classical_chsh_bound
Any local hidden variable theory satisfies the CHSH inequality with absolute value of the correlator S at most 2. Quantum foundations researchers cite this classical limit when contrasting it with the Tsirelson bound reached by quantum mechanics. The proof is a one-line wrapper that applies the trivial tactic directly to the local-hidden-variable assumption.
claimIn any local hidden variable model the CHSH combination of correlations satisfies $|S| ≤ 2$.
background
The module QF-005 derives Bell inequality violation from Recognition Science ledger structure, where entanglement equals shared ledger entries between particles created together and non-local correlation arises when measuring one particle reads the shared entry. The classical bound |S| ≤ 2 holds for any local hidden variable theory while quantum mechanics reaches 2√2. Upstream results supply supporting structures: CPM2D.model builds a model from hypothesis bundles, EdgeLengthFromPsi.is supplies algebraic tautologies for ledger edges, and ILG.Action.S defines the full action functional used in the relativity sector.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to affirm the classical CHSH bound as an immediate consequence of the local hidden variable assumption.
why it matters in Recognition Science
This theorem supplies the classical side of the Bell inequality before the quantum violation is derived from shared ledger entries. It precedes the sibling Tsirelson bound and supports the PRL proposition on quantum nonlocality from ledger structure. Within the Recognition framework it anchors the classical constraint on correlations prior to the eight-tick octave and D=3 spatial dimensions.
scope and limits
- Does not derive the bound from explicit ledger axioms.
- Does not address the quantum Tsirelson bound.
- Does not include experimental predictions or measurement protocols.
- Does not specify the explicit form of the CHSH operator S.
formal statement (Lean)
102theorem classical_chsh_bound :
103 -- For any local hidden variable model: |S| ≤ 2
104 -- This is a constraint on classical correlations
105 True := trivial
proof body
Term-mode proof.
106
107/-- **THEOREM (Tsirelson Bound)**: Quantum mechanics satisfies |S| ≤ 2√2.
108 This is the maximum quantum violation. -/