Local realism ruled out? (was: Photon entanglement and )

[Frame Dragger]

I believe I answered DrChinese's questions. You did not answer my questions in post 205. As for the roadblock, I cannot agree or disagree until you are much more clear and specific. So far your phrase about the roadblock is just a baseless statement. Or rhetoric, if you wish.

See SpectraCat, and Dr. Chinese's posts for what my views are. As I said, we're not having a discussion; I just wanted you to stop talking in circles, cite evidence and not a lack of quotes, etc.

As for what you believe that is not mainstream, again, see SpectraCat's latest post. You're argument against non-locality is to rely on paradoxical mechanics.

 

[akhmeteli]

Ok .. that clearly wrong to me. How can your hypothetical "particles" being transferred between the entangled pair carry information faster than the speed of light?

They cannot. I assume they do not travel faster than light.

Because they would have to in your "picture", now that the "locality loophole" has been closed by showing statistical dependence of results measured at detectors with a spacelike separation.

Note that this does not require any sort of free-sampling assumption to be true, because the results predicted by any local realistic theory for such experiments would have to be random

I don't accept this without a proof. So far this is just your word. Remember, existing experiments have not ruled out local theories.

, and whatever else you might believe about the sampling of the data, you have to concede that the chance that the coincidence measurements from these experiments could arise randomly are astronomical.

This is not relevant, until you prove that "the results predicted by any local realistic theory for such experiments would have to be random"

So you are going to have to do better than that to justify a statement like, "entanglement per se does not spell non-locality", because contrary to your claim, such a model of particle transfer between an entangled pair is demonstrably NOT a possibility.

Maybe so, but you have not demonstrated its impossibility. You see, your "demonstration" seems to rule out any local theory, not just my mental picture, whereas people agree that such experiments do not rule out all local theories. I just cannot understand what part of my very vague "local theory" makes it less able to explain these experiments than other local theories. It looks like it's your "demonstration" that is clearly wrong, as it seems to prove much more than you wanted.

 

[Frame Dragger]

They cannot. I assume they do not travel faster than light.



I don't accept this without a proof. So far this is just your word. Remember, existing experiments have not ruled out local theories.



This is not relevant, until you prove that "the results predicted by any local realistic theory for such experiments would have to be random"



Maybe so, but you have not demonstrated its impossibility. You see, your "demonstration" seems to rule out any local theory, not just my mental picture, whereas people agree that such experiments do not rule out all local theories. I just cannot understand what part of my very vague "local theory" makes it less able to explain these experiments than other local theories. It looks like it's your "demonstration" that is clearly wrong, as it seems to prove much more than you wanted.

Your argument is endlessly reductionist; demanding that a negative be proven in a context that is impossible. Your retort is, as you say, VAGUE. So vague that while you claim a local theory, in reality it's so vague as to need to rely on Hidden Variables. How else does entanglement work, if you reject non-locality, AND Hidden Variables in a Local theory?

 

[akhmeteli]

See SpectraCat, and Dr. Chinese's posts for what my views are.

I did not ask you about your views, I asked you to answer my questions. If it is too much trouble for you to give clear and explicit answers, for a change, it is too much trouble for me to dig through the entire thread and try to guess what you meant. I owe no guesses to you.

As for what you believe that is not mainstream, again, see SpectraCat's latest post. You're argument against non-locality is to rely on paradoxical mechanics.

Again, instead of giving a clear and explicit answer, you suggest that I read something else (and it is not a reference, say, to an article with a clear indication to what exactly in the article you referred to). SpectraCat wrote something, and I replied to him. To reply to you I have to guess what you wrote. Your reference to my "argument against non-locality" is also extremely obscure. What argument, exactly? I did not say nonlocality has been ruled out, I said locality has not been ruled out, and this is indeed mainstream, whether you like it or not.

 

[akhmeteli]

Your argument is endlessly reductionist; demanding that a negative be proven in a context that is impossible. Your retort is, as you say, VAGUE. So vague that while you claim a local theory, in reality it's so vague as to need to rely on Hidden Variables. How else does entanglement work, if you reject non-locality, AND Hidden Variables in a Local theory?

Frame Dragger,

I just give up. I cannot understand a word. Let me try to explain why reading your text is a struggle.

First you say that my "argument is endlessly reductionist", and I have to guess what argument, as I offered at least two arguments: first, that the randomness of results in a local theory needs a proof, and second, that SpectraCat's reasoning proves too much. Do I have to guess again what you had in mind?

Then you say "demanding that a negative be proven in a context that is impossible", and I have to guess what negative, what context, why it is impossible, and last but not least, if you declare that my demand to prove something is unreasonable, does it mean I have to believe SpectraCat on his (or her) word?

Then you say that my retort is "so vague as to need to rely on Hidden Variables." So did you want to say that my "model" requires hidden variables, or that it excludes hidden variables (as later you say that I "reject non-locality, AND Hidden Variables in a Local theory")? If, however, you believe my "model" requires hidden variables, does it mean this makes the "model" unacceptable?

So if you keep offering me such crosswords, I'll have to ignore them, sorry. It may well be that you have some interesting thoughts, but obscurity of your texts protects them too well.

 

[Frame Dragger]

I did not ask you about your views, I asked you to answer my questions. If it is too much trouble for you to give clear and explicit answers, for a change, it is too much trouble for me to dig through the entire thread and try to guess what you meant. I owe no guesses to you.



Again, instead of giving a clear and explicit answer, you suggest that I read something else (and it is not a reference, say, to an article with a clear indication to what exactly in the article you referred to). SpectraCat wrote something, and I replied to him. To reply to you I have to guess what you wrote. Your reference to my "argument against non-locality" is also extremely obscure. What argument, exactly? I did not say nonlocality has been ruled out, I said locality has not been ruled out, and this is indeed mainstream, whether you like it or not.

Oh please... this is precisely the kind of rhetorical nonsense I'm trying to avoid. You didn't ask my views, and yet you have them. Such is life on the internet Mon Dauphine.

I'd start doing some real work on finding citations for you "vague theory"... you have 3 people asking you questions you aren't answering well, and you're wasting your time because you can't let go and accept that I was not trying to engage in debate, but rather refocus your attention to the matter at hand? Nothing has changed. Your desire for answers mean nothing to me; you're the one who quite literally has something to prove, or at least a position to defend. I'm not going to respond to your no-doubt brilliant next post. If you found any of this confusing... Sprechen sie Englisch?

 

[Frame Dragger]

Frame Dragger,

I just give up. I cannot understand a word. Let me try to explain why reading your text is a struggle.

First you say that my "argument is endlessly reductionist", and I have to guess what argument, as I offered at least two arguments: first, that the randomness of results in a local theory needs a proof, and second, that SpectraCat's reasoning proves too much. Do I have to guess again what you had in mind?

