B Bell Non Locality, Quantum Non Locality, Weak Locality, CDP

[morrobay]

When there are EPR/Bell test inequality violations and no signal faster than light, the terms:
Bell Non Locality, Quantum Non Locality, Weak Locality and the Cluster Decomposition Principle:
Initial state of space like systems can be factorized.
Subsystems remain space like separated.
Then final state can be factorized..
With the following diagram how can the above terms be unified in one comprehensive definition and explanation
for Bell test violations ?

 

[PeterDonis]

Initial state of space like systems can be factorized.

If this is the case, then the systems are not entangled and there will be no violation of the Bell inequalities. The QM prediction of violations of the Bell inequalities requires that the systems in question are entangled, which means the state of the system as a whole cannot be factorized.

 

[morrobay]

https://www.physicsforums.com/threads/cluster-decomposition-and-epr-correlations.409861/
I obtained that definition from post # 7 and thought it was in reference to EPR/Bell inequality violations for entangled particles.
And also that this factorization :
p (abIxy,λ) = p (aIx,λ) p (bIy ,λ) is used to derive the inequality : S = (ab) + (ab') + (a'b) - (a'b') ≤ 2
for entangled particles.

 

[stevendaryl]

https://www.physicsforums.com/threads/cluster-decomposition-and-epr-correlations.409861/
I obtained that definition from post # 7 and thought it was in reference to EPR/Bell inequality violations for entangled particles.
And also that this factorization :
p (abIxy,λ) = p (aIx,λ) p (bIy ,λ) is used to derive the inequality : S = (ab) + (ab') + (a'b) - (a'b') ≤ 2
for entangled particles.

Well, that's the heart of Bell's disproof of local hidden variables: Every local hidden variables theory can be "factorized", but an entangled quantum state cannot be. Therefore, entangled quantum states cannot be explained by local hidden variables.

 

[N88]

Well, that's the heart of Bell's disproof of local hidden variables: Every local hidden variables theory can be "factorized", but an entangled quantum state cannot be. Therefore, entangled quantum states cannot be explained by local hidden variables.

Please, where are the errors in the following?

Fact 1: Under the product rule for probabilities (here, wrt EPRB), the following formulation can never be false: p(ab|xy,λ) = p(a|x,λ)p(b|xy,λ,a). (A)
Explanation: This factorisation is based on these facts: the inclusion of irrelevant conditionals in a probability function is irrelevant; irrelevant conditionals are best eliminated by experimental facts (not by relying on erroneous opinions, hypotheses, etc).

Fact 2: Bell-test experiments confirm the necessity of x and "a" in p(b|xy,λ,a) .
Explanation: "a" and "b" are correlated by the common hidden-variable λ and the angle (x,y) between x and y.

Fact 3: Bell-test experiments confirm that the correlation is law-like.
Explanation: Under EPRB, the law in (A) is: p(b|xy,λ,a) = sin² $\tfrac{1}{2}$(x,y). (B)

Fact 4: Many physicists insist that: p(ab|xy,λ) = p(a|x,λ)p(b|y,λ). (C)
Explanation: (C) is called "Bell's locality hypothesis".

Fact 5: There is no justification for thinking that separated local events cannot be correlated as in (A).
Explanation: My garlic crop is correlated with my separate onion crop; the correlated hidden-variable is the separate but correlated underground water-supplies.

Fact 6: Since λ is Bell's random hidden-variable: p(a|x,λ) = p(b|y,λ) = $\tfrac{1}{2}.$ (D)
So under "Bell's locality hypothesis" (C), we must have this permanent error: p(ab|xy,λ) = p(a|x,λ)p(b|y,λ) = $\tfrac{1}{4}.$ (E)
Explanation: (C) is an erroneous hypothesis in that it overlooks the validity of (A) under local-realism when outputs are correlated by the combination of correlated hidden-variables λ and test-settings x and y are correlated by the angle (x,y) between them.

Thanks; N88

 

[stevendaryl]

Please, where are the errors in the following?

Fact 1: Under the product rule for probabilities (here, wrt EPRB), the following formulation can never be false: p(ab|xy,λ) = p(a|x,λ)p(b|xy,λ,a). (A)
Explanation: This factorisation is based on these facts: the inclusion of irrelevant conditionals in a probability function is irrelevant; irrelevant conditionals are best eliminated by experimental facts (not by relying on erroneous opinions, hypotheses, etc).

Fact 2: Bell-test experiments confirm the necessity of x and "a" in p(b|xy,λ,a) .
Explanation: "a" and "b" are correlated by the common hidden-variable λ and the angle (x,y) between x and y.

Fact 3: Bell-test experiments confirm that the correlation is law-like.
Explanation: Under EPRB, the law in (A) is: p(b|xy,λ,a) = sin² $\tfrac{1}{2}$(x,y). (B)

Fact 4: Many physicists insist that: p(ab|xy,λ) = p(a|x,λ)p(b|y,λ). (C)
Explanation: (C) is called "Bell's locality hypothesis".

Fact 5: There is no justification for thinking that separated local events cannot be correlated as in (A).
Explanation: My garlic crop is correlated with my separate onion crop; the correlated hidden-variable is the separate but correlated underground water-supplies.

Fact 6: Since λ is Bell's random hidden-variable: p(a|x,λ) = p(b|y,λ) = $\tfrac{1}{2}.$ (D)
So under "Bell's locality hypothesis" (C), we must have this permanent error: p(ab|xy,λ) = p(a|x,λ)p(b|y,λ) = $\tfrac{1}{4}.$ (E)
Explanation: (C) is an erroneous hypothesis in that it overlooks the validity of (A) under local-realism when outputs are correlated by the combination of correlated hidden-variables λ and test-settings x and y are correlated by the angle (x,y) between them.

Thanks; N88

Well, outside of quantum mechanics, there are no counter-examples to the locality condition P(ab|x,y,\lambda) = P(a|x,\lambda) P(b|y, \lambda). That is, outside of QM, whenever two distant variables are correlated, it is because there is a common cause to each, and they are correlated through that common cause. Of course, assumption (C) is "erroneous"---QM is not locally realistic. Bell's theorem clarifies the way in which it differs from a locally realistic theory.

The correlation between your garlic crop and onion crop is not a counter-example. In that case, \lambda represents the water supply, in common to both.

 

[stevendaryl]

Well, outside of quantum mechanics, there are no examples of the locality condition P(ab|x,y,\lambda) = P(a|x,\lambda) P(b|y, \lambda). That is, outside of QM, whenever two distant variables are correlated, it is because there is a common cause to each, and they are correlated through that common cause. Of course, assumption (C) is "erroneous"---QM is not locally realistic. Bell's theorem clarifies the way in which it differs from a locally realistic theory.

The correlation between your garlic crop and onion crop is not a counter-example. In that case, \lambda represents the water supply, in common to both.

The claim is that if \lambda is a complete description of the common causal influences on a and b, then the probabilities will factor when conditioned on \lambda. It has to be complete for factorization to work.

 

[PeterDonis]

outside of quantum mechanics, there are no examples of the locality condition

I think you mean that outside of QM there are no examples of violations of the locality condition, correct? QM violates it, but we don't know of any other theory that does.

 

[N88]

Well, outside of quantum mechanics, there are no examples of the locality condition P(ab|x,y,\lambda) = P(a|x,\lambda) P(b|y, \lambda). That is, outside of QM, whenever two distant variables are correlated, it is because there is a common cause to each, and they are correlated through that common cause. Of course, assumption (C) is "erroneous"---QM is not locally realistic. Bell's theorem clarifies the way in which it differs from a locally realistic theory.

The correlation between your garlic crop and onion crop is not a counter-example. In that case, \lambda represents the water supply, in common to both.

