I wonder if Joy is not the one who is mixing up his spheres?
At the end of the exploding colourful balls experiment, we have two files containing directions of angular momentum in R^3. Points in S^2.
Two computer files, each on a different USB stick, the files are text files
called, say, AliceDirections.txt and BobDirections.txt.
They contain directions u_k and v_k, k = 1, ..., N encoded in spherical coordinates theta, phi,
and represented in ordinary decimal notation to say 10 significant figures.
Two floating point real numbers, e.g. separated by a few spaces, per line.
N lines of pairs of real numbers in both files.
These four times N numbers are all going to be calculated (but not all at the same time)
sign(a0 . u_k), sign(a90 . u_k), sign(b45 . v_k), sign(b135 . v_k),
k = 1, ..., N,
and these four correlations are all going to be calculated (but not all at the same time)
E(0, 45) = 1/N sum_k sign(a0 . u_k) sign(b45 . v_k) =?= - 0.7071...
E(0, 135) = 1/N sum_k sign(a0 . u_k) sign(b4135 . v_k) =?= 0.7071...
E(90, 45) = 1/N sum_k sign(a90 . u_k) sign(b45 . v_k) =?= - 0.7071...
E(90, 135) = 1/N sum_k sign(a90 . u_k) sign(b135 . v_k) =?= - 0.7071...
I am not going to put these numbers into one spreadsheet. I am not going to call them A, A', B, B'.
I have four different computer programs which will each read the same two data files AliceDirections.txt and BobDirections.txt, and then each compute just one of the four correlations according to Joy's formulas, as agreed in our bet.
If anyone likes I can show them the programs which I am going to use.
I believe that I will observe that one of those correlations is off by 0.2 or more, and if so, I'll report which one it is to the three adjudicators Khrennikov, de Raedt, Weihs. The adjudicators can then check. They also have a copy of the two files on the two USB sticks. They don't have to use my programs, they can use any computer language they like. Everyone will be able to see what calculation is done and what comes out of the calculation. The two data files AliceDirections.txt and BobDirections.txt will be posted on internet so everyone can check that my claim is right (if I'm right), or that Joy's claim is right (if he's right). They can do the calculations in a spreadsheet, by a perl script, with R, Python or with Mathematica, just as they like.
Now the problem for Joy is that by some simple algebra it is easy to check that
- E(0, 45) E(0, 135) - E(90, 45) - E(90, 135) = 1.
I don't mind whether the two computer files come from a real experiment or a simulated experiment. So anyone who can program Joy's model and get those two files to me before Joy gets them to me through his real experiment or through his own computer simulated experiment, is welcome to do so. If they succeed in proving me wrong they'll get 5 000 Euro from me, and undying fame. Joy says his experiment could generate those two files. So he believes that such sets of numbers exist. I believe they don't exist. Prove me wrong.