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

[N88]

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.

Given that Bell writes the LHS of [?] under EPRB, which thus defines the consequent: I am writing RHS (1), the logical consequent of LHS [?] under EPRB.

If my (1) is too general under EPRB -- ie, if (1) may be restricted to [?] as Bell supposes -- then that restriction will be evident from experiments. But, at the time of writing (1) -- where I know (like Clauser) the experimental set-up and the correlated particles, but not the factual outcomes -- I cannot write anything other than (1).

Experiments then confirm the validity of my reasoning in (1) -- from elementary probability theory -- so I remain at a loss as to why Bell (or anyone else) should consider that his formulation [?] has any chance of success?

My writing of (1) is further justified by your own statement: "The whole point of this discussion is that the actual observed probabilities in QM experiments violate the condition [?]." Given the pairwise correlated particles in EPRB, experiments must violate such a false assumption as [?].

In other words: what is the motivation for writing [?] when it logically has no chance of success under EPRB due to the pairwise correlation of the particles?

EDIT: I agree with von Weizsäcker: "I propose the view that general or abstract quantum theory is a general theory of probabilities and nothing else," from Fröhner (1988)
http://zfn.mpdl.mpg.de/data/Reihe_A/53/ZNA-1998-53a-0637.pdf.

[PS: I have no wish to become involved in speculation. For I am no Feynman, nor am I a working physicist: but I understand that Feynman and many working physicists are similarly dismissive. Some believe that Bell was a Bohm fan and that Bell was attempting to justify his fandom by showing that any explanatory theory of EPRB must be like Bohm's. The point for me is: where do I find the motivation for anyone to follow Bell's restrictive [?], which must logically be false under EPRB?]

 

[PeterDonis]

I remain at a loss as to why Bell (or anyone else) should consider that his formulation [?] has any chance of success?

You're missing the point. First, [?] does correctly describe the predictions of every theory we have except QM, and the experimentat results that are correctly predicted by those theories, i.e., any experiment that does not involve correlations between entangled quantum systems. Second, Bell's point with [?] was to give a precise mathematical formulation of a key property of every theory we have except QM, which he called "locality" and which is mathematically expressed by [?]. Bell knew perfectly well that QM predicts violations of [?]; he was investigating what that meant, and how it could be tested experimentally.

 

[zonde]

Any prediction for such a situation cannot be tested in principle and is completely unscientific.

We do not test model independent predictions. We test predictions of models. A model have to apply to physical situation irrespective of particular value of external test parameters. You can't have one model that applies when measurement angles are the same and entirely different model when measurement angles are different. You have to have single consistent model that can cover both possibilities.

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.

Well, Travis Norsen is respected enough for Wiseman to say that there is no consensus (I gave reference in post #47).

 

[rubi]

We do not test model independent predictions.

The prediction that is relevant in the EPR argument has nothing to do with a model. Alice has an experimental setup and the question is whether she can make a prediction (based on her measurements) for the spin of Bob's particle along some angle $\beta$. If that prediction turns out to be correct in 100% of the cases, we say that she can predict the spin with certainty and then we might apply the EPR argument. However, it is impossible to test whether the prediction is correct in 100% of the cases, because it is impossible to even test it. Thus we can't even apply the EPR argument.

We test predictions of models.

You have completely misunderstood the EPR argument.

A model have to apply to physical situation irrespective of particular value of external test parameters. You can't have one model that applies when measurement angles are the same and entirely different model when measurement angles are different. You have to have single consistent model that can cover both possibilities.

This is objectively false, since quantum mechanics is a counterexample. Also, even if we didn't have a counterexample, it would obviously be an invalid argument. Of course, physics needn't behave the same in different experimental setups. There is absolutely no reason to expect this.

Anyway, the very point that Denis wants to make (and fails to make) with the EPR argument is to exclude this situation, so of course one can't assume it from the beginning. That is circular reasoning.

Well, Travis Norsen is respected enough for Wiseman to say that there is no consensus (I gave reference in post #47).

Nobody even cites Norsen expect to disagree with him. Actually, this rather proves my point. If there is really just one person, who is essentially ignored by the whole physics community, then this is as much consensus as one could possibly expect.

