One implication of Bell's theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig (2015) to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite collection of probability zero events whose disjunction exhausts the space of experimental possibilities.

This article takes up a suggestion that the reason we cannot find certain hidden variable theories for quantum mechanics, as in Bell's theorem, is that we require them to assign joint probability distributions on incompatible observables. These joint distributions are problematic because they are empirically meaningless on one standard interpretation of quantum mechanics. Some have proposed getting around this problem by using generalized probability spaces. I present a theorem to show a sense in which generalized probability spaces can't serve as hidden variable theories for quantum mechanics, so the proposal for getting around Bell's theorem fails. 1 Introduction 2 Bell's Theorem and Classical Probability Spaces 2.1 Bell's derivation of the Bell inequalities 2.2 Pitowsky's derivation of the Bell inequalities 3 Incompatible Observables 4 Generalized Probability Spaces 5 A 'No-Go' Theorem 6 Conclusions

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This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then, we apply this approach to analyze the classical limits of unbounded quantities in bosonic quantum field theories, with particular attention to number operators and Hamiltonians. The methods take classical limits in a representation-independent manner and so allow one to compare quantities appearing in inequivalent Fock space representations.

In this paper, I examine the relationship between physical quantities and physical states in quantum theories. I argue against the claim made by Arageorgis (1995) that the approach to interpreting quantum theories known as Algebraic Imperialism allows for "too many states". I prove a result establishing that the Algebraic Imperialist has very general resources that she can employ to change her abstract algebra of quantities in order to rule out unphysical states.