Then you say "demanding that a negative be proven in a context that is impossible", and I have to guess what negative, what context, why it is impossible, and last but not least, if you declare that my demand to prove something is unreasonable, does it mean I have to believe SpectraCat on his (or her) word?

Then you say that my retort is "so vague as to need to rely on Hidden Variables." So did you want to say that my "model" requires hidden variables, or that it excludes hidden variables (as later you say that I "reject non-locality, AND Hidden Variables in a Local theory")? If, however, you believe my "model" requires hidden variables, does it mean this makes the "model" unacceptable?

So if you keep offering me such crosswords, I'll have to ignore them, sorry. It may well be that you have some interesting thoughts, but obscurity of your texts protects them too well.

What part is reductionistic?! Here's a hint... the part I put IN BOLD in the quote. It's really not my fault that forums, or language are not your forte.

 

[DaTario]

Regarding the OP, I would say that technically I would follow Karl Popper, that has said:
No experimental evidence is really able to disprove a theoretical positioning.

This statement is part of his demarcation criteria [\B].

Best Regards,

DaTario

 

[zonde]

In the case of photons created outside each others' light cones, how would that be? The Fair Sampling Assumption is not an issue, since NO local realistic explanation would hold anyway. According to the theoretical assumptions of LR, no such entanglement is possible under ANY scenario. Keep in mind that the photons don't even need to exist at the same time - and yet they are entangled.

That is not very good argument. From this paper:
http://arxiv.org/abs/quant-ph/0409093"
"For this kind of measurement, the two incoming photons must be completely indistinguishable in their spatial, temporal, spectral and polarization mode. The indistinguishability is verified by a Hong-Ou-Mandel experiment [20, 21]."
Basically this means that time from the point in time where incident beam is split in two to point when Bell state measurement is performed is adjusted so that is exactly the same for both arms. You can see there are additional prism after Pump interferometer in Fig.2 for exactly that purpose.
I think this clearly indicates that even if formally two photons are created outside each other light cone you should include incident beams into consideration (even with QM) and at that point it becomes clear that statement that two entangled photons have no causal connection is simply false.

 

[SpectraCat]

Ok .. that clearly wrong to me. How can your hypothetical "particles" being transferred between the entangled pair carry information faster than the speed of light? Because they would have to in your "picture", now that the "locality loophole" has been closed by showing statistical dependence of results measured at detectors with a spacelike separation.

They cannot. I assume they do not travel faster than light.

You did not answer my question .. how can particle exchange at sub-light speeds explain the observed statistical dependence of measurements on detectors with a space-like separation? It is not sufficient just to say "there could be a way, because you can't prove there isn't" .. that is not how physics works. You need to propose a physically-based explanation that explains the results from a local realistic perspective.

Note that this does not require any sort of free-sampling assumption to be true, because the results predicted by any local realistic theory for such experiments would have to be random, and whatever else you might believe about the sampling of the data, you have to concede that the chance that the coincidence measurements from these experiments could arise randomly are astronomical.

I don't accept this without a proof. So far this is just your word. Remember, existing experiments have not ruled out local theories.

Again, it is not incumbent on me to prove that they must be random, because that is what would be expected for uncorrelated photons based on Malus's law. In fact, uncorrelated basically *means* random in this context. Have you looked at the Mermin gedanken experiment? It is quite instructive in this regard.

Therefore since there is a good reason to expect for the local measurement results to be uncorrelated, AND there is no way for the particles to communicate when the detectors have a space-like separation, it is up to YOU to come up with a physically sensible reason for the observed statistical dependence of the coincidence measurements. Otherwise, all of your points reduce to pure sophistry ... which is basically Frame Dragger's point.

So you are going to have to do better than that to justify a statement like, "entanglement per se does not spell non-locality", because contrary to your claim, such a model of particle transfer between an entangled pair is demonstrably NOT a possibility.

Maybe so, but you have not demonstrated its impossibility. You see, your "demonstration" seems to rule out any local theory, not just my mental picture, whereas people agree that such experiments do not rule out all local theories. I just cannot understand what part of my very vague "local theory" makes it less able to explain these experiments than other local theories. It looks like it's your "demonstration" that is clearly wrong, as it seems to prove much more than you wanted.

See there you go with the sophistry again. You seem to be equating Zeilinger's statement that "LR has not been ruled out" with "LR is a reasonable and viable model". As has been pointed out to you time and again in this thread, this is misleading and wrong. Zeilinger is conceding that LR has not been ruled out BEYOND A SHADOW OF A DOUBT ... however what his experiments and others make clear is that there is a whole lot of work that needs to be done to come up with a LR theory that can explain the entire set of experimental results. Since no such theories are forthcoming, and it is very hard to see how they could possible be formulated, it is reasonable to take the position that LR is VERY PROBABLY not viable. We have a theory that is non-local and DOES explain all the results so far .. it is called Quantum Mechanics.

Finally, my "demonstration" did not rule out all possible local models, only those that require information transfer between the entangled particles at sub-light speeds.

 

[Dmitry67]

Sorry, missed too many pages.
So what is consensus?
Is it ruled out or not?
Do you have a good definition of "realism"/"real"?

 

[ThomasT]

Again, I just see some statements, but reasoning or references are missing.

Ok, I'll run the latest by you again. Let me know any statements that aren't clear (and I'll elaborate and/or rephrase) or that you don't agree with. Any critical feedback is appreciated.

Phrase 1: The designs of entanglement experiments contradict Bell locality.

Bell locality entails that P(A,B) = P(A) P(B)

P(A,B) = P(A) P(B) means that events A and B are statistically independent.

Entanglement experiments are designed to produce statistically dependent events (via the emission and data matching processes).

So, the designs of entanglement experiments contradict Bell locality, and vice versa.

-----------------------

Phrase 2: There are loopholes in those (entanglement) experiments.

This just means that there are technical problems associated with Bell tests (eg., the production of entangled disturbances, detection efficiency, data matching/coincidence counting, etc.) -- and, of course, these technical problems might affect the results.

However, it follows from Phrase 1 that no Bell local formulation can ever be in total agreement with the results of any entanglement experiment, whether the experiment is loophole free or not.

-----------------------

To elaborate, Bell's formulation is supposed to represent local common cause via the hidden variable λ and its probability distribution ρ(λ).

Additionally, and most importantly, Bell's formulation is supposed to represent locality via the representation of independence (factorability of the joint probability) between A and B.

The problem is that A and B are not independent due to the data matching process (a trackable local process).

So, Bell's assumption that any LHV formulation of an entangled state must conform to his ansatz is incorrect. In fact, no LHV formulation of an entangled state can possibly conform to his ansatz.