 

[N88]

You're missing the point. First, [?] does correctly describe the predictions of every theory we have except QM, and the experimentat results that are correctly predicted by those theories, i.e., any experiment that does not involve correlations between entangled quantum systems. Second, Bell's point with [?] was to give a precise mathematical formulation of a key property of every theory we have except QM, which he called "locality" and which is mathematically expressed by [?]. Bell knew perfectly well that QM predicts violations of [?]; he was investigating what that meant, and how it could be tested experimentally.

Just addressing your first point for now.

Is this expressed correctly by you? "You're missing the point. First, [?] does correctly describe the predictions of every theory we have except QM."

Because I am missing your point, but I suspect for a different reason: Does [?] describe the prediction for drawing (without replacement) an Ace (A) and a King (B) from a standard deck of 52 playing cards? I think [?] does not and so I do not understand your claim that: "[?] does correctly describe the predictions of every theory we have except QM."

 

[rubi]

We do not test model independent predictions. We test predictions of models. A model have to apply to physical situation irrespective of particular value of external test parameters. You can't have one model that applies when measurement angles are the same and entirely different model when measurement angles are different. You have to have single consistent model that can cover both possibilities.

Well, Travis Norsen is respected enough for Wiseman to say that there is no consensus (I gave reference in post #47).

Look, the situation is really trivial:

We have an experimental setup where Alice has aligned her detector along $\alpha$ and Bob has aligned his detector along $\beta\neq\alpha$.

Denis wants to use the EPR argument to conclude the existence of an element of reality corresponding to the spin of Bob's particle along the angle $\alpha$ in this very experimental setup with unalignen angles. In order to do that, he must satisfy the premises of the EPR argument:
1. Alice must be able to predict the spin of Bob's particle along the angle $\alpha$.
2. We must be able to repeat the experiment and the prediction must be correct in 100% of the cases.
3. There must be no disturbances.

Of course, Alice can easily come up with a prediction. She might make this prediction based on her local measurements or she might come up with a completely different method. However, she can never be sure whether her prediction is correct in 100% of the cases. In fact, the can not even check the prediction in a single case, because it is in principle impossible to measure the spin of Bob's particle along $\alpha$ if the detector is not aligned along $\alpha$. Thus, at least one premise of the EPR argument is not satisfied and the EPR argument cannot be used to conclude the existence of an element of reality corresponding to the spin of Bob's particle along the angle $\alpha$ in the experimental situation stated in the beginning (even if we allow this kind of informal reasoning, which actual scientists don't).

One cannot use experimental tests with a different setup (aligned angles) in place of the experimental test with different angles, because the very point Denis wants to make with the EPR argument is to show that the existence of said element of reality is independent of Bob's detector angle, so naturally one can't assume it from the beginning. That would be circular reasoning.

Anyway, all of this is also completely irrelevant, because we know for a fact that theories can exist which don't have elements of reality associated to unmeasurable quantities. One of them is called quantum mechanics. Denial of this fact is on the verge of crackpottery.

 

[stevendaryl]

Anyway, all of this is also completely irrelevant, because we know for a fact that theories can exist which don't have elements of reality associated to unmeasurable quantities. One of them is called quantum mechanics. Denial of this fact is on the verge of crackpottery.

I consider your last sentence to verge on being abusive. It's a tautology to say that there is a theory that makes the same predictions as quantum mechanics--quantum is an example. The issue is what kind of theory quantum mechanics is.

 

[stevendaryl]

Is this expressed correctly by you? "You're missing the point. First, [?] does correctly describe the predictions of every theory we have except QM."

Because I am missing your point, but I suspect for a different reason: Does [?] describe the prediction for drawing (without replacement) an Ace (A) and a King (B) from a standard deck of 52 playing cards? I think [?] does not and so I do not understand your claim that: "[?] does correctly describe the predictions of every theory we have except QM."

It's just a fact about local realistic theories, which the most complete physical theories prior to quantum mechanics were.

The idea is that in a locally realistic theory, what happens in a small region of spacetime depends only on conditions in that region, not on conditions in far-off regions. What that means is that if there is a correlation between measurements in distant regions, it has to be because there was already a correlation in the conditions in the neighborhoods of those regions.