I thought the water-supply, being common to both crops, was an illustrative analogy: equivalent to \lambda being common to both of Bell's factors. No?

 

[stevendaryl]

I thought the water-supply, being common to both crops, was an illustrative analogy: equivalent to \lambda being common to both of Bell's factors. No?

Sorry, I think I misunderstood your example. I thought you were arguing that C (the assumption of factorizability) was wrong, and that your example showed it.

 

[Denis]

Well, outside of quantum mechanics, there are no counter-examples to the locality condition P(ab|x,y,\lambda) = P(a|x,\lambda) P(b|y, \lambda). That is, outside of QM, whenever two distant variables are correlated, it is because there is a common cause to each, and they are correlated through that common cause.

No, in classical theory it is as well possible that it is the locality condition which fails.

Suspected criminals A and B make the same claims about what has happened at the crime scene. Is this because that really happened, and they have told the truth, or because A has succeeded to tell his friend B about the questions, and his answer?

 

[PeterDonis]

Suspected criminals A and B make the same claims about what has happened at the crime scene. Is this because that really happened, and they have told the truth, or because A has succeeded to tell his friend B about the questions, and his answer?

Neither of these possibilities violate locality. They just postulate different local interactions (at the crime scene, vs. at some other location where A tells B things).

 

[Denis]

Neither of these possibilities violate locality. They just postulate different local interactions (at the crime scene, vs. at some other location where A tells B things).

The point was that it violates P(ab|x,y,λ)=P(a|x,λ)P(b|y,λ). With λ being what they have above known before the interrogations, x and y being the questions asked by the interrogators, and a and b their answers.
Of course, the information transfer in the analogy is not violating Einstein causality, but it violates the law of the state, with the police doing everything to prevent it, so it is also a hidden information transfer. And the guys will do everything to hide it. (If they use smuggled mobiles, the communication may be even faster than sound.)

And the aim of this hidden communication is, exactly, to suggest the police to apply the EPR criterion of reality: Once the interrogation of A allowed to correctly predict what B would answer, without influencing B's interrogation in any way, the answer should correspond to some element of reality.

 

[PeterDonis]

The point was that it violates P(ab|x,y,λ)=P(a|x,λ)P(b|y,λ). With λ being what they have above known before the interrogations

But the only way for the factorizability condition to be violated here is if $\lambda$ does not include information from the actual crime scene. But that's not how $\lambda$ is supposed to be defined. $\lambda$ is supposed to include all information that could have gotten to both measurements by local means--in relativistic terms, it should include all information that is in the intersection of the past light cones of the two measurement events. That has to include information from the actual crime scene.

With $\lambda$ defined to include information from the actual crime scene, then the factorizability condition can't be violated, since all of the correlations between A's and B's answers can be explained by their common knowledge of what happened at the crime scene. Whether that common knowledge comes from both of them being present at the crime scene, or A communicating it to B afterwards, doesn't matter for factorizability.

the aim of this hidden communication is, exactly, to suggest the police to apply the EPR criterion of reality

Which is violated by quantum mechanics, but not by your scenario. Your scenario does not violate locality; as you admit in the above quote, it shows why the EPR criterion is a good criterion for any scenario that does not involve quantum mechanics. In other words, it shows why classical physics does not violate locality.

 

[N88]

Sorry, I think I misunderstood your example. I thought you were arguing that C (the assumption of factorizability) was wrong, and that your example showed it.

Thanks SD. We need to be careful here because, as I see it, you have responded to my position in two ways and neither is correct (as I understand them). So I trust I'm being sufficiently careful in the 4 points that follow:

1: Re your above reply, I AM arguing that (C) is wrong; ie, experimentally false! And I'm also arguing that my example shows it.

That is, Fact 4 is a fact: Many physicists insist [that "Bell's local realism" can be represented by]: p(ab|xy,λ) = p(a|x,λ)p(b|y,λ). (C)
Explanation: (C) is called "Bell's locality hypothesis".

But (C) = p(ab|xy,λ) = p(a|x,λ)p(b|y,λ) is false by observation: so "Bell's local realism" or "Bell's locality hypothesis" is immediately false under EPRB. That is, we know that that "a" and "b" will be correlated (logically dependent) : ie, we know the particles are pairwise correlated and we know the detector settings are correlated --- by a function of the angle (x,y). But (C) is the expression for logical-independence! Hence wrong here -- by observation alone.

2: Further, your original reply was this: "Yes, and your water supply example does not violate the factorizability condition." I disagree. My garlic and onion outputs are also logically dependent because of the correlated water supply; ie, two great crops when the water supply is well maintained; two poor crops when the water supply is neglected.

So my water supply example, with its correlated crops, DOES violate the factorizability condition: which is "Bell's locality hypothesis".

3: Regarding Fact 3: Bell-test experiments confirm that the correlation is law-like.
Explanation: Under EPRB, the law in (A) is: p(b=1)|xy,λ,a=1) = sin²$\tfrac{1}{2}$(x,y). (B)

So, even if our knowledge of λ were complete, our related prediction must still be (B); otherwise it would be experimentally falsified.

4. But, further, I do not understand why anyone might believe that we could ever know "hidden-variables" like Bell's λ completely. [Moreover, I am able to derive the correct experimental results without such knowledge and without nonlocality.] So the fundamental tenet of Bell's (C) -- ie, know λ completely -- can never be satisfied. And QM does not require such: for, again in my view, QM is so well-founded that we are able to encode incomplete-information re "hidden-variables" in probability relations AND derive the correct experimental outcomes.

In conclusion: somewhere in the above there must be a "fact" that we disagree about; maybe one that I am confused about.

HTH. Thanks again, N88

 

[PeterDonis]

My garlic and onion outputs are also logically dependent because of the correlated water supply

The water supply is part of $\lambda$, and $\lambda$ appears in both factors in the factorizability condition. So a correlation due to $\lambda$ can hold without the factorizability condition being violated.

To put it in terms of your garlic and onion crops, if we factor out the common cause, the water supply ($\lambda$), there is no residual correlation between the two crops: the garlic crop ($a$) depends only on factors specific to how you grew garlic ($x$), and the onion crop ($b$) depends only on factors specific to how you grew onions ($y$). That is what the factorizability condition expresses, and it will be true for your garlic and onion case. In other words, that case obeys the Bell locality condition.

In QM experiments on entangled particles, however, the above will not be the case: even after you have factored out the common cause ($\lambda$), you still have correlations--the results on the $a$ side of the experiment do not depend solely on $x$, and the results on the $b$ side of the experiment do not depend solely on $y$. It's as if, even after factoring out the effect of the water supply (and any other common causes), somehow changing the way you grew garlic changed the yield of your onion crop. That does not happen anywhere outside of QM experiments on entangled particles--those are the only experiments anyone has ever done that violate the Bell locality condition.

 

[N88]

The water supply is part of $\lambda$, and $\lambda$ appears in both factors in the factorizability condition. So a correlation due to $\lambda$ can hold without the factorizability condition being violated.

To put it in terms of your garlic and onion crops, if we factor out the common cause, the water supply ($\lambda$), there is no residual correlation between the two crops: the garlic crop ($a$) depends only on factors specific to how you grew garlic ($x$), and the onion crop ($b$) depends only on factors specific to how you grew onions ($y$). That is what the factorizability condition expresses, and it will be true for your garlic and onion case. In other words, that case obeys the Bell locality condition.

