Bell's Inequality is only valid for non-negative numbers

[harpo]

The Bell Inequality tests are only valid for positive numbers, which is reasonable because counts and probabilities cannot be negative. CHSH generates a negative number, which means CHSH experiments are invalid.

Bell's Inequality can be violated by having a negative value.

For example:
P(a,b) -P(a,d)+P(c,b)+P(c,d) <= 2
Which can be calculated as
a+b-a-d+c+b+c+d / a+b+c+d <=2
with
a=1, b=2, c=3 and d= - 4
then
1+2-1-(-4)+3+2+3+(-4) / 1+2+3+(-4) <= 2
10 /2 <= 2
5 <= 2

Is this correct?

 

[DrChinese]

The Bell Inequality tests are only valid for positive numbers, which is reasonable because counts and probabilities cannot be negative. CHSH generates a negative number, which means CHSH experiments are invalid.

CHSH experiments yield results consistent with the predictions of QM. If you make assumptions that are invalid - as the Bell paper does - then it is possible you will obtain predictions inconsistent with experiment. That is what is happening here, the assumptions of locality and realism cannot both be valid.

By the way, your usage of P(a,b) -P(a,d)+P(c,b)+P(c,d) is not in accordance with its intended meaning by CHSH. But that is not important, as mentioned the experiments are valid for the intended purposes.

 

[harpo]

The test used by CHSH is:
E = (N11 + N00 - N10 -N01) / (N11 + N00 + N10 + N01)
S = E1 -E2 + E3 + E4

How does that differ from
P(a,b) -P(a,d)+P(c,b)+P(c,d) <= 2 ?