In any field other than quantum mechanics, this is just considered obviously true. Suppose that you find out that for a pair of twins, if one is a good badminton player, then the odds are that the other will also be a good badminton player. If you're a scientist, you would not be content with such a correlation as a final answer. You wouldn't conclude: "Well, I guess there's a law of physics stating that twins have correlated badminton abilities". Instead, you would look for a mechanism for the correlation. Maybe the correlation is genetic: There is some gene, or combination of genes, that influences a person's badminton ability. Maybe the correlation is environmental: There is some type of nurturing that is likely to produce good badminton players, and twins tend to share this experience. Or maybe it's a combination of nurturing and environment.

The expectation is that we don't really understand the correlation until we have a complete set of causal influences on badminton playing ability. Typically, we might never get to the bottom of such a question, because humans and badminton are too complicated to understand in complete detail. But in principle, we believe that it should be possible to come up with some enumeration of contributing factors to badminton ability:

• F_1 = some gene combination
• F_2 = some in-vitro conditions prior to birth
• F_3 = some physical conditions after birth (weather, terrain, air and water quality in the region where the twins grew up)
• F_4 = parental child-rearing practices affecting the twins
• F_5 = presence of siblings with particular qualities
• F_6 = influence of teachers and coaches
• etc.

Even though such a complete list is unlikely to ever be found, scientists typically believe that there could be such a list. Such a list would completely explain the correlation between the twins' badminton abilities. We would know that the list is complete if we could predict someone's badminton abilities based on knowledge of their variables F_1, F_2, .... If, on the other hand, twins had correlated badminton abilities even after taking into account F_1, F_2, ..., then we would take that to mean that we were missing a causal influence.

 

[zonde]

2. We must be able to repeat the experiment and the prediction must be correct in 100% of the cases.

Would it be ok to say that:
we must be able to repeat the experiment and the prediction must be correct in 100% of the cases except those cases where there is power outage at Bob's laboratory?

 

[N88]

It's just a fact about local realistic theories, which the most complete physical theories prior to quantum mechanics were.

The idea is that in a locally realistic theory, what happens in a small region of spacetime depends only on conditions in that region, not on conditions in far-off regions. What that means is that if there is a correlation between measurements in distant regions, it has to be because there was already a correlation in the conditions in the neighborhoods of those regions.

In any field other than quantum mechanics, this is just considered obviously true. Suppose that you find out that for a pair of twins, if one is a good badminton player, then the odds are that the other will also be a good badminton player. If you're a scientist, you would not be content with such a correlation as a final answer. You wouldn't conclude: "Well, I guess there's a law of physics stating that twins have correlated badminton abilities". Instead, you would look for a mechanism for the correlation. Maybe the correlation is genetic: There is some gene, or combination of genes, that influences a person's badminton ability. Maybe the correlation is environmental: There is some type of nurturing that is likely to produce good badminton players, and twins tend to share this experience. Or maybe it's a combination of nurturing and environment.

The expectation is that we don't really understand the correlation until we have a complete set of causal influences on badminton playing ability. Typically, we might never get to the bottom of such a question, because humans and badminton are too complicated to understand in complete detail. But in principle, we believe that it should be possible to come up with some enumeration of contributing factors to badminton ability:

• F_1 = some gene combination
• F_2 = some in-vitro conditions prior to birth
• F_3 = some physical conditions after birth (weather, terrain, air and water quality in the region where the twins grew up)
• F_4 = parental child-rearing practices affecting the twins
• F_5 = presence of siblings with particular qualities
• F_6 = influence of teachers and coaches
• etc.

Even though such a complete list is unlikely to ever be found, scientists typically believe that there could be such a list. Such a list would completely explain the correlation between the twins' badminton abilities. We would know that the list is complete if we could predict someone's badminton abilities based on knowledge of their variables F_1, F_2, .... If, on the other hand, twins had correlated badminton abilities even after taking into account F_1, F_2, ..., then we would take that to mean that we were missing a causal influence.

It's just a fact about local realistic theories, which the most complete physical theories prior to quantum mechanics were.

The idea is that in a locally realistic theory, what happens in a small region of spacetime depends only on conditions in that region, not on conditions in far-off regions. What that means is that if there is a correlation between measurements in distant regions, it has to be because there was already a correlation in the conditions in the neighborhoods of those regions.

In any field other than quantum mechanics, this is just considered obviously true. Suppose that you find out that for a pair of twins, if one is a good badminton player, then the odds are that the other will also be a good badminton player. If you're a scientist, you would not be content with such a correlation as a final answer. You wouldn't conclude: "Well, I guess there's a law of physics stating that twins have correlated badminton abilities". Instead, you would look for a mechanism for the correlation. Maybe the correlation is genetic: There is some gene, or combination of genes, that influences a person's badminton ability. Maybe the correlation is environmental: There is some type of nurturing that is likely to produce good badminton players, and twins tend to share this experience. Or maybe it's a combination of nurturing and environment.

