Bell Correlation Shape Visualizer
The classical hidden-variable model produces a piecewise-linear triangle correlation (Eq 8.52), while the quantum/Nelson model produces the smooth cosine (Eq 8.61). The “excess curvature” between them is the irreducible quantum excess that violates Bell’s inequality. At finite temperature, thermal noise suppresses the cosine as (1 + 2nth)−2.
CHSH Bell Parameters
- |Sclassical| (Eq 8.56)
- 2.0000
- Bell bound
- |Squantum| (Eq 8.61)
- 2.8284
- Tsirelson bound
- |Sthermal| (Eq 8.91)
- 2.4025
- Bell violation — nth = 0.0425
- Tcrit (Eq 8.87)
- 0.1960 K
- T/Tcrit = 0.77
Verification Against Monograph (Table §8.5.2)
Why the Cosine, Not the Triangle?
Classical (triangle): Each photon carries a hidden polarisation λ. Detection is a sharp threshold: A = sign(cos(2(λ − θA))). The piecewise-linear triangle is the optimal LHV correlation, giving |S| = 2.
Quantum/Nelson (cosine): The Nelson osmotic velocity (Eq 8.58) dynamically correlates both detectors through the shared ether. Photon A’s effective polarisation fluctuates under Nelson diffusion, biased by photon B’s state. This “smooths” the sharp threshold into the Born probability cos²(φ − θ), giving the cosine correlation and |S| = 2√2.
Thermal: At finite temperature, thermal noise at each detector independently replaces quantum detections with random outcomes. The suppression factor (1 + 2nth)−2 degrades the Bell violation as a power law — the ether’s unique prediction (Theorem 8.8).
Beta Tools are under active development. Equations are verified against the monograph but outputs may be refined. Report an issue