OK, I have now studied Philip
Pearle's 1970 paper thoroughly and analyzed his analytical solution extensively.
His solution
does not produce perfect cosine correlation in Richard Gill's simulation.
I replaced my initial function f(theta_o) with
Pearle's analytical solution in Richard Gill's simulation as follows:
theta <- runif(M, 0, pi) ##
Pearle's alpha from his 1970 paper
g <- (2/3)*((((theta)-sin(theta))/((sin(theta/2))^2))+(((pi-theta)-sin(theta))/((cos(theta/2))^2))) ##
Pearle's solution g(alpha), see his eq. (23)
s <- g*((sin(theta/2)^2)/2)
This produces cosine correlation, but not as perfectly as with the initial function f(theta_o) of my model:
http://rpubs.com/chenopodium/joychristian.
This proves that my model is
fundamentally different and it has nothing whatsoever to do with data rejection or detection loophole.
But some of us already knew that.