This thread is about my claim that the Bell-test experiments do not rule out local realism but Bell's implicit assumption of the additivity of expectation values in the proof of his theorem.
I have explained this claim in considerable detail in one of my preprints on the arXiv: https://arxiv.org/pdf/1704.02876.pdf. Let me quote an essential paragraph from the preprint:
The highlighted part is what was recalled by Peter G. Bergmann, who was Einstein's assistant (i.e., his postdoc), and reported by Abner Shimony (my Ph.D. mentor) in one of his papers.
Thus the flaw in Bell's theorem was pointed out by Einstein in 1938 when Bell was hardly ten years old. It is so basic that it is mindboggling why it has not been recognized before.
The flaw has to do with the assumption of the additivity of expectation values in any derivation of a Bell-type inequality. That assumption is illegal for hidden variable theories of any kind, as pointed out by Einstein in the mid-1930s, and independently by Bell himself just before 1964, in the context of von Neumann's theorem against hidden variables. Just because the additivity of expectation values follows by following mathematics does not mean that it is meaningful physically. Einstein saw that clearly, and so did Bell in the above-mentioned context. Consequently, what is ruled out by the Bell-test experiments is not local realism but additivity of expectation values --- which is not permissible for hidden variable theories to begin with.
To understand Einstein's point, let r and s be the eigenvalues of the QM operators R and S, respectively. Then the eigenvalue of the operator R + S is not r + s if R and S do not commute.
Let us say the eigenvalue of the operator R + S is t when R and S do not commute, where t is not equal to r + s.
Then the hidden variable counterpart of the QM equation < R > + < S > = < R + S > is not < r > + < s > = < r + s >. It is < r > + < s > = < t >.
To not recognize this within his theorem is Bell's mistake, as I have explained in considerable detail in my paper: https://arxiv.org/pdf/1704.02876.pdf.
If you do not have time to read my paper, then here is the upshot of it. Bell's derivation of his inequalities involves the additivity of expectation values:
< r > + < s > = < r + s >.
This is an assumption. Whether it is a justified assumption or not is irrelevant. What matters is that without this assumption the derivation of Bell inequalities does not go through.
Now we do the experiments and discover that the bounds of +/-2 on the Bell-CHSH inequalities are exceeded. The only rational conclusion from that is to conclude that the assumption of the additivity of expectation values is ruled out by the experiments. Anything else is pure speculation. That is my argument in a nutshell.
Here is a nice picture of Peter G. Bergmann (the man in the black suit), taken at an old gathering at Osgood Hill, North Andover, Massachusetts. I am kneeling down, second from your left.
Since everything I say is subject to challenge and doubt among some proponents of Bell's theorem, here is proof that I did collaborate with Abner Shimony, my Ph.D. mentor, and Peter G. Bergmann did collaborate with Albert Einstein, his post-doctoral mentor: https://mathscinet.ams.org/mathscinet/f ... ?version=2.
And here is a nice picture of John S. Bell and Abner Shimony. It was taken by me during a historic conference on the foundations of quantum physics, held on Mount Erice, Sicily, 1989.
.