In QM experiments on entangled particles, however, the above will not be the case: even after you have factored out the common cause ($\lambda$), you still have correlations--the results on the $a$ side of the experiment do not depend solely on $x$, and the results on the $b$ side of the experiment do not depend solely on $y$. It's as if, even after factoring out the effect of the water supply (and any other common causes), somehow changing the way you grew garlic changed the yield of your onion crop. That does not happen anywhere outside of QM experiments on entangled particles--those are the only experiments anyone has ever done that violate the Bell locality condition.

It's not clear to me why you "factor out" the common cause?

Let me be clear: the garlic [G] and onion [O] example is in no way meant to reproduce EPRB correlations. But it is meant to be a counterpoint to your following statement (a counterpoint that can be experimentally validated):

• "To put it in terms of your garlic and onion crops, if we factor out the common cause, the water supply ($\lambda$), there is no residual correlation between the two crops:"

I've cut off the underground water supply (so the test conditions are now X) and still the separated crops are correlated; ie, under X, I now get a good crop of each [G⁺, O⁺] half the time, or a poor crop of each [G^-, O^-] half the time, with no crossovers. So:

P(G⁺|X) = P(O⁺|X) = P(G^-|X) = P(O^-|X) = $\tfrac{1}{2}$.

P(G⁺O⁺|X) = P(G⁺|X)P(O⁺|XG⁺) = $\tfrac{1}{2}$ $\neq$ P(G⁺|X)P(O⁺|X).

Given such a clear difference, I take it that our differences must arise from my misunderstanding something?

 

[PeterDonis]

I've cut off the underground water supply (so the test conditions are now X) and still the separated crops are correlated

How? Translating this back into Bell's notation, we have eliminated $\lambda$ (the water supply), so the factorizability condition is $p(ab|xy) = p(a|x) p(b|y)$. If this condition is violated, it means that each crop's yield depends not only on how you grow that crop, but how you grow the other crop. How can that be?

I've cut off the underground water supply (so the test conditions are now X)

No, they aren't. See below.

I take it that our differences must arise from my misunderstanding something?

I think you are misunderstanding Bell's notation. $x$, in his notation, would correspond to the way you grow your garlic crop: by definition, it only contains factors that are local to the garlic crop. Similarly, $y$ only contains factors that are local to the onion crop. That means that, by hypothesis, and using your binary notation for good (+) or poor (-) crops, we would have

$$
P(O^+|X) = P(O^-|X) = P(G^+|Y) = P(G^-|Y) = \frac{1}{2}
$$

But we would not have $P(G^+|X) = P(G^-|X)$, unless you are an incompetent garlic grower, and we would not have $P(O^+|Y) = P(O^-|Y)$, unless you are an incompetent onion grower. In fact, we would expect $P(G^+|X) > P(G^-|X)$ and $P(O^+|Y) > P(O^-|Y)$, since you are adapting your growth techniques to each crop individually.

 

[stevendaryl]

It's not clear to me why you "factor out" the common cause?
I've cut off the underground water supply (so the test conditions are now X) and still the separated crops are correlated; ie, under X, I now get a good crop of each [G⁺, O⁺] half the time, or a poor crop of each [G^-, O^-] half the time, with no crossovers. So:

P(G⁺|X) = P(O⁺|X) = P(G^-|X) = P(O^-|X) = $\tfrac{1}{2}$.

P(G⁺O⁺|X) = P(G⁺|X)P(O⁺|XG⁺) = $\tfrac{1}{2}$ $\neq$ P(G⁺|X)P(O⁺|X).

Given such a clear difference, I take it that our differences must arise from my misunderstanding something?

If even after controlling for water supply, there is a correlation between your garlic crop and your onion crop, then that usually means that there is some other common causal influence other than water supply.

 

[N88]

How? Translating this back into Bell's notation, we have eliminated $\lambda$ (the water supply), so the factorizability condition is $p(ab|xy) = p(a|x) p(b|y)$. If this condition is violated, it means that each crop's yield depends not only on how you grow that crop, but how you grow the other crop. How can that be?

You appear to be confusing logical-implication with causation?? There is no causal influence between the crops; the crop correlations arise from the correlation of the separate local growing conditions (soil, sunlight, rainfall, plough-settings). The outcome correlations in EPRB arise in a similar way; eg, via the correlation of the independent and freely chosen detector settings x and y as a function of their angular difference (x,y).

I think you are misunderstanding Bell's notation. $x$, in his notation, would correspond to the way you grow your garlic crop: by definition, it only contains factors that are local to the garlic crop. Similarly, $y$ only contains factors that are local to the onion crop. That means that, by hypothesis, and using your binary notation for good (+) or poor (-) crops, we would have

$$
P(O^+|X) = P(O^-|X) = P(G^+|Y) = P(G^-|Y) = \frac{1}{2}
$$

But we would not have $P(G^+|X) = P(G^-|X)$, unless you are an incompetent garlic grower, and we would not have $P(O^+|Y) = P(O^-|Y)$, unless you are an incompetent onion grower. In fact, we would expect $P(G^+|X) > P(G^-|X)$ and $P(O^+|Y) > P(O^-|Y)$, since you are adapting your growth techniques to each crop individually.

With 5000 acres of garlic and 6000 acres of onions, the crops are very much dependent on the weather! Our competence allows us to make good profits from both good and bad crops!

So, to more closely match the Bell-formulation, let's use
$$P(O^+|X) = P(O^-|X) = P(G^+|Y) = P(G^-|Y) = \frac{1}{2}. (J)$$
Then we find agriculturally that
$$
P(O^+G^+|XY) = P(O^+|X) P(G^+|XYO^+) = \frac{1}{2} \neq P(O^+|X)P(G^+|Y). (K)
$$
So now we have the local farming conditions X and Y separated like the x and y in Bell's locality hypothesis. And the farming conditions X and Y are correlated via a function of the associated growing conditions: just like Bell's detector settings x and y are correlated via a function of the associated settings.

 

[N88]

If even after controlling for water supply, there is a correlation between your garlic crop and your onion crop, then that usually means that there is some other common causal influence other than water supply.

Indeed, its called the weather (mostly). Remember, I only removed the underground water-supply. And that was done reluctantly: for reasons that I have yet to understand (but see post above this one). There is apparently some reason to remove λ from Bell's formulation for comparison purposes, but that reasoning is currently beyond me.

 

[stevendaryl]

You appear to be confusing logical-implication with causation?? There is no causal influence between the crops; the crop correlations arise from the correlation of the separate local growing conditions (soil, sunlight, rainfall, plough-settings). The outcome correlations in EPRB arise in a similar way; eg, via the correlation of the independent and freely chosen detector settings x and y as a function of their angular difference (x,y).

So the probability of getting a good garlic crop is a function of lots of variables: soil, sunlight, rain, etc. Similarly for an onion crop. Then it's false to say that water supply is the only common causal influence on the two crops. Bell's factorizability condition is only expected to hold if the hidden variable \lambda includes all relevant common causal influences.

 

[stevendaryl]

Indeed, its called the weather (mostly).

Then what that means is that \lambda must include both water supply AND weather. Bell's factorizability condition only holds when ALL common causal influences are held constant.

 

[stevendaryl]

Indeed, its called the weather (mostly). Remember, I only removed the underground water-supply. And that was done reluctantly: for reasons that I have yet to understand (but see post above this one). There is apparently some reason to remove λ from Bell's formulation for comparison purposes, but that reasoning is currently beyond me.

For simplicity, let's assume that there are two states for the water supply, "good" and "bad. And there are two possible types of weather, "good" and "bad. Then there are four possible values of \lambda:

1. \lambda_{++}: good water supply and good weather
2. \lambda_{+-} good water supply and bad weather
3. \lambda_{-+} bad water supply and good weather
4. \lambda_{--} bad water supply and bad weather

If water supply and weather are the only variables that are relevant, then

P(G^+, O^+|\lambda_{++}) = P(G^+|\lambda_{++}) P(O^+ | \lambda_{++})
(and similarly for all other values of \lambda).