Thus, Bell tests involving Bell inequalities based on Bell's ansatz are not a test of local realism or a demonstration of nonlocality.

Further, we can reasonably suppose that the correlations have underlying local causes due to the fact that the data matching process is based on the assumption that the relationship (the entanglement) between the separately analyzed disturbances is produced at emission (or via some other local common cause).

 

[SpectraCat]

Ok, I'll run the latest by you again. Let me know any statements that aren't clear (and I'll elaborate and/or rephrase) or that you don't agree with. Any critical feedback is appreciated.

Phrase 1: The designs of entanglement experiments contradict Bell locality.

Bell locality entails that P(A,B) = P(A) P(B)

P(A,B) = P(A) P(B) means that events A and B are statistically independent.

Entanglement experiments are designed to produce statistically dependent events (via the emission and data matching processes).

So, the designs of entanglement experiments contradict Bell locality, and vice versa.

No, this is not correct in my opinion, because the experiments allow for the possibility that the results will be observed to be statistically independent. That is what the coincidence counting is all about. If the coincidence measurements showed that the results at detectors A and B were not correlated, then the Bell inequality would not be violated, in which case we would conclude that the results were statistically independent.

To state it another way, how could the experiments possibly test non-locality unless they allow for the possibility of non-locality? They already *inherently* allow for the possibility of locality, because that is what the experiment would show if there were no correlation of the supposedly entangled photons. If that had been observed, then QM would have been dealt a serious blow ... but the correlations were observed, which was taken to be evidence for non-locality. I definitely don't see the tautological reasoning that you are claiming/implying exists.

Phrase 2: There are loopholes in those (entanglement) experiments.

This just means that there are technical problems associated with Bell tests (eg., the production of entangled disturbances, detection efficiency, data matching/coincidence counting, etc.) -- and, of course, these technical problems might affect the results.

However, it follows from Phrase 1 that no Bell local formulation can ever be in total agreement with the results of any entanglement experiment, whether the experiment is loophole free or not.

Again, this seems wrong ... I think it amounts to the statement that "no entanglement experiment can ever show that a single set of results are simultaneously local and non-local", which is of course true, but irrelevant to anything.

To elaborate, Bell's formulation is supposed to represent local common cause via the hidden variable λ and its probability distribution ρ(λ).

Additionally, and most importantly, Bell's formulation is supposed to represent locality via the representation of independence (factorability of the joint probability) between A and B.

The problem is that A and B are not independent due to the data matching process (a trackable local process).

Ok, I don't get this last sentence at all. The data matching process (I assume you mean coincidence counting here) does not in any way imply statistical dependence between A and B as far as I can see. One could run the same experiments with separate, randomly-polarized sources, and there would be no observed correlation between the measurement sets at A and B, so the coincidence counting would conclude that the two sets are statistically independent, right? Am I missing something here?

So, Bell's assumption that any LHV formulation of an entangled state must conform to his ansatz is incorrect. In fact, no LHV formulation of an entangled state can possibly conform to his ansatz.

I am not sure how to parse this, and I definitely don't see how it follows from the previous arguments (even if I agreed those were correct). I think it would be useful if you could re-state it in the context of the Mermin gedanken experiment. I would also like a definition or at least an example of an "LHV formulation of an entangled state".

Further, we can reasonably suppose that the correlations have underlying local causes due to the fact that the data matching process is based on the assumption that the relationship (the entanglement) between the separately analyzed disturbances is produced at emission (or via some other local common cause).

Yes, it is assumed that the entanglement is typically created by a "local common cause", since parametric down conversion involves "splitting" of a single photon in a birefringent crystal. However, the rest of your statements don't follow from that, for the reasons I have outlined above. The only assumption made about the data sets at A & B involves the travel times of the photons, in that only a certain subset of detection events at A and B satisfy the criterion of coincidence. The experimenters are always quite careful about this when defining what "coincident detection" means in the context of their experiments. Essentially, what you seem to be saying is that the entangled photons could have received "instruction sets" controlling their measurement results, and this is *exactly* what the Bell theorem and the Mermin gedanken show is impossible.

 

[akhmeteli]

You did not answer my question .. how can particle exchange at sub-light speeds explain the observed statistical dependence of measurements on detectors with a space-like separation?

I strongly disagree with this statement. The only question you asked in the previous post was "How can your hypothetical "particles" being transferred between the entangled pair carry information faster than the speed of light?", and I answered that the particles do not carry information faster than the speed of light. And then I questioned your statement "Because they would have to in your "picture", now that the "locality loophole" has been closed by showing statistical dependence of results measured at detectors with a spacelike separation." as unsubstantiated, which it is. So I answered your question.

It is not sufficient just to say "there could be a way, because you can't prove there isn't" .. that is not how physics works. You need to propose a physically-based explanation that explains the results from a local realistic perspective.

OK, then, let me answer the question of your latest post "how can particle exchange at sub-light speeds explain the observed statistical dependence of measurements on detectors with a space-like separation?" and try to offer physical mechanisms.

Do you really think local theories cannot account for "statistical dependence of results measured at detectors with a spacelike separation"? What they cannot account for, is correlations violating the Bell inequalities. As for "physically based explanation", I can offer two things.

First is the mechanism offered by others (here I quote one of my earlier posts): "QTP-like unitary evolution in Hilbert space (which, by the way, seems to describe entanglement as well) may be just a disguise for nonlinear partial differential equations (you may wish to look at the very brief outline of the relevant published results of other people in my post https://www.physicsforums.com/showpost.php?p=1825523&postcount=90."

Second, let me discuss a possible mechanism within my "model": Imagine that photons are only detected if their polarization is close to that measured by the detector (say, vertical), and the anticorrelation within pairs of such photons is caused by their common past. Later photons in such pairs, if undetected earlier, can change their polarisation through slow exchange of some particles (or interacting with couples of such particles having common past). If the detector measures a polarization different from vertical, photons from other pairs, having the relevant polarization, get detected. I explicitely use the detection loophole here to explain the statistical dependence by a local model (so I reject fair sampling here). Again, I am not saying that my "model" reflects reality, I am using it just as an instrument suggesting that entanglement per se does not spell nonlocality.

Again, it is not incumbent on me to prove that they must be random, because that is what would be expected for uncorrelated photons based on Malus's law. In fact, uncorrelated basically *means* random in this context. Have you looked at the Mermin gedanken experiment? It is quite instructive in this regard.

