Some people do not understand Counterfactual Definiteness

[FrediFizzx]

... (snip boring lecturing)... He [Bell] shows that such a theory cannot reproduce quantum predictions. ...

Too bad Bell was wrong. There is more than one classical theory that shoots him down. And..., don't start mixing it up with Gill's theory nonsense.
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[Justo]

This kind of discussions about the Bell theorem and Bell-type inequalities are very funny because Counterfactual definiteness(CFD) has nothing to do with the Bell inequality.
CFD was a Post-Bell invention. I will appreciate it if somebody can give me a reference where John Bell mentions CFD or makes use of unperformed measurements to derive his inequality.
As far as know the history of the CFD is the following. In 1971 H.P. Stapp made use of CFD to prove that QM is nonlocal. Stapp did not derive a Bell-type inequality, i.e., a falsifiable inequality. Later in 1976/1977, Eberhart used CFD to derive the CHSH inequality. That is how the story began.

I would welcome any historical contribution/correction about this topic.

[gill1109]

This kind of discussions about the Bell theorem and Bell-type inequalities are very funny because Counterfactual definiteness(CFD) has nothing to do with the Bell inequality.
CFD was a Post-Bell invention. I will appreciate it if somebody can give me a reference where John Bell mentions CFD or makes use of unperformed measurements to derive his inequality.
As far as know the history of the CFD is the following. In 1971 H.P. Stapp made use of CFD to prove that QM is nonlocal. Stapp did not derive a Bell-type inequality, i.e., a falsifiable inequality. Later in 1976/1977, Eberhart used CFD to derive the CHSH inequality. That is how the story began.

I would welcome any historical contribution/correction about this topic.

Justo, that is a very funny comment, since from 1971 lots of the people in quantum foundations *do* use the term Counterfactual definiteness. The Bell inequality is a trivial result in elementary probability theory, derivable from trivial logical assertions. Does it have anything to do with physics? If you think QM is just fine as it is, then you don't need Bell and you don't need CFD.

Bell (1964) used the predictions of QM itself to argue for realism and (effectively) CFD. But he knew that his result was not testable (actually that is not quite true, because he also has some words about what could be said if correlations were imperfect).

Apparently, by "the Bell inequality" you mean the Bell 1964 inequality.

Most people nowadays mean the Bell-CHSH inequality

[Heinera]

This kind of discussions about the Bell theorem and Bell-type inequalities are very funny because Counterfactual definiteness(CFD) has nothing to do with the Bell inequality.
CFD was a Post-Bell invention. I will appreciate it if somebody can give me a reference where John Bell mentions CFD or makes use of unperformed measurements to derive his inequality.
[...]

Well, Bell didn't perform any experiments, so all his "measurements" were unperformed.

[gill1109]

This kind of discussions about the Bell theorem and Bell-type inequalities are very funny because Counterfactual definiteness(CFD) has nothing to do with the Bell inequality.
CFD was a Post-Bell invention. I will appreciate it if somebody can give me a reference where John Bell mentions CFD or makes use of unperformed measurements to derive his inequality.
[...]

Well, Bell didn't perform any experiments, so all his "measurements" were unperformed.

[Justo]

Well, Bell didn't perform any experiments, so all his "measurements" were unperformed.

Yes, we can say that every theoretical prediction is about unperformed experiments.
What I meant is that Bell's prediction can be contrasted with experiments that you can actually perform. When you use CFD you cannot do that.
The problem with a counterfactual prediction is basically what minkwe explains in post 1211 of this thread.

minkwe also claims that Bell uses CFD when he says

A prime example of the use of CFD in QM from Bell's paper is the following:

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite
directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the
Spins and , If measurement Of the component , where is some unit vector, yields the value
+ 1 then, according to quantum mechanics, measurement of must yield the value -1 and vice versa.