If you don't control for weather and only control for water supply, then the probabilities will not factor. If you've controlled for every common causal influence, then the probabilities will factor.

 

[PeterDonis]

You appear to be confusing logical-implication with causation?

No, I'm just saying that you are confused about how your scenario matches up with Bell's notation and formulas.

the crop correlations arise from the correlation of the separate local growing conditions (soil, sunlight, rainfall, plough-settings)

In other words, the water supply is not the only common factor between the crops, despite what you said earlier. Ok, fine. Then all of these things that correlate between the growing conditions--soil, sunlight, rainfall, plough settings--are all included in $\lambda$. They aren't included in $x$ and $y$. That's how Bell defined those variables. If you are using different definitions from his, of course you're going to come up with different formulas. But if you want to compare with Bell's formulas, you need to use his definitions.

With 5000 acres of garlic and 6000 acres of onions, the crops are very much dependent on the weather!

Ok, then weather goes in $\lambda$ as well.

So now we have the local farming conditions X and Y separated like the x and y in Bell's locality hypothesis

No, you don't. See below.

the farming conditions X and Y are correlated

This violates Bell's definitions; by definition, Bell's $x$ and $y$ are uncorrelated.

just like Bell's detector settings x and y are correlated via a function of the associated settings

What "function of the associated settings" are you talking about?

 

[PeterDonis]

There is apparently some reason to remove λ from Bell's formulation for comparison purposes

No, only to illustrate what Bell meant by $\lambda$. See the recent responses from stevendaryl and me.

 

[Denis]

But the only way for the factorizability condition to be violated here is if $\lambda$ does not include information from the actual crime scene.

No. It includes everything what above A and B know. If above have been there, that means, it includes all information from the crime scene.

But it does not contain the answer A has invented only during the interrogation to hide what they above have done in reality.

With $\lambda$ defined to include information from the actual crime scene, then the factorizability condition can't be violated, since all of the correlations between A's and B's answers can be explained by their common knowledge of what happened at the crime scene.

Also correlations between lies about what actually happened, lies which have not been planned immediately at the crime scene, simply because above have been unable to know all what the police has been able to find out? Say, the following dialog:

Police: You have said you have left the place late in the afternoon. Please, more details, because you have been seen there at 19:00. When have you left the place?
A: We have left the place 19:30.
Police: Are you sure?
A: Yes, we wanted to see the soccer game which started 20:15 in TV. We have talked about this, I remember, its time to go I have said, else we will miss the begin of the game.
--
Police: You have said you have left the place late in the afternoon. Please, more details, because you have been seen there at 19:00. When have you left the place?
B: We have left the place 19:30.
Police: Are you sure?
B: Yes, we wanted to see the soccer game which started 20:15 in TV. We have talked about this, I remember, its time to go A has said, else we will miss the begin of the game.

Knowledge of the crime scene gives them memories how they have killed C 22:30, and an agreement between them to claim that they have left the place in the late afternoon, because they have not recognized that they have been seen there as late as 19:00, only at 15:00.

Whether that common knowledge comes from both of them being present at the crime scene, or A communicating it to B afterwards, doesn't matter for factorizability.

It matters, because A's memories of the police interrogation are not part of $\lambda$, thus, not accessible to B if factorizability holds.

Which is violated by quantum mechanics, but not by your scenario. Your scenario does not violate locality; as you admit in the above quote, it shows why the EPR criterion is a good criterion for any scenario that does not involve quantum mechanics. In other words, it shows why classical physics does not violate locality.

No, the EPR criterion is not violated by the dBB interpretation of QM, and, therefore, not by QM. Because in the dBB interpretation of QM EPR holds, but is simply inapplicable, because (as described by the guiding equation) the measurement at A, if done before B, causally influences the outcome measured at B later.

 

[PeterDonis]

It includes everything what above A and B know. If above have been there, that means, it includes all information from the crime scene.

Yes, I agree; that's what I was saying in my previous post. And also, if $\lambda$ includes all that information, the factorizability condition will not be violated in your example.

it does not contain the answer A has invented only during the interrogation to hide what they above have done in reality

If A communicates that information to B before the interrogation, then $\lambda$ does include it. And if A does not communicate that information to B before the interrogation, then there will be no correlation between A's and B's answers based on that information alone, which means the factorizability condition will not be violated.

What you appear to be missing is that, if A invents an answer during the interrogation based on information he remembers from the crime scene, and B was also at the crime scene, then A's invention is using information that is in $\lambda$, so the factorizability condition still holds.

What would violate the factorizability condition is if A invented some answer during the interrogation based solely on, say, the color of his interrogator's eyes, and B invented some answer during his interrogation based solely on, say, the pattern of marks on the wall of his interrogation room, and yet there were still correlations between those particular answers of A and B. But you are not claiming such a thing would happen (and of course it wouldn't in a real world interrogation).

A's memories of the police interrogation are not part of λ

Yes, that's correct (since we are assuming that A and B cannot communicate during the interrogation itself). And that means, as above, that there will be no correlation between A's and B's responses based on A's memories of the interrogation alone, so the factorizability condition will not be violated.

But once again, this requires that A invents an answer purely based on his memories of the interrogation, without using any information remembered from the crime scene (or anything else in $\lambda$, such as prior communications with B). That's not what you described. What you described is A inventing answers based partly on his memories of the interrogation, and partly on his memories of the crime scene. That means A is using information in $\lambda$, so his answers being correlated with B's, since B is also using information in $\lambda$, does not violate the factorizability condition.

in the dBB interpretation of QM EPR holds, but is simply inapplicable, because (as described by the guiding equation) the measurement at A, if done before B, causally influences the outcome measured at B later

This causal influence is nonlocal--it violates Bell's locality condition, which is one of the premises required to derive Bell's inequality. So of course the dBB interpretation predicts violations of Bell's inequalities, just like any other interpretation of QM. This is not "EPR holds, but is simply inapplicable". This a straightforward "EPR is violated" (more precisely, Bell's inequalities are violated), just like any other interpretation of QM.

 

[Denis]

What you appear to be missing is that, if A invents an answer during the interrogation based on information he remembers from the crime scene, and B was also at the crime scene, then A's invention is using information that is in $\lambda$, so the factorizability condition still holds.

Only if A's invention is completely defined by what has really happened on the crime scence. The case when A and B have already at the crime scene prepared their excuse. Which is what my version has deliberately excluded - they were not aware that they have been seen at 19:00, thus, have not prepared a version for this event. A had to invent something new.

What would violate the factorizability condition is if A invented some answer during the interrogation based solely on, say, the color of his interrogator's eyes, and B invented some answer during his interrogation based solely on, say, the pattern of marks on the wall of his interrogation room, and yet there were still correlations between those particular answers of A and B. But you are not claiming such a thing would happen (and of course it wouldn't in a real world interrogation).

Indeed. But there is the other possibility that A told B via an illegal mobile phone connection about his interrogation, and what he has invented.

Yes, that's correct (since we are assuming that A and B cannot communicate during the interrogation itself). And that means, as above, that there will be no correlation between A's and B's responses based on A's memories of the interrogation alone, so the factorizability condition will not be violated.

But the factorizability condition is violated. Because it predicts no correlation between the inventions, based on $\lambda$ alone, but what we observe is a large, 100%, correlation.

But once again, this requires that A invents an answer purely based on his memories of the interrogation, without using any information remembered from the crime scene (or anything else in $\lambda$, such as prior communications with B).

No, there is no such requirement. He can use what he wants from his memories in $\lambda$. The only thing which matters is that he has to invent something new.

