Topics

Focused deep-dives into individual results and themes that build on the core quantum mechanics pages. Where the main pages develop the standard formalism and survey the interpretations at a glance, these notes zoom in on a single programme and develop it in full — both its technical machinery and the philosophical questions it raises.

Contents

1. Bohmian Mechanics (the de Broglie–Bohm Pilot-Wave Theory) — the fully deterministic hidden-variable completion of quantum mechanics: the guidance equation, the quantum potential, quantum equilibrium and the derivation of the Born rule, the theory of measurement and effective collapse, non-locality and its relation to Bell's theorem; followed by an in-depth philosophical analysis of determinism, the primitive-versus-nomological ontology, empirical underdetermination, the "surreal trajectories" objection, and the tension with relativity.
2. Bell Nonlocality: The Structure of Quantum Correlations — the convex geometry behind the single CHSH inequality: the local, quantum, and no-signalling sets and their strict nesting; Bell inequalities as facets of the local polytope and Fine's theorem; the PR box and the algebraic maximum; Tsirelson's bound, the NPA hierarchy, and Tsirelson's problem (${\mathrm{MIP}}^{\ast }=\mathrm{RE}$); GHZ/Mermin all-versus-nothing contradictions; Kochen–Specker contextuality; and the device-independent payoff — self-testing, certified randomness, and DIQKD.

Reading order

These build on the standard formalism and the foundations cluster. Read Bohmian Mechanics after the postulates, wave mechanics, entanglement and Bell's theorem, and the survey of interpretations, which this page expands into a self-contained treatment. Bell Nonlocality follows directly from the entanglement and Bell's theorem page, deepening its CHSH result into the full geometry of quantum correlations; pair it with the philosophy of Bell's theorem remark for the interpretive side.