the history of this theory of energetics see Deltete (1983).

  22. 22.

    A copy of this report can be found in WHP, Folder 1260.

  23. 23.

    Heisenberg had met Wildermuth (1921–2005), when Wildermuth was a student at Berlin University during wartime. Wildermuth had been captured by the Soviet army, but fled from captivity, making his way to Göttingen, where he completed his first degree in physics and then became Heisenberg’s Ph.D. student (Fässler and Schmid 2006).

  24. 24.

    PSC IV-I.

  25. 25.

    Einer alten Gewohnheit entsprechend schicke ich Dir das Manuskript einer Arbeit, die von den Elementarteilchen handelt [...] Der Ausgangspunkt ist aber nicht die Quantenelektrodynamik, sondern die Art von allgemeiner Elementarteilchenphilosophie, wie ich sie in den letzten Jahren immer wieder getrieben habe. Nun schien mir, dass man das Programm, das ich mir früher gestellt habe, jetzt mit der neuen Mathematik à la Tomonaga u.s.w. mathematisch sauber durchführen kann. Es sieht also so aus, als stünde man jetzt auf mathematisch festem Grund, und, wie Bohr sagen würde: “man hved, hvad man kan haabe for”.

  26. 26.

    These foundations are of course saturated with empirical input, an input that has been processed to the point where it resembles purely formal constraints on theorizing.

  27. 27.

    There is of course the possibility of starting with just a Majorana or a Weyl spinor. While Heisenberg did consider this at times, he ultimately stuck to the well-known Dirac formulation used in the description of the electron. This provided his fundamental spinor with two additional degrees of freedom.

  28. 28.

    To be quite precise, he proved the existence of divergences that could not be removed by mass and charge divergence, not the existence of an infinite number of primitive divergents, i.e., non-renormalizability in the strict sense.

  29. 29.

    By “c-number” I mean something that is not an operator, i.e., commutes with all other quantities in the quantum theory.

  30. 30.

    Compare Schwinger’s contemporary magnum opus, the trilogy on QED, in particular (Schwinger 1948, Eq. 2.29) and (Schwinger 1949, Eqs. A.1, A.10, and A.29).

  31. 31.

    To be quite precise, Pauli and Villars merely regularized the \(\Delta \) function itself.

  32. 32.

    Most of the biographical information on Lehmann in this paragraph—that which is not drawn directly from archival sources—is taken from Zimmermann (2001).

  33. 33.

    Letter from Lehmann to Heisenberg of 3 August 1950, letter from Heisenberg to Lehmann of 10 November 1950. WHP, folder 1696, Correspondence L-Z 1950.

  34. 34.

    Heisenberg wollte mich unbedingt von seiner Theorie mit fauler Mathematik überzeugen. Amüsant war aber, dass Herr Lehmann ihm auch nichts glaubt. Dieser machte wirklich einen guten Eindruck auf mich.

  35. 35.

    This was somewhat spuriously motivated by his ongoing assumption that the Heisenberg picture commutators would be solutions to the interacting field equations, which, just like their free counterparts, were vanishing for space-like separated points and singular (though less so) at the origin.

  36. 36.

    The approximation mainly lay in the assumption that the states in Hilbert Space I only described free fundamental fermions, even though Heisenberg of course needed the existence of many bound states to reproduce the full spectrum of subnuclear particles.

  37. 37.

    Letter to Pauli of 10 April 1955, PSC IV-III.

  38. 38.

    This joke really only works in German, where the same word is used for a genie (in a bottle) and a ghost.

  39. 39.

    The paper was published on the occasion of the 60th birthday of Friedrich Hund. Heisenberg made the connection to Hund’s work, by likening the proposed selection rule that prevented transitions to ghost states to Hund’s Rule in atomic physics, which is based on the Pauli exclusion principle and thus on the reduction of the Hilbert space to a physically accessible part (anti-symmetrized wavefunctions as analogue of Hilbert Space I).

  40. 40.

    Wesentlich ist mir aber, dass der ganze “Begriff” Hilbert-Raum II ersetzt wird durch eine passende, wohldefinierte indefinite Metrik im Hilbert-Raum, die es einem dann gestattet, den von Dir behaupteten allgemeinen Zusammenhang [...] (Isolation der anomalen Zustände) exakt zu diskutieren. Letter from Pauli to Heisenberg, 23 June 1955, PSC IV-III.

  41. 41.

    Zwischen Ni. un Hei. sehe ich einige Schwierigkeiten voraus. Heisenberg hat sich ganz und gar in die Illusion hineingesteigert, Ni. wäre der Mann, der seine Theorie verstehen und aktiv daran mitarbeiten könne. Nun bin ich trotz Grippe einen Tag länger ins Institut gekommen, um während Hei. Reise nach Bonn, die Ansichten von Ni. zu erkunden (auf englisch!). Man kann sie etwa so schildern: [...] Von Hei. Theorie hält er gar nichts [...] Ni. beklagte sich, weil Hei. ihm geschrieben hatte, er würde sich [...] eine Woche Zeit nehmen, um mit Ni. ein Programm auszuarbeiten an dem Ni. [...] arbeiten könne. Ni. möchte lieber selbstständig arbeiten. Letter from Zimmermann to Lehmann, 30 January 1956, WZP, Folder Lehmann Correspondence.

  42. 42.

    Die Lage mit Nishijima hat sich weiter geklärt. Ich konnte erfahren, dass er nur wegen LSZ nach Göttingen gekommen ist. Letter from Zimmermann to Lehmann, 6 February 1956, WZP, Folder Lehmann Correspondence.

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Blum, A.S. (2019). The Origins of Heisenberg’s Program. In: Heisenberg’s 1958 Weltformel and the Roots of Post-Empirical Physics. SpringerBriefs in History of Science and Technology. Springer, Cham.

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