To start, I'd like to express my appreciation for the

courteous nature of the posts replying to my answer to Dr. Christian's question.

In rereading that post, I noticed that it repeatedly refers to

an "urn model" without explicitly saying what that means, though it

was discussed in a previous post. This addition is to correct that.

One physical model of a "hidden variable" that attempts to reproduce

quantum mechanics thinks of the "hidden variable" as a slip of paper

drawn from an urn with many such slips. identical copies of each slip

are sent to widely separated Alice and Bob. Written on each slip is

what Alice and Bob are to obtain if each performs either one of two possible

measurements, A or A' for Alice and B or B' for Bob.

The formulation of quantum mechanics forbids Alice from performing

measurements A or A' simultaneously, meaning that she cannot read the

whole slip. If she chooses to perform measurement A, she can only read

the part of the slip which specifies the result of measurement A.

But it is possible that a classical observer (Gideon, or God)

can read the whole slip. (Of course, this is just a way of speaking.

Alice's "reading" of the slip is done by measuring A, and "nature"

tells her the result.)

The classical model assumes that

someone can read the slip;

i.e., that it makes sense to talk about Alice's result A and her result

A' even when she has only measured one of them. Put differently,

a so-called "realistic" model assumes that what Alice is measuring (A or A')

"really" exists whether or not it is measured. Thus in the framework

of this classical model, it makes sense to talk about a CHSH sum like

(*) A(t)B(t) + A(t)B'(t) + A'(t)B(t) - A'(t)B'(t)

even though everyone agrees that it doesn't make sense within quantum mechanics.

And it makes sense to talk about the average of such sums, which

leads to the CHSH form of Bell's inequalities, which states that

the average cannot have absolute value greater than 2, often denoted

-2 = <AB> + <AB'> + <A'B> - <A'B'> <= 2 .

Please keep in mind that that quantum mechanics

does permit

experimental determination of each of the separate averages <AB>, etc.

Thus quantum mechanics allows us to test the bounds on the CHSH averages

even though the individual sums (*) whose averages lead to CHSH don't make sense

within quantum mechanics.

If the measured values of the averages in a quantum-mechanical experiment

violates this CHSH inequality, then that shows that the proposed classical model

cannot reproduce the predictions of quantum mechanics.

I'm not sure how to interpret a poster's insistence that nothing

can violate this Bell inequality, given that many experiments have been

done that do violate it. My impression is that he may think that the usual

derivations of this inequality are wrong, and that a bound 4 instead of 2

would result after the errors in the derivation are corrected. But if the

bound of 2 above is replaced by 4, then the result should not be called

a "Bell inequality" because neither Bell, nor any book or paper that I know,

has proposed it.

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I'd like to again suggest that "anti-Bellian" posters might

find it useful to look at the matter from another perspective.

The impossibility of the above classical "urn" model to reproduce quantum

mechanics is equivalent to the impossibiity of finding a probability function

p(i,j,k,m) (defined in previous posts) for which the hypothetical "marginals"

are true marginals. A theorem states that for some quantum marginals, p cannot exist.

If the "anti-Bellians" admit the possibility that this

theorem could be correct, making that clear would focus the discussion.

That's because this theorem is precisely what the "Bellian" view claims,

no more and no less. In that case, the "anti-Bellian"s objections would

in effect question that what I just stated is in fact the traditional

"Bellian" view. That objection would be understandable (though mistaken)

because many formulations in the older literature look somewhat different.

If the "anti-Bellians" think that the theorem's conclusion is wrong,

then they could at one stroke demolish the "Bellian" viewpoint by producing

a counterexample to the theorem. My "Two Suggestions" post pointed out

that this might not be difficult

assuming that the theorem is in fact false.

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I expect that this will be my last post to this group.

I've spent far too much time on this already, and I regret that I started.

If I don't answer replies to this, please don't interpretit as acquiescence or discourtesy.