I am afraid I am unimpressed by Richard Gill’s comments above. In my opinion I have defeated his challenge decisively, by reproducing the entire correlation surface predicted by QM correctly. What is more, I have been able to accomplish this by providing N
pre-selected spin directions, as demonstrated in
this simulation. This suggests that
my proposed experiment will be a spectacular success. It will reproduce the strong correlations exactly as I have predicted in my papers. Contrary to what Richard Gill says, my model has nothing whatsoever to do with the detection loophole or conspiracy theory. It simply points out the correct topology of the physical space, which has been ignored by the Bell community---rather surprisingly---for the past 50 years, as I explain here:
http://arxiv.org/abs/1405.2355.
The evidence I have presented so far has been neatly summarized in this simulation of my 3-sphere model:
http://rpubs.com/jjc/16567.
The most important conceptual point here is that, what appeared as a "post-selection" of states to the flatlanders like Richard Gill, has now been formulated as a "state preparation" of the
pre-selected initial states of the system, originating at the source. This was never a problem from
the perspective of the 3-sphere, but the flatlanders were having a great deal of difficulty understanding my model because of it. But now the N spin directions, "v", which are actually observed by Alice and Bob, are all
pre-selected at the source (rather than post-selected at the detector), thereby removing the last vestige of the Bell-baggage from the simulation.
In summary, N spin directions, "v", as an ensemble of the initial or complete states of the physical system, are pre-selected at the source, after the state preparation within the 3-sphere, just as we prepare initial states in quantum mechanics and experiments. The correlations are then calculated using the standard formula,
E(a, b) = (1/N) Sum_(k=1)^(k=N) [ sign(+a.v_k) * sign(-b.v_k) ] = -a.b ,
where the measurement directions a and b are randomly selected, respectively, by Alice and Bob. Note that not a single one of Bell's assumptions has been dropped.
On the other hand, Richard Gill's incorrect calculations of the four correlations contradict the evidence presented
in this simulation. Note that two of his four correlations do not reside on the correlation surface presented in the simulation. Evidently, he has got his calculations badly mixed up, as I explained previously.