I have a recent paper on vixra: Correlation of - Cos θ Between Measurements in a Bell's Inequality Experiment Simulation Calculated Using Local Hidden Variables
http://vixra.org/abs/1610.0327
In the paper I take Susskind's example of how QM breaks a Bell's Inequality and make a computer simulation using local hidden variables of artificial particles. I obtain exactly (by the dot product projections onto the detector vectors) the same QM values for the proportions which break the inequality as calculated by Susskind. Clearly, my simulation is finding fractional projection proportions of exact unit particle vectors onto exact detector vectors. QM gets the same proportions without knowing the individual particle vectors. But as the answers are the same, the QM proportions are statistically estimated fractional projection values onto exact detector vectors. And these break the inequality.
Having established that the QM proportions breaking the inequality are, or at least match in value, fractional projections onto exact detector vectors, I then calculated the quantum correlation using a similar, local method. Knowing the exact particle vectors allows the fractional projection on each detector for each particle separately, and these fractional values can be correlated. They give the disattenuated quantum correlation (i.e 0.707 for 45 degrees) rather than the mundane, truncated, Bell-limited correlation (0.5). It is also a standard formula that a correlation between two exact vectors is cos theta where cos 45 degrees = 0.707. So my simulation has used proportions on exact detector vectors, and correlations on similar proportions to break the inequality for both proportions and correlations.
All the above is based on real, local, hidden variables of the particles. The particles' exact vectors need to be known for the simulations, whereas QM can estimate the proportions without knowing the hidden variables. And it is great that QM can do this. But unfortunately QM cannot cope with the two dimensional nature of a correlation. QM cannot derive the quantum correlation between exact detector vectors that I have simulated.
For me that should be end-of-game as my simulations show there is nothing spooky about breaking Bell's Inequality using exact fractional values on exact vectors. But QM cannot do the same for correlations on exact vectors, and it must be shown that QM can do this job. So instead ..... CHSH theory bases its calculation on the correlations between fuzzy vectors-on-a-hemisphere! Alice's and Bob's measurements are fuzzy vectors on a hemisphere as they have compactified the rich data of the particle's directions into binary outcomes where +1 represents one hemisphere and -1 represents the the complementary hemisphere. This loss of information in going from exact to fuzzy vectors is a form of loss of precision in measurement. The loss of precision is a loss of reliability of measurement. Loss of reliability of measurement is well known to attenuate a correlation, eg from 0.707 down to 0.5. But QM must be shown to have the power to calculate the disattenuated quantum correlation direct, so here is where the spooky non-locality enters the picture through trying to correlate two fuzzy vectors in order to get the same correlation as one gets between the two exact vectors.
I am currently writing a further vixra paper on the topic of CHSH results. I have simulated a CHSH S = 2.5 statistic by starting with a CHSH S = 2 statistic involving 16*8 measurements of A and B in total. Then maliciously (rather than randomly) tweaking just 4 of the 128 measurements by reversing their signs, sends S from 2 to 2.5. A 2015 real experiment reports S = 2.4 where they are aiming for 2.818 and trying to rise above 2.0.