The expectation is that we don't really understand the correlation until we have a complete set of causal influences on badminton playing ability. Typically, we might never get to the bottom of such a question, because humans and badminton are too complicated to understand in complete detail. But in principle, we believe that it should be possible to come up with some enumeration of contributing factors to badminton ability:

• F_1 = some gene combination
• F_2 = some in-vitro conditions prior to birth
• F_3 = some physical conditions after birth (weather, terrain, air and water quality in the region where the twins grew up)
• F_4 = parental child-rearing practices affecting the twins
• F_5 = presence of siblings with particular qualities
• F_6 = influence of teachers and coaches
• etc.

Even though such a complete list is unlikely to ever be found, scientists typically believe that there could be such a list. Such a list would completely explain the correlation between the twins' badminton abilities. We would know that the list is complete if we could predict someone's badminton abilities based on knowledge of their variables F_1, F_2, .... If, on the other hand, twins had correlated badminton abilities even after taking into account F_1, F_2, ..., then we would take that to mean that we were missing a causal influence.

1:-- I do not understand your claim that "It's just a fact about local realistic theories, which [were] the most complete physical theories prior to quantum mechanics were."

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

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

I now understand you to be saying that: "[?] is a fact about local realistic theories, which [were] the most complete physical theories prior to quantum mechanics were."

Does [?] account for the probability of the joint occurrence of a good Apple crop (A) and a good Banana crop (B) from widely separated farms (in a given region) when the growing conditions are correlated by the common rainfall over that region?

2:-- Are you implying that entanglement (the pairwise correlation of particle pairs) via the conservation of total angular momentum in EPRB and Aspect (2004) is not a sufficient and explanatory common cause?

Thanks, N88

 

[stevendaryl]

1:-- I do not understand your claim that "It's just a fact about local realistic theories, which [were] the most complete physical theories prior to quantum mechanics were."

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

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

I now understand you to be saying that: "[?] is a fact about local realistic theories, which [were] the most complete physical theories prior to quantum mechanics were."

Does [?] account for the probability of the joint occurrence of a good Apple crop (A) and a good Banana crop (B) from widely separated farms (in a given region) when the growing conditions are correlated by the common rainfall over that region?

Yes, as I said, it applies to every non-quantum theory. I gave you an extensive explanation.

 

[stevendaryl]

2:-- Are you implying that entanglement (the pairwise correlation of particle pairs) via the conservation of total angular momentum in EPRB and Aspect (2004) is not a sufficient and explanatory common cause?

Classically, conservation of momentum would be explained in terms of a "hidden variable", namely momentum itself. You have two particles created by (say) the decay of a more massive particle. Later, after the two particles have separated to a sizable distance, two experimenters perform measurements on the momenta of each of the particles.

So let P_1(\vec{p_1}) be the probability distribution for measurements of the momentum of the first particle. Let P_2(\vec{p_2}) be the probability distribution for measurement of momentum of the second particle. Let P(\vec{p_1}, \vec{p_2}) be the probability distribution for the two momenta.

What we find is that P(\vec{p_1}, \vec{p_2}) = 0 unless \vec{p_2} = -\vec{p_1}. So obviously, if P_1(\vec{p_1}) \neq 0 and P_2(\vec{p_2}) \neq 0, then

P(\vec{p_1}, \vec{p_2}) \neq P_1(\vec{p_1}) P_2(\vec{p_2}).

Now, look at it from the point of view of a hidden variable \vec{\lambda}:

Assume that at the moment of creation, one particle has momentum \vec{\lambda} and the other particle has momentum - \vec{\lambda}. So we can take \vec{\lambda} as the hidden variable.

P(\vec{p_1} | \vec{\lambda}) = 0 unless \vec{p_1} = \vec{\lambda}
P(\vec{p_2} | \vec{\lambda}) = 0 unless \vec{p_2} = - \vec{\lambda}

So in terms of \lambda, we have:

P(\vec{p_1}, \vec{p_2} | \vec{\lambda}) = P_1(\vec{p_1} | \vec{\lambda}) P_2(\vec{p_2} | \vec{\lambda}).