That's not what you described. What you described is A inventing answers based partly on his memories of the interrogation, and partly on his memories of the crime scene. That means A is using information in $\lambda$, so his answers being correlated with B's, since B is also using information in $\lambda$, does not violate the factorizability condition.

There is no such restriction. The example shows that we observe 100% correlation of the answers (and given that it contains a lot of bits, this is already good enough statistics). It can be easily explained if we have the information channel, so that P(ab|x,y,λ)=P(a|x,λ)P(b|a,y,λ) is all we need. But P(ab|x,y,λ)=P(a|x,λ)P(b|y,λ) does not hold, once a is the result of some invention, which may depend on x (the questions, and something influencing his free decision) as well as on λ. Nothing in these formulas introduces a necessity of some independence of whatever on λ. The difference between the two cases is that P(b|a,y,λ) can depend on what A has answered.

It is the cheated police officer who believes that, given that no hidden information channel exists, P(ab|x,y,λ)=P(a|x,λ)P(b|y,λ) holds. And that this allows to conclude that by receiving A's answer a he has really, with 100% certainty, and without in any way influencing B's following interrogation, been able to predict the outcome of B's interrogation. And that, therefore, B's answer was predefined by λ. Not invented in some way somehow using λ, not. Predefined by λ.

This causal influence is nonlocal--it violates Bell's locality condition, which is one of the premises required to derive Bell's inequality. So of course the dBB interpretation predicts violations of Bell's inequalities, just like any other interpretation of QM. This is not "EPR holds, but is simply inapplicable". This a straightforward "EPR is violated" (more precisely, Bell's inequalities are violated), just like any other interpretation of QM.

Sorry, no. What is violated is - you name it - the locality condition, not realism, not the EPR criterion. Bell's inequalities are not "more precisely" the EPR criterion, but something completely different. Namely a conclusion, which holds only if we apply EPR as well as locality (to get the "predict in no way disturbing" part of the EPR criterion).

In BM, the measurement at A disturbs the measurement at B. In my example, the interrogation of A disturbs the interrogation of B, because A tells B about what happened there and influences his answer. So, in above cases the EPR criterion, which contains the "in no way disturbing" as a condition, is simply not applicable.

 

[rubi]

QM respects locality in the strong sense of EPR.

Easily accessible explanation: https://arxiv.org/abs/1512.01443
Strict mathematical proof: http://aapt.scitation.org/doi/abs/10.1119/1.14965

 

[PeterDonis]

Which is what my version has deliberately excluded - they were not aware that they have been seen at 19:00, thus, have not prepared a version for this event. A had to invent something new.

the factorizability condition is violated. Because it predicts no correlation between the inventions, based on $\lambda$ alone, but what we observe is a large, 100%, correlation.

Then what explains this large, 100% correlation? I assume you are not claiming that A and B are entangled quantum particles and that the interrogators are running EPR experiments on them. So what mechanism are you postulating that explains A's and B's correlated inventions? And why do you think it is consistent with the laws of physics?

In other words, it looks to me like you are saying that the factorizability condition can be violated in a non-QM setting, based on a made up scenario that could never actually happen. Am I reading you correctly?

In my example, the interrogation of A disturbs the interrogation of B, because A tells B about what happened there and influences his answer

I don't get it. I thought you said that A and B did not communicate (except for both being at the crime scene). So how can A tell B what happened in A's interrogation?

If A does tell B about his interrogation, then everything that happened in A's interrogation is part of $\lambda$, so the factorizability condition is not violated.

You are either very confused or you are changing your scenario at your whim.

 

[Denis]

Then what explains this large, 100% correlation?

The hidden communication channel. Namely, A uses the smuggled phone to tell B about the surprise (they have been seen at 19.00) and what he has invented as the reaction. B has understood and acted appropriately. Clearly, a smuggled mobile phone connection between two incarcerated suspects violates laws, but only human laws, not physical laws.

In other words, it looks to me like you are saying that the factorizability condition can be violated in a non-QM setting, based on a made up scenario that could never actually happen. Am I reading you correctly?

No, such things happen all the time. It is the reason why the police tries to prevent communication between suspects in the same crime. It is the reason why these suspects try to communicate, and try to hide the fact of their communication. The suspects want a 100% correlation between their claims, in a way that the police does not know about their communication. Because this suggests the police to apply the EPR principle, and to believe that the correlated claims correspond to reality, instead of being inventions to hide reality.

I don't get it. I thought you said that A and B did not communicate (except for both being at the crime scene). So how can A tell B what happened in A's interrogation?

? I wrote in #13:

Of course, the information transfer in the analogy is not violating Einstein causality, but it violates the law of the state, with the police doing everything to prevent it, so it is also a hidden information transfer. And the guys will do everything to hide it. (If they use smuggled mobiles, the communication may be even faster than sound.)

And the aim of this hidden communication is, exactly, to suggest the police to apply the EPR criterion of reality: Once the interrogation of A allowed to correctly predict what B would answer, without influencing B's interrogation in any way, the answer should correspond to some element of reality.

If A does tell B about his interrogation, then everything that happened in A's interrogation is part of $\lambda$, so the factorizability condition is not violated.

No. $\lambda$ is what is predefined, what is fixed before the two "measurements" in form of police interrogations. What is transferred is the measurement result of the interrogation of A, that means, a.

You are either very confused or you are changing your scenario at your whim.

Sorry, but I see the confusion on your side.

Here the consistent (quote me if you find some inconsistency) scenario:

$\lambda$ the shared memories of A and B about their crime, and their initial version to hide it which failed.
x,y the questions of the interrogators
a,b the answers given by A and B.
we observe 100% correlation. Which is easily explained by the hidden communication.
The police does not know about the hidden communication, thus, thinks that P(ab|x,y,λ)=P(a|x,λ)P(b|y,λ), thus, thinks, using EPR, that the shared excuse has an element of reality, was predefined, was part of their shared memories $\lambda$. And therefore erroneously concludes, that the excuse is reality.
But the excuse was no reality, it was invented by A during the interrogation and send, violating human law, to B. P(ab|x,y,λ)=P(a|x,λ)P(b|y,λ) does not hold, instead P(ab|x,y,λ)=P(a|x,λ)P(b|a,y,λ) holds.

 

[Denis]

Griffiths writes in https://arxiv.org/abs/1512.01443:

However the derivation of the CHSH version of a Bell inequality, which is Eq. (1) in [1], has as one of its assumptions that Sx, Sz, and other components of spin can be replaced by classical, which is to say commuting, quantities, which have a joint probability distribution, directly contrary, as Fine pointed out, to the principles of quantum mechanics.

This is, again, a case of a very old point made by Bell in Bertlmann's socks and the nature of reality:

It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. ... It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis.

It is inferred, using as the EPR principle of reality, as Einstein causality, to prove that the measurement at A really does not disturb the measurement at B.

 

[rubi]

Griffiths writes in https://arxiv.org/abs/1512.01443:

This is, again, a case of a very old point made by Bell in Bertlmann's socks and the nature of reality:

It is inferred, using as the EPR principle of reality, as Einstein causality, to prove that the measurement at A really does not disturb the measurement at B.

The EPR principle cannot be used to infer this. Bob's detector angle is random and thus Alice cannot predict with certainty what Bob's outcome is. This is possible only in the case of fixed detector angles and in that case, a local hidden variable explanation is possible with no problems. The fact that the detector angles must be chosen randomly and independently prevents the application of the EPR principle. It would be possible, if the spins along all directions could be measured simultaneously, but as Griffithis points out, this is in direct conflict with the principles of QM.

If you want to apply the EPR principle, you must presuppose that the spins along all angles are simultaneously well-defined.

