Setting the detectors angles at 90 and 135 degrees, and using this fragment of R code extracted from JC's original simulation of his S^3 model
###
N = 10^6
alpha = 90 * pi / 180
beta = 135 * pi / 180
a = c(cos(alpha),sin(alpha))
b = c(cos(beta), sin(beta))
s = runif(N, 0, pi)
t = runif(N, 0, pi)
x = cos(s)
y = -1 2.08 / sqrt(1 (3 * t / pi))
e = rbind(x, y)
###
the sample correlation of the spin measurements computed by
mean(sign(colSums(e * a)) * sign(colSums(-e * b)))
is -0.275062, in disagreement with the -cos QM prediction computed as
-sum(a * b)
which gives us the result
-0.7071068
But things are much worst than this: QM predicts other things that are in total disagreement with JC's S^3 model. For instance, QM says that at each detector the expectation of the spin measurements is exactly zero. Let's see what JC's S^3 model has to say about this. Computing the sample average of the spin measurements at detector A with
mean(sign(colSums(e * a)))
we find, amazingly, that it is exactly equal to one! The situation is even worst. JC's S^3 model results in ALL measurements of spin at detector A begin exactly equal to one! Check out what happens for the first 100 measurements:
sign(colSums(e * a))[1:100]
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[35] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[69] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Of course, this is total disagreement with mother Nature and the predictions of QM. The singlet state is a little bit more symmetric than this. But please, don't believe me. Download R and paste the commands to see it by yourself.
