The resulting theory is about the system of all particles in the universe, each located in ordinary, 3-dimensional space. The paper takes up Bell's (1987) “Everett (?) theory” and develops it further. I conclude by reassessing the theorem's broader historical and scientific significance. 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. 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.
Second, it was responsive to specific mathematical and theoretical problems faced by Dirac and Jordan's statistical transformation theory (then called ‘quantum mechanics’). First, his axiomatization was what I call a Hilbert-style axiomatic completion indeed, it developed from work initiated by Hilbert (and Nordheim). I show that this reading of von Neumann's theorem is obvious once one recalls several factors of his work. 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). Section 1 contains, besides an introduction, also the papers five claims and a preview of the arguments supporting these claims so Part I, Section 1 may serve as a summary of the paper for those readers who are not interested in the detailed arguments. For reasons of length, the paper is published in two parts Part I appeared in the previous issue of this journal. The paper is self-contained and presupposes only basic knowledge of quantum mechanics.
Since the analysis is performed from the perspective of Suppes structural view (‘semantic view’) of physical theories, the present paper can be regarded not only as a morsel of the internal history of quantum mechanics, but also as a morsel of applied philosophy of science. The present paper claims to be a comprehensive analysis of one of the pivotal papers in the history of quantum mechanics: Schrödingers equivalence paper. To Procrustean places we go, where we can demonstrate the mathematical, empirical and ontological equivalence of ‘the final versions of’ matrix mechanics and wave mechanics. During the period 1926–1932 the original families of mathematical structures of matrix mechanics and of wave mechanics were stretched, parts were chopped off and novel structures were added. In order to make the theories equivalent and to prove this, one has to leave the historical scene of 1926 and wait until 1932, when von Neumann finished his magisterial edifice. The author endeavours to show two things: first, that Schrödingers (and Eckarts) demonstration in March (September) 1926 of the equivalence of matrix mechanics, as created by Heisenberg, Born, Jordan and Dirac in 1925, and wave mechanics, as created by Schrödinger in 1926, is not foolproof and second, that it could not have been foolproof, because at the time matrix mechanics and wave mechanics were neither mathematically nor empirically equivalent.
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