The following table demonstrates this inequality by the author using three coins.
Throw p(A,B) p(A,C) p(B,C) p(a,b) p(a,c) p(b,c) 1 a,B,C 1 2 a,B,c 1 3 A,b,c 1 4 a,B,C 1 5 A,B,C 1 1 1 6 a,b,c 1 1 1 7 A,b,C 1 8 a,B,C 1 9 a,B,C 1 10 a,b,C 1 11 a,B,c 1 12 A,b,c 1 13 a,b,c 1 1 1 14 A,b,C 1 15 A,B,c 1 16 A,b,c 1 Total 2 2 5 3 4 5 Result 2 < (2 + 5) 3 < (4 + 5)
The following table describes the results of a hypothetical test.
The column p(A) shows if a photon in the A direction is tested. The same for p(B) and p(C)
The column p(A,A) shows the correlation if both for photon 1 and photon 2 the A direction is measured.
The results shows that the two photons are strongly negative correlated in the A direction.
The column p(A,B) shows the correlation if for photon 1 the A direction and photon 2 the B direction is measured.
The expected value is 0 meaning no correlation.
The results show a small correlation between each photon pair in the A and B direction.
The column p(A,C) shows the correlation if for photon 1 the A direction and photon 2 the B direction is measured.
The results show a small correlation between each photon pair in the A and C direction.
photon 1 p(A) photon 2 p(A) p(A,A) p(B) p(A,B) p(C) p(A,C) 1 a,B,C -1 A,b,c 1 -1 -1 1 -1 1 2 a,B,c -1 A,b,C 1 -1 -1 1 1 -1 3 A,b,c 1 a,B,C -1 -1 1 1 1 1 4 a,B,C -1 A,b,c 1 -1 -1 1 -1 1 5 A,B,C 1 a,b,c -1 -1 -1 -1 -1 -1 6 a,b,c -1 A,B,C 1 -1 1 -1 1 -1 7 A,b,C 1 a,B,c -1 -1 1 -1 -1 -1 8 a,B,C -1 A,b,c 1 -1 -1 1 -1 1 9 a,B,C -1 A,b,c 1 -1 -1 1 -1 1 10 a,b,C -1 A,B,c 1 -1 1 -1 -1 1 11 a,B,c -1 A,b,C 1 -1 -1 1 1 -1 12 A,b,c 1 a,B,C -1 -1 1 1 1 1 13 a,b,c -1 A,B,C 1 -1 1 -1 1 -1 14 A,b,C 1 a,B,c -1 -1 1 1 -1 -1 15 A,B,c 1 a,b,C -1 -1 -1 -1 1 1 16 A,b,c 1 a,B,C -1 -1 1 1 1 1 Total -2 2 -16 0 4 0 2
The following table describes the results of a hypothetical test.
The column p(A) shows if a photon in the A direction is tested. The same for p(B) and p(C)
The column p(A,A) shows the correlation if both for photon 1 and photon 2 the A direction is measured.
The results shows that the two photons are not correlated in the A direction.
The column p(A,B) shows the correlation if for photon 1 the A direction and photon 2 the B direction is measured.
The expected value is 0 meaning no correlation.
The results show a small correlation between each photon pair in the A and B direction.
The column p(A,C) shows the correlation if for photon 1 the A direction and photon 2 the B direction is measured.
The results show no correlation between each photon pair in the A and C direction.
photon 1 p(A) photon 2 p(A) p(A,A) p(B) p(A,B) p(C) p(A,C) 1 a,B,C -1 A,b,C 1 -1 -1 1 1 -1 2 a,B,c -1 a,b,c -1 1 -1 1 -1 1 3 A,b,c 1 a,b,C -1 -1 -1 -1 1 1 4 a,B,C -1 a,b,C -1 1 -1 1 -1 1 5 A,B,C 1 a,B,c -1 -1 1 1 -1 -1 6 a,b,c -1 a,B,C -1 1 1 -1 1 -1 7 A,b,C 1 a,B,c -1 -1 1 1 -1 -1 8 a,B,C -1 a,b,C -1 1 -1 1 1 -1 9 a,B,C -1 A,B,C 1 -1 1 -1 1 -1 10 a,b,C -1 a,b,C -1 1 -1 1 1 -1 11 a,B,c -1 a,B,c -1 1 1 -1 -1 1 12 A,b,c 1 a,b,C -1 -1 -1 -1 1 1 13 a,b,c -1 A,b,C 1 -1 -1 1 1 -1 14 A,b,C 1 A,B,c 1 1 1 1 -1 -1 15 A,B,c 1 a,B,C -1 -1 1 1 1 1 16 A,b,c 1 a,b,c -1 -1 -1 -1 1 1 Total -2 -8 -2 -2 4 4 -1The overall result is that when the photons are random there is no correlation measured.
For some there are experiments done which show that clasical knowledge is not complete. Those experiments apperently show that there is a relation between the A and B component. The explanation is that faster than light communication is involved because the measurement of one analyzer influences the results of the other analyzer. Unfortunate no detail about those test is available, neither if this influence is a function between the distance of the analyzer and the source (point of collision) of the photons, nor which analyzer influences which analyzer.
The issue is that there are certain experiments with agree with the inequality equation. See Answer part 4 - 3 coins above. In that case 3 coins are tested, each simulating the +X,+Y and +Z axis.
The type of experiments used to demonstrate Quantum Mechanics involve entanglement. In that case there is a certain correlation between the observations when the same axis are measured in both directions. That does not exist in case the inequality theorem is tested using coins.
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