I do not see CFD in the statement, I see that he uses only conditionals, not counterfactual conditionals. However, that is not important because, here, Bell is only deriving determinism. The important point is that he does not use CFD to derive his inequality.

I would like to have references of Bell's mentioning CFD or unperformed experiments in his derivations. I am afraid that CFD does not even exist in the philosophical nomenclature.

[Heinera]

I would like to have references of Bell's mentioning CFD or unperformed experiments in his derivations. I am afraid that CFD does not even exist in the philosophical nomenclature.

CFD is a necessary prerequisite in order for Bell's definition of "locality" to have meaning. In the introduction to his 1964 paper he writes "It is
the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."

"the result of a measurement on one system be unaffected by operations on a distant system" is only meaningful if you consider a counterfactual possibility, namely that the state of the distant system could be something else than its actual state a the time of measurement of the first system.

So you could say that CFD is implicit in Bell's setup of his model, rather than being referred to in the mathematical proof of the upper bound for the correlations.

[Justo]

CFD is a necessary prerequisite in order for Bell's definition of "locality" to have meaning. In the introduction to his 1964 paper he writes "It is
the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."

"the result of a measurement on one system be unaffected by operations on a distant system" is only meaningful if you consider a counterfactual possibility, namely that the state of the distant system could be something else than its actual state a the time of measurement of the first system.

So you could say that CFD is implicit in Bell's setup of his model, rather than being referred to in the mathematical proof of the upper bound for the correlations.

It is not very important if you want to understand the definition of locality counterfactually. It can be done but it is not necessary. Scientific theories normally make predictions in the form of conditionals, not counterfactual conditionals or counterfactual modality.

The subject that really matters and is at stake here is whether the Bell inequality is a counterfactual prediction. I maintain that it is not, it can be interpreted as a conditional, not a counterfactual conditional.
The Bell inequality says, if you perform the experiment then your result is less or equal 2. You can see it as a theorem; if P then Q.
Theorems are expressed using normal logic not the logic of counterfactuals.
Sure you can easily turn that into a counterfactual statement if you wish, but that is not the point.

Thus subject under discussion is whether the Bell inequality is a falsifiable prediction or not.

[Joy Christian]

I would like to have references of Bell's mentioning CFD or unperformed experiments in his derivations. I am afraid that CFD does not even exist in the philosophical nomenclature.

CFD is a necessary prerequisite in order for Bell's definition of "locality" to have meaning. In the introduction to his 1964 paper he writes "It is
the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."

"the result of a measurement on one system be unaffected by operations on a distant system" is only meaningful if you consider a counterfactual possibility, namely that the state of the distant system could be something else than its actual state a the time of measurement of the first system.

So you could say that CFD is implicit in Bell's setup of his model, rather than being referred to in the mathematical proof of the upper bound for the correlations.

None of these matters. The main problem with Bell's theorem is that in its proof local realism is not implemented correctly. When this defect is corrected and local realism is implemented correctly in Bell's argument, the bounds on the CHSH inequalities work out to be +/-2\/2 instead of +/-2, thus mitigating the concussion of the theorem. That is all there is to Bell's attempt.
.

[gill1109]

CFD is a necessary prerequisite in order for Bell's definition of "locality" to have meaning. In the introduction to his 1964 paper he writes "It is
the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty."

"the result of a measurement on one system be unaffected by operations on a distant system" is only meaningful if you consider a counterfactual possibility, namely that the state of the distant system could be something else than its actual state a the time of measurement of the first system.

So you could say that CFD is implicit in Bell's setup of his model, rather than being referred to in the mathematical proof of the upper bound for the correlations.

It is not very important if you want to understand the definition of locality counterfactually. It can be done but it is not necessary. Scientific theories normally make predictions in the form of conditionals, not counterfactual conditionals or counterfactual modality.

