gill1109 wrote:I think we can now say publicly that Christian's bid to win my challenge before June 11 has failed. Gregor Weihs and Hans de Raedt have independently calculated the four correlations from both of Christian's recent submissions and in every case at least one of those correlations deviated more than 0.2 from target (+/- 0.7071).

On the contrary, I have

defeated Richard Gill's challenge

decisively, by not only unambiguously constructing the N spin vectors he had claimed were impossible to construct (as a “proof of concept” for my proposed experiment), but also by constructing

the entire correlation surface correctly:

http://rpubs.com/jjc/19298.

The evidence I have presented in the above simulation is here for everyone to see. On the other hand, it is also easy to see that the four correlations calculated by Richard Gill are simply wrong. Two of his results do not even lie on the correlation surface constructed in the above simulation. In other words, the four correlations he has calculated are not predicted by my model or my proposed experiment, or supported in any way by the data files of directions extracted from the simulation. As Fred has so clearly demonstrated above, one can easily feed the spin directions back into the simulation and see that they reproduce the correlation surface

exactly.

What is more, I have been able to generate the above correlation surface in a manifestly local-realistic manner, by providing the N

pre-selected spin directions. This suggests that

my proposed experiment will be a spectacular success. It will reproduce the strong correlations exactly as I have predicted in several of

my papers.

The evidence I have presented over the years for my 3-sphere model has been neatly summarized in this simulation:

http://rpubs.com/jjc/16567.

The most important conceptual innovation 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/or 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) ] = -cos(alpha - beta),

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.

In conclusion,

the Gill challenge is no more.

I have defeated it decisively, by explicitly constructing the spin vectors he had claimed were impossible to construct.