 

[PeterDonis]

The hidden communication channel. Namely, A uses the smuggled phone to tell B about the surprise (they have been seen at 19.00) and what he has invented as the reaction. B has understood and acted appropriately

Ok, then all the information in that conversation is part of $\lambda$, and the factorizability condition is not violated.

such things happen all the time

People talk on cell phones all the time, sure. But talking on cell phones does not and cannot violate the Bell inequalities. If you are seriously claiming that it can, then you have a serious misunderstanding of the physics involved.

$\lambda$ is what is predefined, what is fixed before the two "measurements" in form of police interrogations

That might be your definition, but it's not Bell's definition. Bell's definition is that $\lambda$ includes all information that is available at both measurement events. It doesn't matter how it gets there.

One feature of your scenario that is different from the standard EPR experiment is that your "measurement" events (the interrogations) are timelike separated, not spacelike separated. That means that $\lambda$ can include information that happens after one interrogation but before the other, such as the information A tells B during the cell phone call. As long as the information is available at both interrogations, it goes in $\lambda$.

If the interrogations were in fact spacelike separated, then you would be correct that $\lambda$ would only include information that happened prior to both interrogations. But if the two interrogations were spacelike separated, A would not be able to use a smuggled cell phone to call B and tell him what happened in his interrogation.

(quote me if you find some inconsistency)

Your definition of $\lambda$ is wrong. See above.

 

[Denis]

But talking on cell phones does not and cannot violate the Bell inequalities.

The Bell inequalities can be easily violated if there is no restriction on the distribution of information. You cannot prove the Bell inequalities with the EPR (realism) alone, you need Einstein locality too. This has nothing to do with quantum theory, as the whole proof of the Bell inequalities has nothing to do with it.

One feature of your scenario that is different from the standard EPR experiment is that your "measurement" events (the interrogations) are timelike separated, not spacelike separated.

Indeed, and this makes the communication possible, compatible with physical laws. So, the Bell inequalities can be violated without using quantum effects. It does not change the fact that if you can exclude (for whatever reasons) any communication about the interrogations, than you can prove the Bell inequalities. If not, you cannot.

The EPR principle cannot be used to infer this. Bob's detector angle is random and thus Alice cannot predict with certainty what Bob's outcome is.

Alice can predict, with certainty, what would be the result of Bob measuring in direction $\alpha$, by measuring in the same direction $\alpha$. This possibility does not depend on what is reality measured. It is a possibility: If we can predict:

If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

This is applied to the value of the physical quantity defined by the spin measurement in direction $\alpha$. What is used (and necessarily used) is Einstein causality, in above direction. In one direction, to obtain the "predict" (instead of "postdict"), in the other direction to obtain the "without in any way disturbing a system".

That means, what Bob would measure in direction $\alpha$ is something we can, using EPR in combination with Einstein causality, assign an element of reality. This consideration is not about what is actually measured, but about what can be measured in principle. Thus, it does not depend on any actual choice of $\alpha$, but holds for all values of $\alpha$. Thus, the values have a corresponding element of reality for all values of $\alpha$.

If you want to apply the EPR principle, you must presuppose that the spins along all angles are simultaneously well-defined.

No. It is sufficient to presuppose Einstein causality, to be sure that the measurement of $\alpha$ at A does in no way distort a possibly following measurement of $\alpha$ at B. And to know that if the same angle is measured there is 100% correlation.

 

[PeterDonis]

The Bell inequalities can be easily violated if there is no restriction on the distribution of information.

There is in your scenario: information can only travel at the speed of light.

You cannot prove the Bell inequalities with the EPR (realism) alone, you need Einstein locality too

Einstein locality is equivalent to information travel being limited to the speed of light. Your scenario obeys that restriction.

the Bell inequalities can be violated without using quantum effects

I'm sorry, but your handwaving scenario doesn't prove what you think it does. Either provide a valid reference (textbook or peer-reviewed paper) that supports this claim, or show the math yourself, in detail, or stop making the claim.

 

[Denis]

There is in your scenario: information can only travel at the speed of light.

The analogy is "Information cannot travel between different prison cells/interrogation cells." Which is the assumption the police makes evaluating the results of the interrogations.

I'm sorry, but your handwaving scenario doesn't prove what you think it does. Either provide a valid reference (textbook or peer-reviewed paper) that supports this claim, or show the math yourself, in detail, or stop making the claim.

Ok, let's consider the classical Bell game. Three cards, red or black, color hidden but predefined. I claim that left and middle card have the same color, middle and right card have the same color, left and right card have different color. One of the three claims is wrong. Thus, if you test one claim by opening two cards you have a chance greater equal 1/3 to find the wrong claim.

You can easily trick in this scenario if you, after the opening of the first card, are able to change the color of the yet closed cards. So, with this cheating you can reach maximal violation of BI, probability 0 instead of greater equal 1/3.

To make this closer to Bell, use two packets of the three cards, claimed to be identical, in two rooms without communication. And open one card in each room. Sometimes the same card may be tested, this serves as a test that the three cards are indeed always the same and really fixed before. With this test possibility, we do not have to care about the cards themselves, but can restrict ourselves to listening the answer of the guy in this room. But, once I'm able to send a signal to the other room which card was asked, one can, again, make it impossible to identify the false claim.

PS: Looks like I'm no longer allowed to reply in this thread, so sorry for not answering the claims below.

 

[rubi]

Alice can predict, with certainty, what would be the result of Bob measuring in direction $\alpha$, by measuring in the same direction $\alpha$. This possibility does not depend on what is reality measured. It is a possibility: If we can predict:

This is applied to the value of the physical quantity defined by the spin measurement in direction $\alpha$. What is used (and necessarily used) is Einstein causality, in above direction. In one direction, to obtain the "predict" (instead of "postdict"), in the other direction to obtain the "without in any way disturbing a system".

That means, what Bob would measure in direction $\alpha$ is something we can, using EPR in combination with Einstein causality, assign an element of reality. This consideration is not about what is actually measured, but about what can be measured in principle. Thus, it does not depend on any actual choice of $\alpha$, but holds for all values of $\alpha$. Thus, the values have a corresponding element of reality for all values of $\alpha$.

No. It is sufficient to presuppose Einstein causality, to be sure that the measurement of $\alpha$ at A does in no way distort a possibly following measurement of $\alpha$ at B. And to know that if the same angle is measured there is 100% correlation.

No, you don't understand. A Bell test experiment is only interesting in the case where Alice does not know Bob's angle and vice-versa. Otherwise, it is no problem to come up with a local hidden variable theory matching the observations. Bob must be able to choose his angle independent of Alice (and vice-versa). Thus, Alice cannot (with certainty) align her detector along Bob's angle. But if Alice cannot align her detector (with certainty) along Bob's angle, then she cannot (with certainty) measure her particle along Bob's angle and thus not predict from her measurements, with certainty, Bob's outcome. As an undeniable matter of fact, Alice cannot, in an interesting Bell test experiment, predict with certainty the value of a physical quantity associated with Bob's particle and hence cannot use the EPR criterion to conclude the existence of an element of reality corresponding to a physical quantity associated to Bob's particle, because she might measure the wrong angle (which must be possible in an interesting Bell test experiment).

Of course, Alice can "predict" (this is actually the wrong word) what Bob would have measured if he had aligned his detector along the same angle. But this is not sufficient for the EPR criterion. You are rather proposing your personal version of the EPR criterion. The EPR criterion doesn't allow for counterfactual reasoning. And this is precisely what allows QM to violate the Bell inequality, because Bohr's complementarity principle (which is made rigorous in state-of-the-art interpretations like consistent histories) prevents you from making such counterfactual statements. In each history, a particle never has two (or more) physical quantities associated to spin directions.