So classically, conservation of momentum is explained in a locally realistic way, and Bell's factorizability condition holds. Quantum-mechanically, if the momenta are entangled, then the correlation is not explained in a locally realistic way, and the factorizability condition does not hold.

 

[stevendaryl]

Does [?] account for the probability of the joint occurrence of a good Apple crop (A) and a good Banana crop (B) from widely separated farms (in a given region) when the growing conditions are correlated by the common rainfall over that region?

I believe that if you actually knew all the causal influences on apple and banana crops, then Bell's factorizability condition would hold. Conversely, I believe that if the factorizability condition doesn't hold, that means that there is some common causal influence that you haven't taken into account. This has been said many many times, but you keep asking the question again (in some variation). So what exactly are you looking for?

Something to keep in mind:

1. Pre-quantum physics was deterministic.
2. Every deterministic theory is factorizable in Bell's sense.

You can actually go further, and allow some nondeterminism, as long as the nondeterminism is local randomness. For example, suppose you have a world that is deterministic (with causal influences limited by the speed of light) except for coin flips, and a coin flip gives a completely unpredictable 50/50 chance of getting heads or tails. As long as coin flips of different coins are independent, then Bell's factorizability condition will hold.

 

[PeterDonis]

Does [?] describe the prediction for drawing (without replacement) an Ace (A) and a King (B) from a standard deck of 52 playing cards?

No, because there are no independent measurement settings $a$ and $b$ in this scenario; the first draw affects the "settings" of the second draw, because one card is now missing from the deck when the second draw is made.

I do not understand your claim that: "[?] does correctly describe the predictions of every theory we have except QM."

Set up a scenario where the measurements, whose settings are described by $a$ and $b$, are spacelike separated, and stipulate that $a$ and $b$ are independent. Include all information that is in the past light cones of both measurement events in $\lambda$. Then every theory we have except QM predicts that [?] will hold for the correlations between measurement results.

Technically, the spacelike separated condition is not necessary, as long as you can ensure that the settings $a$ and $b$ are independent, and properly distinguish those independent settings from the information $\lambda$ that is common to both measurements. But your repeated attempts to construct scenarios in this thread have illustrated how hard it is in practice to do that properly for measurements that are not spacelike separated.

 

[rubi]

I consider your last sentence to verge on being abusive. It's a tautology to say that there is a theory that makes the same predictions as quantum mechanics--quantum is an example. The issue is what kind of theory quantum mechanics is.

It is perfectly clear what kind of theory quantum mechanics is, because there are axiomatic formulations, in which it is an undeniable fact that only measurable things have a correspondence in the theory. Denying this is a personal belief and completely unscientific. We have clear terms for people who think that their personal beliefs can replace scientific knowledge. One can't expect to be entitled an opinion on scientific questions if one refuses to accept scientific standards.

Would it be ok to say that:
we must be able to repeat the experiment and the prediction must be correct in 100% of the cases except those cases where there is power outage at Bob's laboratory?

Power outages are the same situation. Even if were possible to check the predictions in situations of unaligned angles (reminder: it isn't), we still couldn't be sure if they were still true in the case of power outages. Of course, for practical purposes this doesn't matter. The difference is that the power outage situation is sufficiently classical and it so happens that there is enough decoherence going on and the system behaves like one would classically expect. But of course, it is theoretically possible (but practically impossible) to shield macroscopic objects from decohering and then of course, the state of the power could also be entangled with the system.

 

[PeterDonis]

Even if were possible to check the predictions in situations of unaligned angles (reminder: it isn't)

Can you clarify what you mean by this? We can certainly run experiments with unaligned angles at the two measurements, and collect data on the correlations between the results, and compare those with the predictions from theory on the correlations.

 

[stevendaryl]

It is perfectly clear what kind of theory quantum mechanics is, because there are axiomatic formulations, in which it is an undeniable fact that only measurable things have a correspondence in the theory. Denying this is a personal belief and completely unscientific.

Well, I disagree.

 

[rubi]

Can you clarify what you mean by this? We can certainly run experiments with unaligned angles at the two measurements, and collect data on the correlations between the results, and compare those with the predictions from theory on the correlations.

