![]() ![]() ![]() ![]() Contra Bell, the theory is argued to satisfy the minimal desiderata for a Bohmian theory within the Primitive Ontology framework (for which we offer a metaphysically more perspicuous formulation than is customary). The distribution of its spontaneous localisations in configuration space is given by the Born Rule probability measure for the universal wavefunction. This many-particle system as a whole performs random jumps through 3 N-dimensional configuration space – hence “ Tychistic Bohmian Mechanics” (TBM). 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). ![]()
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