Let me explain, why your proposed counterfactual EPR criterion is flawed. Suppose I predict that there is a tiny teapot orbiting the sun between Earth and Mars and I predict that there is the number 5 engraved on the bottom. Clearly I haven't disturbed any system by making this prediction. Am I allowed to use the EPR criterion to conclude the existence of an element of reality corresponding to a number engraved on a teapot orbiting the sun? Of course not. In order to draw a conclusion from a physical prediction, I must be able to test it. The situation is completely analogous when it comes to counterfactual statements. Of course Alice can make a prediction about a hypothetical physical quantity corresponding to Bob's particle and she doesn't even need to make this prediction based on some local measurement on her particle. However, it is in principle impossible to test this prediction, because it is in principle impossible for Bob to measure the spin of his particle along two different axes. No experimenter can in principle design such an experiment. Hence, you are suggesting that we should be allowed to draw conclusions from predictions that cannot even in principle be falsified. Of course, this is scientifically untenable and any argument based on such an idea must be invalid. And by the way, it is universally agreed upon among physicists that the assumption of hidden variables is indeed an extra assumption that can be denied.

 

[PeterDonis]

The analogy is "Information cannot travel between different prison cells/interrogation cells."

Oh, this is just an analogy? Then how does it support your claim that the Bell inequalities can be violated without using quantum effects? Analogies aren't physics.

once I'm able to send a signal to the other room which card was asked, one can, again, make it impossible to identify the false claim.

This doesn't support your claim that the Bell inequalities can be violated without using quantum effects. All it shows is that, if the "measurement" events are timelike separarated, the information in $\lambda$ will include information communicated from one measurement event to the other.

You're not proving anything except that you misunderstand the math.

 

[zonde]

A Bell test experiment is only interesting in the case where Alice does not know Bob's angle and vice-versa. Otherwise, it is no problem to come up with a local hidden variable theory matching the observations. Bob must be able to choose his angle independent of Alice (and vice-versa). Thus, Alice cannot (with certainty) align her detector along Bob's angle. But if Alice cannot align her detector (with certainty) along Bob's angle, then she cannot (with certainty) measure her particle along Bob's angle and thus not predict from her measurements, with certainty, Bob's outcome. As an undeniable matter of fact, Alice cannot, in an interesting Bell test experiment, predict with certainty the value of a physical quantity associated with Bob's particle and hence cannot use the EPR criterion to conclude the existence of an element of reality corresponding to a physical quantity associated to Bob's particle, because she might measure the wrong angle (which must be possible in an interesting Bell test experiment).

A situation where (assuming Einstein's causality) Alice can only predict measurement outcome for cases where Alice's measurement settings match Bob's measurement settings but can not draw any conclusions in other cases can be modeled only by superdeterministic models. If we exclude superdeterministic models EPR argument assuming Einstein's causality goes trough.

And by the way, it is universally agreed upon among physicists that the assumption of hidden variables is indeed an extra assumption that can be denied.

Denis in post #33 gave a reference that contradicts your statement. What can you propose to back up your statement?

 

[rubi]

A situation where (assuming Einstein's causality) Alice can only predict measurement outcome for cases where Alice's measurement settings match Bob's measurement settings but can not draw any conclusions in other cases can be modeled only by superdeterministic models. If we exclude superdeterministic models EPR argument assuming Einstein's causality goes trough.

No, you are mistaken here. It is completely unrelated to superdeterminism. The question is: Can the EPR argument be applied to the situation when Alice and Bob measure different angles? And the answer is undeniably no, it can't, because in such a situation, Alice would have to make a prediction that cannot even in principle be tested experimentally. She could randomly flip a coin to come up with her prediction. As an undeniable matter of fact, we can never test the prediction in situations, where the angles of the detectors aren't aligned. And of course, one cannot draw scientifically sound conclusions from untestable predictions. Thus, it is impossible to use the EPR argument to argue about elements of reality in case of unaligned detectors. We can't draw scientific conclusions from untestable predictions. Period.

Of course, it is impossible to draw mathematical conclusions from informal arguments such as the EPR argument anyway, but it is enlightening to understand why the argument is invalid.

Denis in post #33 gave a reference that contradicts your statement. What can you propose to back up your statement?

Bell's argument is of course invalidated by contemporary research. I gave a like to an article in post #30 that proves mathematically beyond doubt that the claim is invalid. The author addresses Bell's and Denis' claims and refutes them. If you cannot spot an error in the proof, then please refrain from making unjustified claims.

 

[zonde]

No, you are mistaken here. It is completely unrelated to superdeterminism. The question is: Can the EPR argument be applied to the situation when Alice and Bob measure different angles? And the answer is undeniably no, it can't, because in such a situation, Alice would have to make a prediction that cannot even in principle be tested experimentally. She could randomly flip a coin to come up with her prediction. As an undeniable matter of fact, we can never test the prediction in situations, where the angles of the detectors aren't aligned. And of course, one cannot draw scientifically sound conclusions from untestable predictions. Thus, it is impossible to use the EPR argument to argue about elements of reality in case of unaligned detectors. We can't draw scientific conclusions from untestable predictions. Period.

You are mixing up reality with models of reality. In science we do not make direct statements about reality. We develop models of reality and than test them against reality.
So when I say that EPR argument goes through I mean that there are no models of reality (that assume Enstein's locality) that can escape EPR argument except superdeterministic models.
You on the other hand talk about model independent predictions of Alice.

Bell's argument is of course invalidated by contemporary research. I gave a like to an article in post #30 that proves mathematically beyond doubt that the claim is invalid. The author addresses Bell's and Denis' claims and refutes them. If you cannot spot an error in the proof, then please refrain from making unjustified claims.

What this has to do with the part in your statement that refers to consensus among physicists? You said: "it is universally agreed upon among physicists that the assumption of hidden variables is indeed an extra assumption that can be denied."

 

[rubi]

You are mixing up reality with models of reality. In science we do not make direct statements about reality. We develop models of reality and than test them against reality.
So when I say that EPR argument goes through I mean that there are no models of reality (that assume Enstein's locality) that can escape EPR argument except superdeterministic models.
You on the other hand talk about model independent predictions of Alice.

I am not mixing up anything and I did not say anything about reality. Denis wants to use the EPR argument to argue that any model must be a hidden variable model. In order to use the EPR argument, one must satisfy its premises, among which there is one that requires that one can predict the value of some physical quantity with certainty. As a matter of fact, the value in question cannot be predicted with certainty, because it is in principle impossible to test the prediction. Hence, the EPR argument doesn't apply and we can't conclude that all models must be hidden variable models. (Which is not possible anyway, because in math, such informal arguments are worthless.) Thus there may be local models that are not hidden variable models and my post #30 proves that there are indeed such models.

This has exactly nothing to do with superdeterminism. We know from Bell that local hidden variable theories must be superdeterministic. But we don't know that local models without hidden variables must be superdeterministic (in fact, they don't, the model in post #30 is not superdeterministic). And the EPR argument is completely unrelated to superdeterminism.

What this has to do with the part in your statement that refers to consensus among physicists? You said: "it is universally agreed upon among physicists that the assumption of hidden variables is indeed an extra assumption that can be denied."

Yes and that is true. You claimed that Bell is a counterexample and I showed you that he is refuted. You will not find modern accepted literature about Bell's theorem that follows your interpretation. Not even Bohmians dare to question that.

 

[stevendaryl]

This has exactly nothing to do with superdeterminism. We know from Bell that local hidden variable theories must be superdeterministic. But we don't know that local models without hidden variables must be superdeterministic (in fact, they don't, the model in post #30 is not superdeterministic). And the EPR argument is completely unrelated to superdeterminism.

