Göttingen 2025 – wissenschaftliches Programm

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SYHQ: Joint DPG and EPS History of Quantum Physics Symposium

SYHQ 2: History of Quantum Mechanics II: Foundation, Dissemination, Politicization

SYHQ 2.1: Hauptvortrag

Montag, 31. März 2025, 14:00–14:30, ZHG010

Model and Target: Von Neumann's Mathematische Grundlagen — •Michael Stöltzner — University of South Carolina, Columbia, SC, USA

Based on joint work with Hilbert and Nordheim in 1927 and amended with a detailed discussion of measurement, von Neumann's 1932 `Mathematische Grundlagen der Quantenmechanik' was generally considered as the definitive formulation of the theory in rigorous mathematical terms. Especially the no-hidden-variable theorem was often read as a philosophically motivated finality claim. Accordingly, it became attacked by proponents of alternative interpretations, in the case of John Bell even together with mathematical physics as such. But this misunderstands the place that the book had in von Neumann's own work -- he quickly moved on from Hilbert spaces to operator algebras -- and in his increasingly opportunist understanding of mathematics. Understanding the context of von Neumann's book, including why he stressed the uniqueness and non-extendibility of quantum mechanics, helps to understand the multiple roles his work would play shortly after his death when a renaissance of mathematical physics took place in quantum field theory, and eventually also in atomic physics.

Keywords: John von Neumann; Mathematical Foundations of Quantum Mechanics; The Role of Mathematical Physics; Uniqueness and no-hidden variable theorems