EPR & the Foundations of Quantum Mechanics

Abstract

This thesis argues that the apparent clash between Einstein-Podolsky-Rosen reasoning and the empirical violation of Bell inequalities is not best explained by "action at a distance," but by a structural conflict between the classical, distributive logic tacitly built into locality arguments and the non-distributive lattice that governs quantum propositions. It develops the Tractarian-Stone picture of classical logical space, and sets it against the Hilbert-space framework. Because span strictly exceeds union, distributivity generally fails, and with it the classical route to factorization that locality arguments require. Methodologically, the thesis contributes (i) a semantics-first comparison of classical Boolean lattices with the orthomodular lattice of closed subspaces, showing how Boolean "centers" of compatibility persist locally within a non-distributive structure; (ii) a reconstruction of the counterfactual step that isolates exactly which independence assumptions are doing empirical work; and (iii) an operational reading that connects finite-data tests to locality via matching conditions without invoking signaling. The result is a unified account in which violations of Bell inequalities register the failure of classical distributivity to extend to quantum disjunction, not evidence for hidden superluminal influence. Locality survives in its minimal, experimentally accessible form - no signaling - while classical factorization is revealed as a special case valid only inside compatible sublattices.