Quantum Logic and Possibility Structures

Dissertation, University of Maryland, College Park (1992)

Quantum mechanics is difficult to understand not because it is irreducibly probabilistic. It is difficult to understand because the probabilities themselves seem to defy reasonable interpretation. I propose that quantum logic, realistically construed as telling us something about the physical world, is one part of such a reasonable interpretation. ;The main idea behind a realist quantum logic is that a logic generates a possibility structure, and that quantum logic generates the possibility structure of quantum mechanical systems. Most work on quantum logic has involved a description of this possibility structure, and arguments for why the differences between the classical and quantum possibility structures account for the differences between classical and quantum mechanical systems. Less attention has been paid to the physical meaning of the quantum possibility structure. This is primarily the issue I will address. In doing so it will be necessary to consider a variety of issues including: what a possibility structure is, how, in general, possibility structures are given physical meaning, and how the possibility structure generated by quantum logic is related to other modalities occurring in quantum mechanics. ;The dissertation is divided into five chapters. The first is an argument that, despite first appearances, classical logic and probability are not disconfirmed by the experimental violations of Bell's inequalities. Thus, one cannot argue for quantum logic on empirical grounds. The second chapter is a consideration of Pitowsky's quantum logic, and an argument against his claim that all realist quantum logics are non-local hidden-variables theories. In the third chapter, I present an account of physical modality based upon logical modality and physical theory. Chapter four is an argument that there are two levels of modality in quantum mechanics: one corresponding to the possibility structure given by quantum logic, and the other corresponding to the theory's probabilistic character. In the last chapter, I present a version of quantum logic and show how it characterizes the possibility structure of quantum mechanics
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