Relational Quantum Dynamics (RQD) and Bell’s Inequalities: A Category-Theoretic Analysis

Relational Quantum Dynamics (RQD) is a relational interpretation of quantum theory that rejects any absolute, observer-independent properties. We present a rigorous mathematical formulation of RQD’s account of Bell’s inequality violations, using category theory and sheaf theory to formalize quantum contextuality. In this framework, measurement outcomes form a presheaf over contexts, i.e., sets of jointly measurable observables, and the impossibility of a global hidden-variable assignment is interpreted as the absence of a global section of this presheaf. We demonstrate how Bell’s theorem emerges naturally: Any attempt to assign predetermined outcomes to all measurements is obstructed by a cohomological twist, reflecting the contextual nature of quantum reality. We use Čech cohomology to quantify this obstruction, showing that a non-trivial cohomology class serves as a rigorous witness to contextuality and to the violation of Bell’s inequalities. Throughout, we balance formalism with intuition, using a “jigsaw puzzle” analogy to illustrate why local pieces (measurement contexts) cannot be assembled into a single classical picture. This exposition integrates mathematical detail with conceptual clarity to show how the relational ontology of RQD naturally resolves the apparent non-locality of Bell correlations without invoking hidden variables or action-at-a-distance.