The subject that really matters and is at stake here is whether the Bell inequality is a counterfactual prediction. I maintain that it is not, it can be interpreted as a conditional, not a counterfactual conditional.
The Bell inequality says, if you perform the experiment then your result is less or equal 2. You can see it as a theorem; if P then Q.
Theorems are expressed using normal logic not the logic of counterfactuals.
Sure you can easily turn that into a counterfactual statement if you wish, but that is not the point.

Thus subject under discussion is whether the Bell inequality is a falsifiable prediction or not.

Of course. Bell proved a theorem about local realism and quantum mechanics. He made empirical predictions. People prove the CHSH inequality while assuming local realism. Local realism = CFD + locality + no-conspiracy. CFD is just part of what "local realism" means.

The Bell inequality is not a counterfactual prediction. But who said it is? It is a lemma in the proof of a theorem; CFD is part of the *assumption* of the lemma.

[Justo]

The Bell inequality is not a counterfactual prediction. But who said it is? It is a lemma in the proof of a theorem; CFD is part of the *assumption* of the lemma.

It seems to me that you don't believe that yourself. In your Statistical Science paper, you give a brilliant statistical derivation of the CHSH inequality based on "experimentally observed averages". It seems that you have a very lucid mind as a statistician but for some reason, your mind obnubilates when turning to physics.

[gill1109]

The Bell inequality is not a counterfactual prediction. But who said it is? It is a lemma in the proof of a theorem; CFD is part of the *assumption* of the lemma.

It seems to me that you don't believe that yourself. In your Statistical Science paper, you give a brilliant statistical derivation of the CHSH inequality based on "experimentally observed averages". It seems that you have a very lucid mind as a statistician but for some reason, your mind obnubilates when turning to physics.

CFD is a mathematical feature which a mathematical model might or might not have. I do not do physics. I do maths and I do statistics.

I suspect that the phrase “CHSH inequality” means something different for you than for me. In my paper in Statistical Science I derived a CHSH-like inequality. It was not a “statistical derivation”. It was a mathematical derivation of an elementary inequality in a pretty simple probability model. I would not call it brilliant since it is all so utterly simple and should all be well known and well understood.

[Heinera]

The subject that really matters and is at stake here is whether the Bell inequality is a counterfactual prediction.

Of course it's not. Now it would be interesting to hear what you think is the definition of "counterfactually definite"?

[Justo]

The subject that really matters and is at stake here is whether the Bell inequality is a counterfactual prediction.

Of course it's not. Now it would be interesting to hear what you think is the definition of "counterfactually definite"?

Sorry, I suppose we are discussing different things.

[gill1109]

Agreed!

[minkwe]

minkwe also claims that Bell uses CFD when he says

A prime example of the use of CFD in QM from Bell's paper is the following:

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite
directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the
Spins and , If measurement Of the component , where is some unit vector, yields the value
+ 1 then, according to quantum mechanics, measurement of must yield the value -1 and vice versa.

I do not see CFD in the statement, I see that he uses only conditionals, not counterfactual conditionals. However, that is not important because, here, Bell is only deriving determinism. The important point is that he does not use CFD to derive his inequality.

I would like to have references of Bell's mentioning CFD or unperformed experiments in his derivations. I am afraid that CFD does not even exist in the philosophical nomenclature.

Question for you then. Does the validity of the statement "according to quantum mechanics, measurement of must yield the value -1 and vice versa. " depend on what measurement was actually made?

Then let us go back to Bell 1964 and take a look at the text just after equation 14 where Bell says:

It follows that c is another unit vector

Please explain the basis for factoring within the integral as Bell does?

[gill1109]

Suppose a, b, c = +/-1. Then ab(ac - 1) = bc - ab, but in your rendition of Bell, Bell would have ab - ac.

Well spotted, Michel! This generates a sign error and “ac” instead of “bc”. But in the next displayed formula he has taken an absolute value and also corrected the “ac” to “bc” error. I believe that his final result is OK.

I suspect that this was a typo...

