For those not familiar with my work (or not wanting to read my arXiv reply to Gill), let me summarize the elementary conceptual mistake Gill and other Bell devotees have been making for the past 50 years.
Let the four numbers A, A’, B, and B’ take binary values +1 or -1, and consider the four averages, <AB>, <AB’>, <A’B>, and <A’B’>.
These four averages happen to be of physical interest in the actual EPR-Bohm type experiments.
Now in 1964 Bell noticed a century old observation by Boole that the absolute value of the average
<AB + AB’ + A’B – A’B’> = <A(B + B’) + A’(B – B’)>
cannot exceed the value 2, simply because if B + B’ = 2 then B – B’ = 0, and vice versa.
From this Bell jumped to the conclusion that, therefore, the absolute value of the string of averages,
| <AB> + <AB’> + <A’B> - <A’B’> |
also cannot exceed the value 2.
But any schoolboy can see that within the context of the EPR-Bohm type experiments the single average
<AB + AB’ + A’B – A’B’>
is
not the same as the string of four averages
<AB> + <AB’> + <A’B> - <A’B’> .
To be sure, average of sum = sum of averages assumption is fine when all A, A', B, and B' are on equal footing (or are
standardized variables), but not at all fine within the context of the EPR-Bohm type experiments involving
spin measurements about
different directions in the physical space. This is essentially the point brought out is some detail in the above reply to Gill. He and other Bell devotees have simply failed to understand the physics and 3D geometry involved in any such experiment:
http://arxiv.org/pdf/1501.03393.pdf.
Moreover, it so happens that in almost every single physical experiment Bell has been proven wrong. The absolute value of the above string of averages has been shown in many experiments to exceed the value 2. But the Bell devotees like Gill do not take this experimental verdict on face value and accept that Bell has been proven wrong. Rather, they see the experimental refutation of Bell as a vindication of their belief that there is voodoo in the world, whereby our actions here may have instantaneous reactions at the remote parts of the universe. Well, the proposed macroscopic experiment discussed above aims to rectify this sad state of affairs.