Pro Tier Module

Bell / CHSH Inequality (Quantum Nonlocality)

Deterministic, in-browser computation of the CHSH (Clauser-Horne-Shimony-Holt 1969) form of Bell theorem, three ways.

See it run - a worked example, 100% in this browser tab

What it is

Deterministic, in-browser computation of the CHSH (Clauser-Horne-Shimony-Holt 1969) form of Bell theorem, three ways. Analytic: for a two-qubit singlet or Werner state of visibility V, the correlators E(a,b) = -V*cos(a-b) give the CHSH statistic S, bounded by |S| <= 2 for any local-hidden-variable theory but reaching the Tsirelson bound |S| = 2*sqrt(2) ~ 2.828 (Cirel`son 1980) at the canonical angles - the exact quantum ceiling; violation requires V > 1/sqrt(2). Monte-Carlo experiment: simulates N entangled-pair measurements drawing +/-1 outcomes with the exact quantum joint probabilities, so the estimated S exceeds the local bound by many standard errors, with honest sampling error. Local-hidden-variable baseline: simulates a fully local deterministic model whose S provably saturates at 2 and cannot reach the quantum value - the falsification made concrete. The correlations are the standard QM predictions; this is a theory calculator and a faithful simulator, not a physical experiment (no detector or locality loopholes modeled). The GeoNum verdict is the conditioning of the statistic (the correlator reductions and the residual against 2*sqrt(2)), checked against the published Tsirelson ceiling. No API, no key, no network, no AI.

Honest scope

Deterministic and citation-backed: every figure is exact arithmetic or a cited rule. Any year- or jurisdiction-indexed value is a confirmable input, never an eternal hardcode. This is a computation tool, not professional (legal, tax, medical, or financial) advice - confirm against the controlling authority for your context.

Authorities cited

Run it on your own data

Open it inside GDBS to save runs to Sandbox, attach results to a Worklog case, or share through a Gate client portal - all in the browser, nothing uploaded to anyone’s cloud.

GDBS by VaultSync Solutions Inc. - Verifiable Computation. gdbs.getvaultsync.com