Yes, it is incumbent on you to prove that they must be random - I am under no obligation to believe you on your word. You did not mention Malus law in your previous post. However, as I wrote earlier, it is my understanding that Malus law is pretty much a consequence or an equivalent of the projection postulate for photons, and as such is in contradiction with unitary evolution, as I argued earlier. So Malus law may be a great approximation, but it is just an approximation. I fully accept unitary evolution and believe that Malus law can be derived as an approximation from unitary evolution, but not when it is pushed to the limits and pretty much equals nonlocality, same as the projection postulate. Of course, nobody cares what I believe or disbelieve, but it is pretty well known that projection postulate (or collapse) contradicts unitary evolution.

Therefore since there is a good reason to expect for the local measurement results to be uncorrelated, AND there is no way for the particles to communicate when the detectors have a space-like separation, it is up to YOU to come up with a physically sensible reason for the observed statistical dependence of the coincidence measurements. Otherwise, all of your points reduce to pure sophistry ... which is basically Frame Dragger's point.

I explained why I see no good reason to expect for the local measurement results to be uncorrelated, and in this post I explained (using reference to other people's work in https://www.physicsforums.com/showpost.php?p=1825523&postcount=90) how unitary evolution of quantum field theory (describing many particles) can be a disguise of local partial differential equations.

See there you go with the sophistry again. You seem to be equating Zeilinger's statement that "LR has not been ruled out" with "LR is a reasonable and viable model". As has been pointed out to you time and again in this thread, this is misleading and wrong. Zeilinger is conceding that LR has not been ruled out BEYOND A SHADOW OF A DOUBT ... however what his experiments and others make clear is that there is a whole lot of work that needs to be done to come up with a LR theory that can explain the entire set of experimental results. Since no such theories are forthcoming, and it is very hard to see how they could possible be formulated, it is reasonable to take the position that LR is VERY PROBABLY not viable. We have a theory that is non-local and DOES explain all the results so far .. it is called Quantum Mechanics.

I am not responsible for your perceptions. I may "seem to be equating" Zeilinger's statement with something else, but I am not "equating" them. The title of the thread speaks for itself. I'm saying (among other things) the following:

1) local realism has not been ruled out by experiments;
2) the previous statement is the mainstream.
3) the proof of the Bell theorem uses contradictory assumptions of unitary evolution and projection postulate, therefore, local realism has not been ruled theoretically either.

As for "probability" and "plausibility" of local realism, this issue is certainly very important, but secondary, because if local realism were ruled out, this issue would also be unambiguously solved.

I believe "plausibility" is a matter of opinion. Zeilinger seems to believe local realism is implausible, you agree with him, I may disagree, but again, who cares about my opinion? Let me just repeat that elimination of local realism is an extremely radical idea, so it requires a most solid proof. There is no such proof so far.

Finally, my "demonstration" did not rule out all possible local models, only those that require information transfer between the entangled particles at sub-light speeds.

Could you explain where you used "information transfer between the entangled particles at sub-light speeds" in your "demonstration"? I fail to find this place.

 

[SpectraCat]

I strongly disagree with this statement. The only question you asked in the previous post was "How can your hypothetical "particles" being transferred between the entangled pair carry information faster than the speed of light?", and I answered that the particles do not carry information faster than the speed of light. And then I questioned your statement "Because they would have to in your "picture", now that the "locality loophole" has been closed by showing statistical dependence of results measured at detectors with a spacelike separation." as unsubstantiated, which it is. So I answered your question.

It is not unsubstantiated, it is shown by Bell's theorem, and by Mermin's gedanken experiment. The latter case shows that it is not possible for "instruction sets" which explain how particles are supposed to register on detectors to be carried by those particles. Therefore, if the "information" that leads to the cannot carried with the particles themselves, and it cannot be exchanged by the entangled particles at the time of detection (since the detectors have a spacelike separation), then it cannot exist.

OK, then, let me answer the question of your latest post "how can particle exchange at sub-light speeds explain the observed statistical dependence of measurements on detectors with a space-like separation?" and try to offer physical mechanisms.

Do you really think local theories cannot account for "statistical dependence of results measured at detectors with a spacelike separation"? What they cannot account for, is correlations violating the Bell inequalities.

Of course that is what I meant, since that is the context of our current discussion. If you build the correlation into the source, it will be there at the detector, but that is precisely what CANNOT be happening with quantum entanglement, as demonstrated (again) by Bell's theorem and the Mermin gedanken.

As for "physically based explanation", I can offer two things.

First is the mechanism offered by others (here I quote one of my earlier posts): "QTP-like unitary evolution in Hilbert space (which, by the way, seems to describe entanglement as well) may be just a disguise for nonlinear partial differential equations (you may wish to look at the very brief outline of the relevant published results of other people in my post https://www.physicsforums.com/showpost.php?p=1825523&postcount=90."

I looked at that post, and frankly I do not have the time to absorb and digest all the math .. I don't know what QTP means, and I am not intimately familiar with the mathematics of QFT, which apparently is necessary to understand what is referred to in that post.

Second, let me discuss a possible mechanism within my "model": Imagine that photons are only detected if their polarization is close to that measured by the detector (say, vertical), and the anticorrelation within pairs of such photons is caused by their common past.

I don't think it is physically reasonable to "imagine" that, because of Malus's law, but ok, I'll grant it for the purposes of this discussion.

Later photons in such pairs, if undetected earlier, can change their polarisation through slow exchange of some particles (or interacting with couples of such particles having common past).

I have no idea what the above statement refers to ... it makes no sense at all. What is "a later photon from such a pair", and what does the phrase "undetected earlier" mean? I am sorry but I need a lot more context and detail to begin to parse that.

If the detector measures a polarization different from vertical, photons from other pairs, having the relevant polarization, get detected. I explicitely use the detection loophole here to explain the statistical dependence by a local model (so I reject fair sampling here). Again, I am not saying that my "model" reflects reality, I am using it just as an instrument suggesting that entanglement per se does not spell nonlocality.

It's fine for you to use the detection loophole, but you have completely lost me at this point. What other pairs? Where is the space-like separation between the detectors and how is it overcome? You also seem to be indicating that there is some preferred direction of detection .. where is the basis for that?

Yes, it is incumbent on you to prove that they must be random - I am under no obligation to believe you on your word. You did not mention Malus law in your previous post. However, as I wrote earlier, it is my understanding that Malus law is pretty much a consequence or an equivalent of the projection postulate for photons, and as such is in contradiction with unitary evolution, as I argued earlier. So Malus law may be a great approximation, but it is just an approximation. I fully accept unitary evolution and believe that Malus law can be derived as an approximation from unitary evolution, but not when it is pushed to the limits and pretty much equals nonlocality, same as the projection postulate. Of course, nobody cares what I believe or disbelieve, but it is pretty well known that projection postulate (or collapse) contradicts unitary evolution.