I think that the discussion of the consistent histories interpretation deserves its own thread. The sense in which consistent histories is both local and realistic is a little mysterious.

 

[rubi]

I think that the discussion of the consistent histories interpretation deserves its own thread. The sense in which consistent histories is both local and realistic is a little mysterious.

Since this would probably be a long discussion, I probably can't participate in such a thread before sunday. But here are my thoughts on this:
Whether some theory is "realistic" or not depends heavily on how one translates this term into mathematics. CH is not realistic in the mathematical sense of Bell's theorem, but the question is whether this mathematical notion captures the philosophical idea of realism adequately. What Griffiths means when he says that CH is realistic is that in each history, all quantities that can be measured in principle can be assumed to exist independently of whether one actually measures them or not (if one wishes), but there are no quantities associated to things that cannot even be measured in principle (contrary to the realism assumption in Bell's theorem). I don't know (and don't care too much) whether this satisfies the philosophical idea of realism as long as the math is correct.

 

[zonde]

In order to use the EPR argument, one must satisfy its premises, among which there is one that requires that one can predict the value of some physical quantity with certainty. As a matter of fact, the value in question cannot be predicted with certainty, because it is in principle impossible to test the prediction.

A model does not have to predict external test parameters. So obviously model's predictions have to be conditioned on external test parameters i.e. we should observe perfect correlations whenever Alice's and Bob's measurement angles are the same. Then we can create experimental situation where randomly chosen measurement angles sometimes turn out to be the same. This would be a valid test for the model.

Not even Bohmians dare to question that.

Interesting choice of words - "dare".
But still there is Travis Norsen. And Wiseman is at least questioning consensus on that: https://arxiv.org/abs/1402.0351 (see the chapter "7. The Two Camps").

 

[rubi]

A model does not have to predict external test parameters. So obviously model's predictions have to be conditioned on external test parameters i.e. we should observe perfect correlations whenever Alice's and Bob's measurement angles are the same. Then we can create experimental situation where randomly chosen measurement angles sometimes turn out to be the same. This would be a valid test for the model.

No, of course, this will not establish the existence of elements of reality in the case of unaligned detectors. Among your data set, there will never be a point with unaligned detector angles but outcomes for different angles on each side. Any prediction for such a situation cannot be tested in principle and is completely unscientific. And as I explained, you can't draw legitimate conclusions from untestable predicitons. Anyone can predict anything, but if it cannot be tested even in principle, then it is worthless for scientific arguments. If would be okay, if this were religion, but unfortunately, we (at least I) are rather interested in science.

It is in principle impossible to test the claim that in the case of unaligned detector angles, Alice can make a correct prediction. You want people to accept unscientific arguments.

Interesting choice of words - "dare".
But still there is Travis Norsen. And Wiseman is at least questioning consensus on that: https://arxiv.org/abs/1402.0351 (see the chapter "7. The Two Camps").

Travis Norsen isn't a respected physicist and not taken seriously by anyone in the physics community. It's like pretending that there was no consensus about the correctness of Bell's theorem and citing Joy Christian as a counterexample. If you want to want to question consensus, you would have to cite at least one authority who supports your claim and there is none.

 

[N88]

Dear stevendaryl and PeterDonis: thanks for your replies.

The farm analogy was intended to clarify my position re the foundations of Bell's theorem via a secretly controllable [by me, thus a hidden-variable to others] underground water supply; it was not intended to be a substitute for the specified quantum experiment.

It was also intended to help me correct any wrong ideas of mine. The idea being that I had only to assume pairwise correlation [of two spacelike separated locally causal factors] to conclude that Bell's analysis must lead to difficulties and dilemmas: the analogy being that the particles that Bell deals with are also randomly pairwise correlated [like the water supply -- analogously]!

I now see that my farming analogy is not working because it cannot reflect my position clearly. So, for easier comparison with (Bertlmann's term) "Bell's Locality Hypothesis": I'll rephrase my position in the context of Aspect's (2004) experiment [denoted by $α$] https://arxiv.org/pdf/quant-ph/0402001v1.pdf using Bell (1964) http://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf

I begin with a complete specification of "Bell's Locality Hypothesis":

$P(A_iB_i|αa_ib_iλ_i)=P(A_i|αa_iλ_i)P(B_i|αb_iλ_i);$ [?]

$A_i = ±1 = A^±$ = Alice's possible outcomes when her detector is set to $a_i$ in the i-th run of experiment $α$.
$B_i = ±1 = B^±$ = Bob's possible outcomes when his detector is set to $b_i$ in the i-th run of experiment $α$.
$λ_i$ = a parameter (independent of $a$ and $b$) in the i-th run that determines the result of the individual outcomes $A_i$ and $B_i$ per Bell (1964:195).
$i = 1, 2, …, n$ where $n$ is enough to deliver adequate accuracy.
$α$ = the experiment in Aspect (2004).
[?] = my identification of "Bell's Locality Hypothesis" in the same way that I would question a possible error in correspondence. Here's why:

Since [?] contains $λ_i$ in each term, logic tells me that $A_i$ and $B_i$ may be correlated. To allow for that possibility, I am forced (by this incomplete information and logic) to rewrite [?] using the standard product rule for probabilities (to encode my incomplete information):

$P(A_iB_i|αa_ib_iλ_i)=P(A_i|αa_iλ_i)P(B_i|αa_ib_iλ_iA_i)$. (1)

Note that (1) is a consequence of logical implication; not of remote AAD/spooky causation. Logic then allows me to simplify (1) as follows: I will hold the detector settings constant in a given run, so $a_i$ = $a$, $b_i$ = $b$. Further, since I have no knowledge of $λ_i$, I am forced (by logic and this incomplete information) to allow $λ_i$ to be $λ$, a pairwise-correlated random variable (RV). Thus, from (1):

$P(A_iB_i|αabλ)=P(A_i|αaλ)P(B_i|αabλA_i)$. (2)

Then, focussing on one pair of outcomes, $A^+$ and $B^+$, I have from (2):

$P(A^+B^+|αabλ)=P(A^+|αaλ)P(B^+|αabλA^+)$. (3)

Thus, under $α$, Bell's [?] can be written as:

$P(A^+B^+|αabλ) = P(A^+|αaλ)P(B^+|αbλ).$ [??]

Then, under (3), observing $α$, I see that my RV assumption and my correlation assumption are confirmed:

$P(A^+|αaλ) = P(B^+|αbλ) = \frac{1}{2}.$ (4)

$P(A^+B^+|αabλ) = P(A^+|αaλ)P(B^+|αabλA^+) = \frac{1}{2}cos^2(a,b).$ (5)

I also see [??] disconfirmed:

$P(A^+B^+|αabλ) = P(A^+|αaλ)P(B^+|αbλ) = \frac{1}{4} \neq \frac{1}{2}cos^2(a,b).$ [?]

Since the above analysis has been in my head since I first read of Bell's theorem (BT), I'd welcome the identification of any errors. I've corresponded with many working physicists who seem to dismiss BT similarly.

PS: I believe Feynman may have had a similar objection? And Peres said that BT is no part of QM. But I understand that John Clauser, the first to begin experimental testing of BT, expected BT to hold!

Thanks, N88

 

[PeterDonis]

rewrite [?] using the standard product rule for probabilities

That's not what you're doing in [1]. In [1] you are adopting an assumption that is contrary to [?], because it is more general and allows for possibilities that [?] does not. [?] is a restriction on the correlations, as compared with what the standard product rule for probabilities, which you wrote in [1], would give you. The whole point of this discussion is that the actual observed probabilities in QM experiments violate the condition [?], while they are of course consistent with the product rule for probabilities [1], which applies to any probabilities whatsoever.