How is Bell’s Inequality converted to the CHSH inequality?

[Lazarus]

Bell’s inequality is S = P(a,b)-P(a,d)+P(c,b)+P(c,d) <= 2, which is calculated as S = a*b – a*d + c*b + c*d <= 2

The CHSH version is:

E = (N11 + N00 - N10 -N01) / (N11 + N00 + N10 + N01)

S =  E1 - E2 + E3 + E4  /  E1 + E2 + E3 + E4 <= 2

N11 is the number of correlations, etc

E is the Correlation Coefficient

There appears to be a significant difference between Bell’s and CHSH’s inequalities.  For comparison, converting the  Correlation Coefficient to Probability makes it possible to enter the values directly into Bell’s Inequality.  The conversion to Probability is the Correlation Coefficient divided by 2 then adding .5.  Using the much mentioned values for E of +.707,   -.707, +.707 and +.707 as a, b, c and d, Bell’s Inequality is calculated as S = -.8535*.8535 – ( .8535*-.8535) + .8535*.8535 + .8535*.8535 = -.728 + .728 + .728 + .728 = 1.456.

 

So using the real Bell’s Inequality, there is no violation.

 

Please explain the justification for the CHSH Inequality.

[swansont]

!

Moderator Note

It’s derived in the paper that they wrote, according to the CHSH entry on Wikipedia. Consult that.

J.F. Clauser; M.A. Horne; A. Shimony; R.A. Holt (1969), "Proposed experiment to test local hidden-variable theories", Phys. Rev. Lett., 23 (15): 880–4

you have been warned not to bring this topic up again, so this is closed.