I was referring to my earlier posts in this thread. What I'm saying is that it is impossible in principle to measure the spin of a particle along two different angles $\alpha$ and $\alpha'$ simultaneously. No experimenter can design an experiment that can accomplish this. You can't calculate correlations between such angles, because they never co-occur. The correlations in Bell tests are of a different kind. They correlate things that can be measured simultaneously (a single spin of Alice commutes with a single spin of Bob) an do indeed co-occur.

Well, I disagree.

Then I have to refer you to the peer-reviewed literature on CH for instance, where it is stated unamiguously. If you disagree, scientific standards would require you to respond to the literature and undergo a peer-review process.

 

[stevendaryl]

Then I have to refer you to the peer-reviewed literature on CH for instance, where it is stated unamiguously. If you disagree, scientific standards would require you to respond to the literature and undergo a peer-review process.

If there were anything like a consensus that consistent histories is the correct interpretation of quantum mechanics, there would not be any discussions such as this. I think your pretending that there is a consensus when there is none is just bullying.

 

[rubi]

If there were anything like a consensus that consistent histories is the correct interpretation of quantum mechanics, there would not be any discussions such as this. I think your pretending that there is a consensus when there is none is just bullying.

I'm not saying that there is consensus that it is the correct interpretation. I'm saying that it is one working example of a theory, where only measurable things are represented within the theory. One example is enough to debunk zonde's claims.

(By the way, CH is just Copenhagen, formulated in a conceptually clear and axiomatic way. It's not like it was non-standard. Everyone is using it already without knowing.)

 

[stevendaryl]

If there were anything like a consensus that consistent histories is the correct interpretation of quantum mechanics, there would not be any discussions such as this. I think your pretending that there is a consensus when there is none is just bullying.

Reluctantly, I am planning to take advantage of the "ignore" option here.

 

[Strilanc]

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.

That's incorrect. There are many thought-experiment models that violate the Bell inequalities without allowing for communication. For example, "non-local boxes".

A specific classic example is the "Popescu-Rohrlich Box", which is a thought-experiment where you have a magic pair of boxes that wins CHSH games more than quantum mechanics can. Yet having such a pair of boxes still doesn't allow for FTL communication. There are many many other variants of this idea. If we managed to find a PR-box in the real world, that would prove there was major flaws in quantum mechanics.

 

[stevendaryl]

That's incorrect. There are many thought-experiment models that violate the Bell inequalities without allowing for communication. For example, "non-local boxes".

I think @PeterDonis meant that there are no examples consistent with pre-quantum physics.

 

[Strilanc]

I think @PeterDonis meant that there are no examples consistent with pre-quantum physics.

That's correct. iI you limit yourself to classical physics with a finite speed of propagation for forces, then you don't have these effects.

 

[PeterDonis]

What I'm saying is that it is impossible in principle to measure the spin of a particle along two different angles $\alpha$ and $\alpha'$ simultaneously.

Ah, ok, got it.

 

[rubi]

There are some situations, where the factorization condition can also be violated classically. For example, if you perform post-selection on some data set. Assume Alice and Bob throw dies and the corresponding data sets are $(A_i)_i$ and $(B_i)_i$. Then you can post-select only those events where $A_i = B_i$ and you will get perfect correlations even though the factorization condition will be violated. There are also some other ways to violate the condition. Classically, all of them can be fixed by coming up with more general conditions, but it already shows that the factorization condition is a heuristic rather than a law of nature.

 

[zonde]

I will try to make my point using older statement in this thread:

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.

This statement is of course correct but it is missing the point.
So I would ask different question: Can the EPR argument be applied to the model that is Einsten's local and not superdeterministic?
And the answer is yes, using following reasoning:
1) For a model that is not superdeterministic measurement angles are external parameters and it has to produce predictions for any measurement angle.
2) If model is Einsten's local it has to produce predictions independently for Alice and Bob (when Alice's and Bob's measurements are spacelike separated).
Putting 1) and 2) together the model has to produce two sets of independent predictions for Alice and Bob that can be compared and for the cases where Bob's and Alice's measurement angles are the same we can apply EPR argument.

So the next question would be - can we compare (correlate) predictions of model where Alice's and Bob's measurement angles are different? And the answer to this question seems to be that they better be comparable as we do that a lot in real entanglement experiments.

 

[rubi]

This statement is of course correct but it is missing the point.

No, it doesn't miss the point. You don't want to acknowledge the fact that unmeasurable quantities don't need to exist and that models needn't model unmeasurable quantities. And there are examples that prove that you are wrong.

