B Was Bell's hypothesis verified?

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The nonlocality theorem uses a linear combination of covariances :
##C(a,b)-C(b,c)+C(a,c)=\int A(a,s)B(b,s)-A(b,s)B(c,s)+A(a,s)B(c,s)ds##


This uses the renaming of the parameter s. In a "Refutation of Bell's theorem" by Adenier, it is said that the parameter s should in fact be different in each covariance (due to the fact that classically s could represent the photon polarization and that it cannot be in 3 places at a time).

Was this checked by measuring experimentally by comparing the average of the product of the covariances ##\int ds A(a,s)B(b,s)A(b,s)B(c,s)A(a,s)B(c,s)ds##

##\int dsdtdu A(a,s)B(b,s)A(b,t)B(c,t)A(a,u)B(c,u)ds##
?
 

stevendaryl

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The nonlocality theorem uses a linear combination of covariances :
##C(a,b)-C(b,c)+C(a,c)=\int A(a,s)B(b,s)-A(b,s)B(c,s)+A(a,s)B(c,s)ds##


This uses the renaming of the parameter s. In a "Refutation of Bell's theorem" by Adenier, it is said that the parameter s should in fact be different in each covariance (due to the fact that classically s could represent the photon polarization and that it cannot be in 3 places at a time).
That's just a crackpot response, it seems to me. Bell defines a pretty precise definition of what he means by a "local realistic theory", and the manipulations that result in his inequality follow from that definition. So their violation shows that quantum mechanics is not a local realistic theory. This suggestion that the hidden variable should be different in each covariance is just nonsensical.
 

stevendaryl

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That's just a crackpot response, it seems to me. Bell defines a pretty precise definition of what he means by a "local realistic theory", and the manipulations that result in his inequality follow from that definition. So their violation shows that quantum mechanics is not a local realistic theory. This suggestion that the hidden variable should be different in each covariance is just nonsensical.
Bell's assumed model for the EPR experiment is that you have two experimenters, Alice and Bob, and some source of twin pairs. For each twin pair, Alice chooses a detector orientation ##a## and Bob chooses a detector orientation ##b## and each performs a measurement that gives ##\pm 1##.

Bell assumes that for each twin pair produced, there is an associated parameter ##\lambda## and two associated functions ##A(a,\lambda)## and ##B(b,\lambda)## giving Alice's result and Bob's result, respectively.

From this model, if we assume that the parameter ##\lambda## has a probability distribution ##P(\lambda)##, then the correlation of Alice's and Bob's results will be given by:

* ##C(a,b) = \sum_\lambda P(\lambda) A(a, \lambda) B(b, \lambda)##

Bell's inequality follows mathematically from the expression *, which follows from his assumed locally realistic model.
 

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