Abstract
Prior to her extended stay in Leipzig and her 1935 essay on the foundations of quantum mechanics, Grete Hermann had written a manuscript on ‘Determinism and Quantum Mechanics’, which she had sent to some of the main quantum physicists at the time but had since disappeared. This manuscript was rediscovered by us in the Dirac Archive and appears in translation as Chap. 14 of this volume. In this chapter we give a first analysis of this fascinating manuscript, in which Hermann criticises known arguments for the incompatibility of quantum mechanics and determinism, including the theorem in von Neumann’s 1932 book, and sketches what a completion of quantum mechanics might have to look like.
Work for this chapter was carried out in part while EC was a postdoctoral research fellow at the Hebrew University’s Edelstein Center for the academic year 2013–2014. She wishes to thank the Edelstein Center for their generous support.
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Notes
- 1.
Our special thanks to Dieter Krohn for bringing this letter to the attention of the workshop participants.
- 2.
Dirac’s book appeared in German translation in the same year as the first English edition (Dirac 1930); the second English edition followed only in 1935.
- 3.
We have checked the contents of Hermann’s Nachlass with regard to her correspondence with Heisenberg, Weizsäcker and Van der Waerden in late 1933–early 1934, as well as the Dirac Archive, but found no evidence of his reply.
- 4.
Translations of both Hermann (1933) and Hermann (1935) are included in this volume as Chaps. 14 and 15, respectively. German editions of both and of a selection of Hermann’s correspondence (among which the letter to Dirac, the letter from Heckmann and correspondence with both Heisenberg and Weizsäcker—including the latter’s reply to Hermann’s manuscript on behalf of Bohr) are included in a forthcoming volume edited by Herrmann (2017).
- 5.
In the 1935 essay Hermann takes care to disentangle causality and predictability , since determining the causes of an event need not mean determining them in advance.
- 6.
We use ‘undetermined’ here, because Hermann clearly takes the German ‘unbestimmt’ to (misleadingly) suggest the reading ‘that which has not been determined but has a value’ rather than ‘that which does not have a determinate value in the first place’.
- 7.
Indeed, on 16 June 1934 she wrote to her mother that Heisenberg had finally had the upper hand in their debates (Herrmann 2017, Part III, Letter 8).
- 8.
Heisenberg may have been referring to the collection of four of Bohr’s essays, then (in December 1933) in preparation, to be published in 1934 under the title Atomic Theory and the Description of Nature (Bohr 1934).
- 9.
Von Neumann’s proof first appeared in fact in a paper presented by Max Born to the 11 November 1927 session of the Gesellschaft der Wissenschaften zu Göttingen (von Neumann 1927). Hermann may also have known of it already, but her presentation in 1933 appears to follow that in Chapter IV of von Neumann’s book (von Neumann 1932).
- 10.
- 11.
The question whether Bell is fairly criticising von Neumann for imposing an absurd condition on the hypothetical hidden variables has been fairly widely debated in the literature (already [Jammer 1974, p. 273] points out the significance of von Neumann’s footnote). On this, see the very convincing re-appraisal of von Neumann’s proof by Bub (2010) , as well as our further comments at the end of this section.
- 12.
- 13.
See e.g. again his Einstein (1953), written in fact for the festschrift in honour of Born’s retirement from Edinburgh.
- 14.
For instance, while treating the electron as a classically oscillating charge density leads to a useful semi-classical method of calculating the radiation emitted by an electron, one cannot describe the interaction of two charged particles as mediated by such semi-classical fields: the interaction of two charges is already fully described by the interaction term in the Schrödinger equation—see e.g. (Schrödinger 1928/2009, p. 411–414).
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Crull, E., Bacciagaluppi, G. (2016). Grete Hermann’s Lost Manuscript on Quantum Mechanics. In: Crull, E., Bacciagaluppi, G. (eds) Grete Hermann - Between Physics and Philosophy. Studies in History and Philosophy of Science, vol 42. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-0970-3_8
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