Alain Aspect, a professor of physics at the École Polytechnique, is known for the most rigorous experimental tests of the
Bell inequalities.
His experiments changed the settings of the distant particle tests while the particles are in flight, to prevent signals exchanged between the original settings from influencing the results.
In his contribution to
Quantum [Un]Speakables, the 2002 memorial volume for John Bell, Αspect derived the polarization coefficient E(Θ) as a function of the angle between the polarizers
We can compare Aspect's result to the local hidden variables polytope.
Both diagrams show Bell's linear (straight line) inequality and the odd "kinks" at the corners (0, π/2, π, 3π/2), where Bell's values correspond to the quantum mechanical values.
In 1976, Bell gave us this diagram of the "kinks" in his local hidden variables inequality. He says,
Unlike the quantum correlation, which is stationary in θ at θ = 0, the hidden variable correlation must have a kink there.
("Einstein-Podolsky-Rosen Experiments," republished in Speakable and Unspeakable in Quantum Mechanics," 1987, p. 85)
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