I didn't ask you to believe me on my word, and I didn't mention Malus's law before because I didn't think I had to, since it has already come up in this thread. Malus's law has been extensively tested and never shown to be incorrect. So now you are not just questioning well accepted physical theorems, you are going after laws as well. Go for it!

I explained why I see no good reason to expect for the local measurement results to be uncorrelated, and in this post I explained (using reference to other people's work in https://www.physicsforums.com/showpost.php?p=1825523&postcount=90) how unitary evolution of quantum field theory (describing many particles) can be a disguise of local partial differential equations.

Unfortunately I can't understand the details of that post, as I already mentioned. However, even if I accepted its content, I am not sure why it is relevant to this discussion ... and earlier you said "nonlinear" PDE's, only here do you mention that they are local. Can you please break down the physical significance of this statement in the current context, or link to a post where you described it previously?

I am not responsible for your perceptions. I may "seem to be equating" Zeilinger's statement with something else, but I am not "equating" them. The title of the thread speaks for itself. I'm saying (among other things) the following:

1) local realism has not been ruled out by experiments;
2) the previous statement is the mainstream.
3) the proof of the Bell theorem uses contradictory assumptions of unitary evolution and projection postulate, therefore, local realism has not been ruled theoretically either.

Ok, so your point 3 above is really the only thing to take issue with. I confess I have not really spent much time trying to understand it's significance. I will try to do that and post when I have something more to say about it.

As for "probability" and "plausibility" of local realism, this issue is certainly very important, but secondary, because if local realism were ruled out, this issue would also be unambiguously solved.

I believe "plausibility" is a matter of opinion. Zeilinger seems to believe local realism is implausible, you agree with him, I may disagree, but again, who cares about my opinion? Let me just repeat that elimination of local realism is an extremely radical idea, so it requires a most solid proof. There is no such proof so far.

You say it is radical .. I don't agree, but I guess you are in good company .. Einstein couldn't accept it either. Q.M. predicts non-local correlations in a manner that is consistent with all available experimental evidence. Furthermore, Q.M. is also consistent with all classical results as well .. and classical systems are where local realism really makes sense, and as far as I know, there are no classical systems that are inconsistent with LR. So perhaps LR is a consequence of the Bohr correspondence principle somehow, and like CM is contained and explained within the context of Q.M. in the large mass/high quantum number limit.

Could you explain where you used "information transfer between the entangled particles at sub-light speeds" in your "demonstration"? I fail to find this place.

The post in question was entirely about why the experimental closing of the "locality loophole" showed that the entangled pairs could not be exchanging sub-light particles, as you had hypothesized. I didn't use or introduce that concept .. YOU did. I explained/argued why it cannot be used to explain the experimental results under discussion. You chose not to accept my explanation/argument, and I am still trying to understand why.

 

[zonde]

The latter case [Mermin's gedanken experiment] shows that it is not possible for "instruction sets" which explain how particles are supposed to register on detectors to be carried by those particles. Therefore, if the "information" that leads to the cannot carried with the particles themselves, and it cannot be exchanged by the entangled particles at the time of detection (since the detectors have a spacelike separation), then it cannot exist.

Quick googling about Mermin's gedanken experiment led me to two links.
One is simple explanation of Mermin's experiment:
http://public.fh-wolfenbuettel.de/~ruediger/lehre/EPRapplet/EPRappletDescription.pdf"
Second shows how Mermin’s gedanken experiment fails if unfair sampling is used:
http://www.Newtonphysics.on.ca/uncertainty/index.html"
In short this second link shows that required probabilities appear if one chooses instruction sets RRG;RGR;GRR and discards every second detection of R.
It can be easily made symmetrical in respect to R/G if we additionally take instruction sets GGR;GRG;RGG but for those instruction sets we discard every second detection of G.

So this Mermin’s gedanken experiment is no argument against local realism + hypothetical unfair sampling.

 

[Frame Dragger]

Of course that is what I meant, since that is the context of our current discussion.

Watch out, Ahkmeteli has 'issues' with context... among other things.

 

[Eye_in_the_Sky]

Can you tell where do you yourself see the problem?

... Thank you zonde ... for helping to open me Eye.
____________________________________________

Let's say do you see Proposition 1 (locality Λ PC Λ CF → local determinism) as not valid? Or is it valid but wrongly applied to physical situation? ... or neither.

I see the proposition as valid [... modulo other premises (e.g. free-choice of Alice and Bob)], and that it can be correctly applied to the "Bell argument" in terms of the joint-probability-function of the particle pair. (For anyone interested, the "Bell argument" is repeated at the end of this post.)

[I am, however, encountering a certain difficulty which I cannot seem to resolve. It centers on the question:

Is it possible that, as a matter of principle, there can be no such thing as "a full specification of the state" of the particle pair?]
________________

Do you see any problems in this statement?
"If measurement of the component σ1∙a, where a is some unit vector, yields the value +1 then, according to quantum mechanics, measurement of σ2∙a must yield the value -1 and vice versa."

It is unclear to me what you are getting at here. Nonetheless, I would prefer to write the statement in this way (with no mention of QM):

If measurement of the component σ1∙a, where a is some unit vector, yields the value +1, then measurement of σ2∙a must yield the value -1; and vice versa.

This statement can be said to be a theorem of Quantum Mechanics. Yet, it makes an infinity of assertions, only one of which, in any "real-world" instantiation, can ever be factual (the remaining ones then being counterfactual).

... Zonde, is this what you are getting at?
____________________________________________

The "Bell argument" is as follows (originally included as part of post #170 of this thread):

Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stem-Gerlach magnets, on selected components of the spins σ₁ and σ₂. If measurement of the component σ₁∙a, where a is some unit vector, yields the value +1 then, according to quantum mechanics, measurement of σ₂∙a must yield the value -1 and vice versa. Now we make the hypothesis [2], and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other. Since we can predict in advance the result of measuring any chosen component of σ₂, by previously measuring the same component of σ₁, it follows that the result of any such measurement must actually be predetermined.
----------
[2] "But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system S₂ is independent of what is done with the system S₁, which is spatially separated from the former." A. EINSTEIN in Albert Einstein, Philosopher Scientist, (Edited by P. A. SCHILP) p. 85, Library of Living Philosophers, Evanston, Illinois (1949).

 

[Eye_in_the_Sky]

... It seems to me I understand what you wrote, but I don't quite see from your post where my misconception is. Could you please explain?

Let's try a different approach.

Please answer the two questions below.


1) Do you believe you understand the concept expressed by the following statement?

Alice and Bob's outcomes are governed by local determinism.


2) Do you consider the following statement to be true?

On the basis of the single assumption of "local determinism of Alice and Bob's outcomes", one can derive a Bell inequality.