For a model that is not superdeterministic measurement angles are external parameters and it has to produce predictions for any measurement angle.

That's just false. You have just stated your personal belief without any argument. You have hidden variables in mind and think that your intuitions about them also hold for non-hidden variable models. But there is just no way to argue that unmeasurable quantities must exist.

What you and Denis are trying to argue is: There must be predictions for any angle and thus we can use the EPR argument to conclude that there must be predictions for any angle. It's circular reasoning and cannot be saved. Either you postulate it as an axiom, as you just did. Then it can be denied (for instance by QM). Or you try to use the EPR argument, but then you must admit that your reasoning is circular and therefore unacceptable.

So the next question would be - can we compare (correlate) predictions of model where Alice's and Bob's measurement angles are different? And the answer to this question seems to be that they better be comparable as we do that a lot in real entanglement experiments.

We don't correlate quantities that never co-occur, such Bob's spins along different angles. It doesn't even make sense to speak about correlations of things don't co-occur. QM beautifully prevents us from doing this by having the corresponding operators not commute. The correlations between Alice and Bob can of course also be calculated in QM, but that's irrelevant for your argument, since correlations for different angles are not perfect and thus can't be used to predict anything with certainty, contrary to what the EPR argument would require.

 

[zonde]

You don't want to acknowledge the fact that unmeasurable quantities don't need to exist and that models needn't model unmeasurable quantities.

I acknowledge that unmeasurable quantities don't need to exist and that models needn't model unmeasurable quantities.

For a model that is not superdeterministic measurement angles are external parameters and it has to produce predictions for any measurement angle.

That's just false.

Which part is false?
Is this part false? - "For a model that is not superdeterministic measurement angles are external parameters"
Or the other part?
Argument for the other part (if the first part is ok) is as follows:
As measurement angles are external parameters, experimentalist can choose whichever angle he wants and test prediction for that angle. Predictions have to be made before test is performed.
As experimentalist's choice lies outside the model, predictions have to be made independently from that choice and before the measurement.
For me it seems enough to claim that the model should be capable of producing predictions for any measurement angle.

 

[rubi]

Is this part false? - "For a model that is not superdeterministic measurement angles are external parameters"

Yes, this part is false. QT is capable of modeling measurement angles within the model and it is definitely not superdeterministic. No fine-tuning is required.

Or the other part?
Argument for the other part (if the first part is ok) is as follows:
As measurement angles are external parameters, experimentalist can choose whichever angle he wants and test prediction for that angle. Predictions have to be made before test is performed.
As experimentalist's choice lies outside the model, predictions have to be made independently from that choice and before the measurement.
For me it seems enough to claim that the model should be capable of producing predictions for any measurement angle.

This is false as well. An experimenter can predict whatever he or she wants. This does not imply that there must be something corresponding to that prediction. If I predict that there is a pink unicorn behind you, it is not necessarily true. If Alice predicts that the spin of Bob's particle along the angle $\alpha$ is so and so, even though his detector is aligned along a different angle $\beta\neq\alpha$, this doesn't imply that Bob's particle has a spin along the angle $\alpha$. And given that it is impossible in principle to test such a prediction, there is no reason to expect that the prediction would be correct. And we understand the issue very well. QT is contextual and that means that properties that don't commute with all observables emerge from the experimental setup rather than existing independent of the setup.

 

[zonde]

Yes, this part is false. QT is capable of modeling measurement angles within the model and it is definitely not superdeterministic. No fine-tuning is required.

Well, but you can model only one measurement angle at the same time, and which particular angle you are modeling you take from outside the model as external parameter.
Maybe this will be more clear - "For a model that is not superdeterministic choice of measurement angle is external parameter"

This is false as well. An experimenter can predict whatever he or she wants. This does not imply that there must be something corresponding to that prediction. If I predict that there is a pink unicorn behind you, it is not necessarily true.

"Pink unicorn behind you" is hypothesis not prediction. Prediction would be statement about what I would observe if I turn around.

If Alice predicts that the spin of Bob's particle along the angle $\alpha$ is so and so, even though his detector is aligned along a different angle $\beta\neq\alpha$, this doesn't imply that Bob's particle has a spin along the angle $\alpha$.

Predictions are conditional. If you do such and such you will observe this. What you are talking about is hypothesis not prediction.