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

[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.

 

[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