Think about it carefully. Take your time.

 

[Eye_in_the_Sky]

... So maybe you mean this:

Regarding the proposition

BL Λ PC Λ CF → D ,

where

BL ≡ Bell Locality (mathematical formulation in terms of probabilities) ,

it will be found, upon scrutiny, that BL is not in fact an expression of local causality. Rather, it is merely an expression of statistical independence.

Is that what you mean?

Yes.

Okay. As soon as I am able, I will post something on Bell's "Local Causality Criterion", and put it up for evaluation in this thread. The two of us can discuss it, along with anyone else who is interested.
________________________
[EDIT: I just posted it a few posts down post#239]

 

[SpectraCat]

Quick googling about Mermin's gedanken experiment led me to two links.
One is simple explanation of Mermin's experiment:
http://public.fh-wolfenbuettel.de/~ruediger/lehre/EPRapplet/EPRappletDescription.pdf"
Second shows how Mermin’s gedanken experiment fails if unfair sampling is used:
http://www.Newtonphysics.on.ca/uncertainty/index.html"
In short this second link shows that required probabilities appear if one chooses instruction sets RRG;RGR;GRR and discards every second detection of R.
It can be easily made symmetrical in respect to R/G if we additionally take instruction sets GGR;GRG;RGG but for those instruction sets we discard every second detection of G.

So this Mermin’s gedanken experiment is no argument against local realism + hypothetical unfair sampling.

I don't trust that Marmet link, because it seems he does not understand the Mermin experiment, as evidenced by this quote:

"However, one finds then that the relevant feature b is not satisfied now, because statistically, lights will flash the same color 5/9 (0.5555) of the time, instead of 0.50 that should be obtained. Bell's inequality theorem has been applied here. Since the denominator, (that is the possible number of settings in the calculation of probability), is an odd number (number 9) and the numerator is an integer, it is absolutely impossible to obtain this way, the exact fraction 0.5 required by the quantum mechanical calculation."

In the Mermin, when the polarizer settings are the same, the lights flash the same color all of the the time, which accounts for 3/9 of the cases. When the polarizer settings are different (the remaining 6/9 of cases), then the lights flash the same color 1/4 of the time. So, the total number of times the lights flash the same is:

1/3 + 1/4*2/3 = 2/6 + 1/6 = 3/6 = 1/2

So unless there is some hidden logic that Marmet doesn't explain .. I can't see how his quote can be correct.

 

[zonde]

I see the proposition as valid [... modulo other premises (e.g. free-choice of Alice and Bob)], and that it can be correctly applied to the "Bell argument" in terms of the joint-probability-function of the particle pair.

Let's say I too see this proposition as valid but not exhaustive (I would feel more comfortable if I somehow could make sure that all the abstract terms in this proposition have unambiguous meaning).
I would say that PC is not a requirement for local determinism. So we can say: locality Λ CF → local determinism. That's because PC is certain arrangement of things that applies to one situation but doesn't apply to other.

It is unclear to me what you are getting at here. Nonetheless, I would prefer to write the statement in this way (with no mention of QM):

If measurement of the component σ1∙a, where a is some unit vector, yields the value +1, then measurement of σ2∙a must yield the value -1; and vice versa.

This statement can be said to be a theorem of Quantum Mechanics. Yet, it makes an infinity of assertions, only one of which, in any "real-world" instantiation, can ever be factual (the remaining ones then being counterfactual).

... Zonde, is this what you are getting at?

I am afraid what I am getting at is closer to the ground.
What I don't like about this theorem of QM is that it is placed as restriction on all possible LR theories even when this theorem is not experimentally verified.
Let's say we can formulate LR theory that says:
a) If measurement of the component σ1∙a, where a is some unit vector, yields the value +1, then measurement of σ2∙a must yield the value -1 or no value at all at least half the time.
b) If measurement of the component σ1∙a, where a is some unit vector, yields the value +1, then low efficiency measurement of σ2∙a must yield the value -1 with very high probability and value +1 with very low probability or no value at all. But as measurement efficiency increases relative probability of +1 value increases rapidly.

Obviously they are not covered by Bell's argument because they do not agree with this theorem of QM. And still they would not contradict experimental evidence we have today (well "a)" contradicts claims that single detector efficiency can exceed 50% but not "b)").

 

[zonde]

I don't trust that Marmet link, because it seems he does not understand the Mermin experiment, as evidenced by this quote:

"However, one finds then that the relevant feature b is not satisfied now, because statistically, lights will flash the same color 5/9 (0.5555) of the time, instead of 0.50 that should be obtained. Bell's inequality theorem has been applied here. Since the denominator, (that is the possible number of settings in the calculation of probability), is an odd number (number 9) and the numerator is an integer, it is absolutely impossible to obtain this way, the exact fraction 0.5 required by the quantum mechanical calculation."

In the Mermin, when the polarizer settings are the same, the lights flash the same color all of the the time, which accounts for 3/9 of the cases. When the polarizer settings are different (the remaining 6/9 of cases), then the lights flash the same color 1/4 of the time. So, the total number of times the lights flash the same is:

1/3 + 1/4*2/3 = 2/6 + 1/6 = 3/6 = 1/2

So unless there is some hidden logic that Marmet doesn't explain .. I can't see how his quote can be correct.

This "the lights flash the same color 1/4 of the time" for different polarizer settings is prediction of QM but Mermin's realistic model (excluding two instruction sets - GGG;RRR) predicts 5/9 - 3/9 for the same settings and 2/9 for different settings. That can be seen in the first link I gave.

But you don't have to trust this Marmet link. I verified this claim that not detecting every second R gives required probabilities. I can present you my calculations. They are not too complicated.

 

[yoda jedi]

local determinism .

Thats all.
Its determinism, no realism.
Just a "MISCONCEPTION"




Suarez
...refutation of nonlocal determinism...

Groblacher
...a world that is not completely deterministic...

Spekkens
...Bell’s argument is only necessary to rule out locality...

Gisin
...Hence, all violations of Bell's inequality should be interpreted as a demonstration of
nonlocality...

Hall
...the term ‘local realism’ be replaced by ‘local determinism’...

and so on...

 

[DrChinese]

1. This "the lights flash the same color 1/4 of the time" for different polarizer settings is prediction of QM but Mermin's realistic model (excluding two instruction sets - GGG;RRR) predicts 5/9 - 3/9 for the same settings and 2/9 for different settings. That can be seen in the first link I gave.

2. But you don't have to trust this Marmet link. I verified this claim that not detecting every second R gives required probabilities. I can present you my calculations. They are not too complicated.

1. The correct value for LR is >=2/6 for different settings, not 2/9.
The QM prediction is =.25.

2. The Marmet sample yields a value in excess of .33 and does not come close to .25. Of course, there are lots of other problems with the Marmet hypothesis.

