OBSERVATION CONTRACT
Spin-half singlet, not polarization
E(a,b) = −V cos(a−b)P(A,B) = ¼[1−AB V cos(a−b)]
A and B are ±1; 0≤V≤1. This is a coplanar spin-half singlet model. It does not use the doubled angle of a photon-polarization model.
OBSERVATION CHAMBER / ACTIVE
Bell Correlation Observatory
Choose spin measurement directions and compare singlet correlations with a local hidden-variable model through CHSH values and seeded samples.
quantum / correlation
Observation Model
ROUTE 95 / STRUCTURE / QUANTUM BELL CORRELATION
SPIN-½ SINGLET / FOUR SETTINGS
Four settings, two correlation laws
Turn the analyzer axes and compare the smooth singlet law with a local classical reference. SAMPLE draws one equal-size batch for each setting. Read the expected CHSH value separately from its finite estimate.
READYThe curve is an expectation, not a particle trajectory. Focus this canvas: S / Space SAMPLE, R RESET, 1 MAX, 2 ALIGNED, 3 NOISY.
Canvas 2D is unavailable. All values and four-setting counts remain available in the tables below. PNG is unavailable.
- Quantum expected S
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- Classical expected S
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- Quantum sampled S
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- Classical sampled S
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- Quantum sampled |S|
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- Classical sampled |S|
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- Quantum theoretical SE(S)
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- Classical paired empirical SE(S)
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FOUR-SETTING LEDGER
Joint counts, with no discarded outcomes
Accepted quantum pairs / classical shared-lambda trials: —
Every four-number cell is ordered ++ / +− / −+ / −−. Exact A and B marginals are each 1/2. Finite counts fluctuate. Tables remain usable without Canvas.
| SETTING | E quantum | E classical | P quantum | Quantum counts | Classical counts | Ê quantum | Ê classical |
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DETERMINISTIC SELF-TEST
Numerical acceptance —
Tests cover exact fixtures, probability normalization, marginals, analytic bounds, paired classical bounds, reproducibility, input caps, and a fixed 16-seed distribution check. PASS tests this implementation, not a physical Bell experiment.
| CHECK | VALUE | LIMIT / REFERENCE | RESULT |
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Observation report
CLASSICAL REFERENCE
One λ for four questions
A = sign cos(a−λ)B = −sign cos(b−λ)
λ is uniform on [0,2π); sign(0)=+1. Each trial reuses λ for all four settings, so Sᵢ=±2 and every finite classical average obeys |S|≤2. Its exact curve is −1+2d/π, where d=acos cos(a−b).
MODEL NOTE
A local calculation of a joint law
The quantum sampler draws the joint outcome centrally in this browser, using independent batches for each setting. It is not an implementation of two isolated local boxes. No detector physics, loophole-free proof, or faster-than-light communication is claimed.
Formula note
S = E(a,b)+E(a,b′)+E(a′,b)−E(a′,b′)
MAX gives S=−2√2 V; ALIGNED gives S=−2 at V=1. The analytic quantum bound is |S|≤2√2. Finite quantum estimates can exceed it through sampling; they are not clamped. Quantum SE is theoretical: √[Σ(1−Eⱼ²)/N]. Classical SE uses the sample variance of the paired Sᵢ: √[(ΣSᵢ²−(ΣSᵢ)²/N)/(N(N−1))]. It does not treat the four classical correlators as independent.
Exact marginal probabilities do not depend on the other analyzer angle. This mathematical no-signaling property does not turn this educational sampler into an experiment.
OBSERVATION GUIDE
Read expectations before sampling
Start with MAX and V=1. Compare expected S=−2√2 with the classical −2. Press SAMPLE and compare the signed estimates, their absolute values, and their standard errors.
- Choose NOISY to halve the quantum correlation. Choose ALIGNED to test perfect anticorrelation.
- Increase N to reduce typical sampling noise; a finite batch is not guaranteed to violate a bound. Use the seed to reproduce a batch, not to select favorable trials.
- REPORT records all four count rows. PNG saves the current curve and CHSH ledger. RESET and input edits clear previous outputs.
Educational probability model only. No real particle, visitor, or device is measured.
Runs in the browser without upload or registration.
OBSERVATION POLICY
This spin-half singlet and local hidden-variable comparison runs in your browser. Settings, sampled pairs, reports, and images stay local. It does not measure real particles or visitors.
Route
This chamber belongs to Structures & Symmetries.
STRUCTURE Back to Structures & Symmetries Route.