[Justo]

Question for you then. Does the validity of the statement "according to quantum mechanics, measurement of must yield the value -1 and vice versa. " depend on what measurement was actually made?

No, it does not. Let us say that P= "Experiment X is performed" and Q=" Result Y is obtained". Then the implication is not a counterfactual conditional irrespective of P being actually performed or not.

Then let us go back to Bell 1964 and take a look at the text just after equation 14 where Bell says:

It follows that c is another unit vector

Please explain the basis for factoring within the integral as Bell does?

The mathematical operations on the right side have nothing to do with counterfactual definiteness. They are mathematical operations and have nothing to do with the way the experiment was performed or is supposed to be performed.
All that is assumed is that , the left side is an experimental result or is supposed to be one. The right side is its mathematical expression. Once you assume this, you can transform the right side with whatever legal mathematical operation without changing its physical meaning.

[minkwe]

Question for you then. Does the validity of the statement "according to quantum mechanics, measurement of must yield the value -1 and vice versa. " depend on what measurement was actually made?

No, it does not.

So you agree that after the experiment, in which a different measurement was "in fact" made, by Bob, the statement "according to quantum mechanics, measurement of must yield the value -1 and vice versa. " is still valid. If that is not the definition of counterfactual definiteness, then you don't know what counterfactual definiteness means.

Let us say that P= "Experiment X is performed" and Q=" Result Y is obtained". Then the implication is not a counterfactual conditional irrespective of P being actually performed or not.

The statement is a conditional statement. Nobody is suggesting that it is a counterfactual statement. It only becomes counterfactual in the specific context in which is fact and it is no longer possible for to be true. Counterfactual Definiteness means the statement is valid and as a result of is definite even in the context in which is counterfactual. If you disagree, please provide your definition.

please explain the basis for factoring within the integral as Bell does?

The mathematical operations on the right side have nothing to do with counterfactual definiteness. They are mathematical operations and have nothing to do with the way the experiment was performed or is supposed to be performed.

You didn't answer the question. You just made an empty proclamation that is unfounded. What is the basis for factoring? Within the integral, we have AB - BC and then it is factored into AB(AC-1). AB corresponds to the result if measurements A & B are performed together (note that only two measurements can ever be performed together. AC corresponds to the result if measurements A & C are performed together.

Therefore it should be obvious to anyone that AC is counterfactual to AB. If AB was measurement, then AC was not measured and could no longer be measured. Yet you place AB and AC side by side, and perform the factoring to obtain AB(AC-1). This is an assumption of counterfactual definiteness.

All that is assumed is that , the left side is an experimental result or is supposed to be one. The right side is its mathematical expression. Once you assume this, you can transform the right side with whatever legal mathematical operation without changing its physical meaning.

Sorry, this is just wrong.

Suppose a, b, c = +/-1. Then ab(ac - 1) = bc - ab, but in your rendition of Bell, Bell would have ab - ac.

Well spotted, Michel! This generates a sign error and “ac” instead of “bc”. But in the next displayed formula he has taken an absolute value and also corrected the “ac” to “bc” error. I believe that his final result is OK.

I suspect that this was a typo...

The typo was mine. There should be no minus in front of the second expression. I'm focused on the factoring not the sign.

[gill1109]

“ Within the integral, we have AB - BC and then it is factored into AB(AC-1). AB corresponds to the result if measurements A & B are performed together (note that only two measurements can ever be performed together. AC corresponds to the result if measurements A & C are performed together.”.

Within the integral we have some functions. Since A takes the values +/-1, AB(AC -1) = BC - AB. Equality of two functions. What minkwe says about what BC and AB correspond to is true; according to the assumed model, BC is a function of lambda which corresponds to the product of the measured outcomes which would be obtained if .....

You can call it counterfactual if you like. So what? It is what it is. The maths are legal, and we are working within a mathematical model. If you get conclusions (about relations between correlations observed in different experiments) which do not hold in reality then you know the model does not describe reality.