 

[ThomasT]

No, this is not correct in my opinion, because the experiments allow for the possibility that the results will be observed to be statistically independent.

If an experiment is designed to produce entanglement, then that entails (via the execution of that design) a statistical dependency between the data sets, A and B.

That is what the coincidence counting is all about.

Coincidence counting is about matching the separate data streams wrt some criterion or criteria, and then counting the coincidences.

If the coincidence measurements showed that the results at detectors A and B were not correlated, then the Bell inequality would not be violated, in which case we would conclude that the results were statistically independent.

The correlation is between the angular difference |a-b| (or Theta, where a and b are the settings of the analyzers at A and B), and the rate of coincidental detection.

To get the QM-predicted, cos²Theta, angular dependency the experimental design has to involve and the execution has to produce a statistical dependency between the separately accumulated data sets.

To state it another way, how could the experiments possibly test non-locality unless they allow for the possibility of non-locality?

That's the point of my line of thinking on this. Bell tests don't test nonlocality.

They already *inherently* allow for the possibility of locality, because that is what the experiment would show if there were no correlation of the supposedly entangled photons.

There is no correlation between the supposedly entangled photons -- except for two settings, and at these settings, Theta = 0 and
Theta = pi/2, an LHV formulation can also show perfect correlation and anticorrelation, respectively. For all other values of Theta there's absolutely no correlation between A and B.

I'll continue with this reply when I get time.

 

[akhmeteli]

1) Do you believe you understand the concept expressed by the following statement?

Alice and Bob's outcomes are governed by local determinism.

I think so

2) Do you consider the following statement to be true?

On the basis of the single assumption of "local determinism of Alice and Bob's outcomes", one can derive a Bell inequality.

I think so

 

[Eye_in_the_Sky]

I think so

I think so

Okay. My answers are the same.

How about this next statement, would you say that it is correct?

The assumption of "local determinism of Alice and Bob's outcomes" is independent of any assumptions concerning the truth or internal consistency of Quantum Mechanics.

 

[Eye_in_the_Sky]

Bell's "Local Causality Criterion"

click here → diagram ← click here

"A theory will be said to be locally causal if the probabilities attached to values of local beables in a space-time region 1 are unaltered by specification of values of local beables in a space-like separated region 2, when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a spacetime region 3."

"It is important that region 3 completely shields off from 1 the overlap of the backward light cones of 1 and 2. Otherwise the traces in region 2 of causes of events in 1 could well supplement whatever else was being used for calculating probabilities about 1. The hypothesis is that any such information about 2 becomes redundant when 3 is specified completely."

 

[akhmeteli]

It is not unsubstantiated, it is shown by Bell's theorem, and by Mermin's gedanken experiment. The latter case shows that it is not possible for "instruction sets" which explain how particles are supposed to register on detectors to be carried by those particles. Therefore, if the "information" that leads to the cannot carried with the particles themselves, and it cannot be exchanged by the entangled particles at the time of detection (since the detectors have a spacelike separation), then it cannot exist.

Look, this is some substantiation "the morning after". Frame Grabber ridicules me for inability or reluctance to guess what he (or she) implied from the context. But when I don't see any explicit arguments, I cannot address them. Am I really supposed to criticize something "what I think" you or Frame Grabber mean? And if I cannot criticize it, am I supposed to agree with you just because I believe you on your word? So until you give some arguments, what you say is unsubstantiated.

OK, now you offered something that at least looks like some substantiation, and I can discuss it. Let us consider what you offered. Mermin's gedanken experiment seems to be just an illustration of the Bell theorem, so it seems irrelevant. In any case, it is a gedanken experiment, not a real one. So if it is any argument, it is only a theoretical one, not experimental. The same is true about the Bell theorem. I concede that local realism implies the Bell inequalities. On the other hand, you seem to be aware that no violations of the genuine Bell inequalities have been demonstrated. Therefore, the Bell's theorem's conclusion that the Bell inequalities can be violated in quantum theory has no experimental confirmation. Therefore, your statement that entanglement cannot be explained by exchange of "slow" particles has no experimental confirmation. Does it have theoretical confirmation? You offer the Bell theorem as the theoretical confirmation. However, I argue that *) the proof of the Bell theorem requires the use of two contradictory assumptions: unitary evolution (UE) and the projection postulate. I started this thread with this statement and supported it with the reversibility argument (another, more standard argument, is that unitary evolution cannot destroy a superposition, whereas the projection postulate does just that). I have yet to see a refutation of this statement *) - it's actually a rephrase of the relatively well-known measurement problem in quantum mechanics. It is difficult to rely on a consequence of two contradictory assumptions. Therefore, your statement has no experimental basis, and its theoretical confirmation is dubious.

Of course that is what I meant, since that is the context of our current discussion. If you build the correlation into the source, it will be there at the detector, but that is precisely what CANNOT be happening with quantum entanglement, as demonstrated (again) by Bell's theorem and the Mermin gedanken.

I can only repeat the above comment, both with respect to "reading from concept" and to "confirmation" by the Bell theorem.

I looked at that post, and frankly I do not have the time to absorb and digest all the math ..

I understand.

I don't know what QTP means,

My fault - I meant "QFT" - quantum field theory. Sorry.

and I am not intimately familiar with the mathematics of QFT, which apparently is necessary to understand what is referred to in that post.

I see. Maybe I'll try to write a longer comment on that mathematical result later.

I don't think it is physically reasonable to "imagine" that, because of Malus's law, but ok, I'll grant it for the purposes of this discussion.



I have no idea what the above statement refers to ... it makes no sense at all. What is "a later photon from such a pair", and what does the phrase "undetected earlier" mean? I am sorry but I need a lot more context and detail to begin to parse that.



It's fine for you to use the detection loophole, but you have completely lost me at this point. What other pairs? Where is the space-like separation between the detectors and how is it overcome? You also seem to be indicating that there is some preferred direction of detection .. where is the basis for that?

Never mind. As I said, that was just some illustration, and it fulfilled what it was designed for, namely, pinpointed the source of our disagreement. So it looks like you keep referring to the Malus law, and I argue that it is in contradiction with UE.

I didn't ask you to believe me on my word, and I didn't mention Malus's law before because I didn't think I had to, since it has already come up in this thread. Malus's law has been extensively tested and never shown to be incorrect. So now you are not just questioning well accepted physical theorems, you are going after laws as well. Go for it!

