What does this example say about the applicability of Bell's inequalities?

[billschnieder]

The inequality is based on three simultaneously existing values. The experiment can only generate two values at a time.

Hi ThomasT,
You are right. Clearly, the experiment in the OP violates the inequality in the OP therefore either one of the assumptions required to obtain the inequality or one of the assumptions used to generate terms from the experiment is wrong.

I take this to be your vital assumption. That is, this is the assumption that is contradicted via the violation of the inequality by the coin-toss test.

The experimenters mistakenly thought that expectation values obtained from just pairs of coins would be valid terms. However a simple inspection reveals that

a*b=-1, a*c=-1, b*c=-1

can only occur if the individual outcomes change with time. Let us start with a=-1, b=1 we get ab=-1, in order to get ac = -1 it means "c" must be +1 but b is already +1 so bc can not be -1 at the same time. The scenario is impossible if we have all three outcomes at the same time. However if each coin is dynamic with the values changing, it is possible to obtain the scenario, just as in the OP experiment. Therefore, in this case, the cause of the violation is the assumption that pairs taken at different times from a dynamic system are appropriate substitutes for the LHS of the inequality. Note that if we include the bias of the unmeasured coin from the OP for each toss into a list of triples of outcomes such as:

a b c
+ - -
- + +
...
etc

and the from this list we calculate <ab>, <ac>, <bc>, the inequality will not be violated. It is now obvious why the so-called "DrC challenge" misses the point completely.

I also take it that this is what you consider to be the effective cause of BI violation in Bell tests. Which would mean that what Bell stated as being the vital assumption was not the vital assumption, and the locality (or independence) condition encoded in Bell's formulation is precluded from being the effective cause of BI violation.

Yes, this is the argument made by De Raedt and Sica in the articles cited above.

 

[morrobay]

The experimenters mistakenly thought that expectation values obtained from just pairs of coins would be valid terms. However a simple inspection reveals that

a*b=-1, a*c=-1, b*c=-1

can only occur if the individual outcomes change with time.

So I take the outcomes changing with time as a hidden variable, based on sin (t)
In the other Bells Inequalities with entangled states are there also outcome time rate of changes ?

 

[DrChinese]

So I take the outcomes changing with time as a hidden variable, based on sin (t)
In the other Bells Inequalities with entangled states are there also outcome time rate of changes ?

This is a red herring that has nothing to do with anything. It is just a way of generating a random number. This has absolutely nothing to do with physics, much less quantum physics, much less Bell. It is equivalent to a card game. Imagine shuffling a deck and seeing whether you get red or black cards. Same thing.

This is all just a trick to make things seem like there is a physical underpinning. I am sorry, you have been snookered.

 

[jtbell]

Time out, pending a decision by the Mentors (moderators).