Mitsch, Chris (2022) Hilbert-Style Axiomatic Completion: On von Neumann and Hidden Variables in Quantum Mechanics. [Preprint]
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Abstract
In this paper I provide a detailed history of von Neumann’s “No Hidden Variables” theorem, and I argue it is a demonstration that his axiomatization mathematically captures a salient feature of the statistical transformation theory (namely, that hidden variables are incompatible). I show that this reading of von Neumann’s theorem is obvious once one recalls several factors of his work. First, his axiomatization was what I call a Hilbert-style axiomatic completion; indeed, it developed from work initiated by Hilbert (and Nordheim). Second, it was responsive to specific mathematical and theoretical problems faced by Dirac and Jordan’s statistical transformation theory (then called ‘quantum mechanics’). Third, the axiomatization was completed across his 1927 papers and 1932 book when he identified the basic assumptions underwriting quantum mechanics, showed that these suffice for deriving the trace rule, and showed that the trace rule is incompatible with hidden variables. With this reading in mind, his claim that quantum mechanics was in “compelling logical contradiction with causality” appears as a straightforward consequence of his theorem. I conclude by reassessing the theorem’s broader historical and scientific significance.
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Item Type: | Preprint | ||||||
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Additional Information: | accepted at Studies in History and Philosophy of Science | ||||||
Keywords: | von Neumann, quantum mechanics, hidden variables, Bohm, Bell, Hilbert, axiomatization, no-go | ||||||
Subjects: | Specific Sciences > Mathematics > Methodology General Issues > History of Science Case Studies Specific Sciences > Physics > Quantum Mechanics |
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Depositing User: | Chris Mitsch | ||||||
Date Deposited: | 30 Jun 2022 17:12 | ||||||
Last Modified: | 30 Jun 2022 17:12 | ||||||
Item ID: | 20825 | ||||||
Subjects: | Specific Sciences > Mathematics > Methodology General Issues > History of Science Case Studies Specific Sciences > Physics > Quantum Mechanics |
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Date: | June 2022 | ||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/20825 |
Available Versions of this Item
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Hilbert-Style Axiomatic Completion: The (Not So) Hidden Contextuality of von Neumann's "No Hidden Variables" Theorem. (deposited 10 Sep 2021 18:00)
- Hilbert-Style Axiomatic Completion: On von Neumann and Hidden Variables in Quantum Mechanics. (deposited 30 Jun 2022 17:12) [Currently Displayed]
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