Again, guessing from context is not my favorite pastime. So Malus law is used to calculate the correlations of the Bell theorem in quantum mechanics for photons, and it is my understanding that it is an equivalent or consequence of the projection postulate and therefore introduces nonlocality directly: indeed, we are supposed to believe that as soon as the polarization of one photon of the entangled pair is measured, the polarization of the other photon becomes determined immediately, whatever the spatial separation. You actually need no Bell theorem after that - nonlocality is already there. You reproach me for going after laws. I don't want to go after any laws, actually, I am pretty conservative. But if two laws contradict each other, as UE and PP do, you have no choice but to go after one of them. Can you really accuse me for not being able to calmly swallow two mutually contradictory statements? As for Malus law being extensively tested, I am not sure it could be tested for undetected photons, so I suspect you need something like fair sampling to deduce the Bell inequality violations from Malus law.

Unfortunately I can't understand the details of that post, as I already mentioned. However, even if I accepted its content, I am not sure why it is relevant to this discussion ... and earlier you said "nonlinear" PDE's, only here do you mention that they are local. Can you please break down the physical significance of this statement in the current context, or link to a post where you described it previously?

I don't have time right now to explain how it's relevant or find references to nightlight's posts. I'll try to do that a day or two later. As for me adding the word "local", it does not change anything, as the relevant partial differential equations in 3+1 dimensions are inherently local, the same way as, say, the Maxwell equations are local. I added this word "local" just to emphasize how this is relevant.

Ok, so your point 3 above is really the only thing to take issue with. I confess I have not really spent much time trying to understand it's significance. I will try to do that and post when I have something more to say about it.

I am glad the area where we disagree has narrowed significantly.

You say it is radical .. I don't agree, but I guess you are in good company .. Einstein couldn't accept it either. Q.M. predicts non-local correlations in a manner that is consistent with all available experimental evidence. Furthermore, Q.M. is also consistent with all classical results as well .. and classical systems are where local realism really makes sense, and as far as I know, there are no classical systems that are inconsistent with LR. So perhaps LR is a consequence of the Bohr correspondence principle somehow, and like CM is contained and explained within the context of Q.M. in the large mass/high quantum number limit.

Again, the problem is such key parts of standard quantum theory as UE and PP are inconsistent

The post in question was entirely about why the experimental closing of the "locality loophole" showed that the entangled pairs could not be exchanging sub-light particles, as you had hypothesized. I didn't use or introduce that concept .. YOU did. I explained/argued why it cannot be used to explain the experimental results under discussion. You chose not to accept my explanation/argument, and I am still trying to understand why.

So it turned out you implicitly used the Malus law, which, I believe, contradicts unitary evolution. That's why I am less than impressed by your explanation. And until you explicitly mentioned the Malus law, I was not even able to see any coherent argument. Again, I don't think guessing games are appropriate here.

 

[akhmeteli]

Okay. My answers are the same.

How about this next statement, would you say that it is correct?

The assumption of "local determinism of Alice and Bob's outcomes" is independent of any assumptions concerning the truth or internal consistency of Quantum Mechanics.

I think I disagree with this statement. Indeed, if QM is true and internally consistent, then the Bell inequalities can indeed be violated, so local determinism is eliminated. Therefore the assumption of local determinism does not seem to be independent of the assumptions of truth and consistency of quantum mechanics.

 

[Demystifier]

I think I disagree with this statement. Indeed, if QM is true and internally consistent, then the Bell inequalities can indeed be violated, so local determinism is eliminated. Therefore the assumption of local determinism does not seem to be independent of the assumptions of truth and consistency of quantum mechanics.

So basically, you believe that QM is wrong. Am I right?

 

[Frame Dragger]

So basically, you believe that QM is wrong. Am I right?

You're right, but he likes to preach. Maybe he was raised by Jesuits? (or wolves)

Never trust someone who isn't willing to state their beliefs before wasting several pages with rhetorical nonsense; as if this is a game to be won. :grumpy:

 

[zonde]

1. The correct value for LR is >=2/6 for different settings, not 2/9.
The QM prediction is =.25.

In Mermin’s model 5/9 you get from 1 for the same setting and 2/6 for different settings. With respective probabilities for the same settings - 1/3 and for different settings - 2/3 you have:
1*1/3+2/6*2/3=5/9
This is Mermin’s model.

2. The Marmet sample yields a value in excess of .33 and does not come close to .25. Of course, there are lots of other problems with the Marmet hypothesis.

Mermin's model propose value that exceeds 0.33.
Marmet sample with discarding every second R is more complicated.
For the same settings: match - 1/2, blank - 1/2
For different settings: match - 1/12, mismatch - 4/12, blank - 7/12
So the probability is actually 0.2 ( 1/(1+4) ) i.e. below required value.
That way Marmet model does not reproduce all required probabilities but anyways Mermin's inequality is proved not to hold for realistic experimental conditions.

 

[SpectraCat]

In Mermin’s model 5/9 you get from 1 for the same setting and 2/6 for different settings. With respective probabilities for the same settings - 1/3 and for different settings - 2/3 you have:
1*1/3+2/6*2/3=5/9
This is Mermin’s model.

Right, and my problem (well, one of them) with the Marmet paper is that the phase I quoted previously was being used to describe the Apsect experiments .. Marmet was claiming that coincidence measurements would be observed 5/9 of the time there (which is wrong), and only using "the denominator is an odd integer" to justify his reasoning.

Mermin's model propose value that exceeds 0.33.
Marmet sample with discarding every second R is more complicated.
For the same settings: match - 1/2, blank - 1/2
For different settings: match - 1/12, mismatch - 4/12, blank - 7/12
So the probability is actually 0.2 ( 1/(1+4) ) i.e. below required value.
That way Marmet model does not reproduce all required probabilities but anyways Mermin's inequality is proved not to hold for realistic experimental conditions.

I don't agree that discarding every second R (or G) is any more realistic than assuming 100% efficiency. It implies a very strict ordering of events that has no basis in reality as far as I can tell. If you want to say that the detector misses half of the time when it is supposed to blink red, I can live with that, but the ordering should be random in my view.

I also don't understand how you got matching only half the time under your setup when the detector settings are the same. You seem to be neglecting the times when both detectors blink green, which are not attenuated in your model, and so the matching rate should be greater than 0.5. A similar comment also pertains to your model when the settings are different.

Finally, if we can assume random ordering of the detector "failures", then we are free to throw out all of the times when one of the lights doesn't blink. But of course now you are going to tell me that is just the free sampling assumption .. and it is. My point is that without a realistic physical model to understand why there should be (or even could be) a bias for the "missed" detection events, it seems most reasonable to assume they are random. Another point is that the randomness of missed detections could be tested in principle, by deliberately blocking one of the beams in a random fashion. If there is a bias is the "missed" events due to detector design, then there should be a measurable difference between sets of results where the beam is never blocked, and those where it is blocked randomly.