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Simple question: Why has the original Bell inequality not been tested experimentally? There have been tons of tests focused on the CHSH but not a single on the original Bell inequality. The answer must be very revealing.

In this paper, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512796/ Andrei Khrennikov argues that testing the original Bell inequality should provide an even bigger deviation from classically since the ratio of the RHS between QM and classical is bigger than for CHSH. He also hints at the reason why the original Bell inequality is often ignored

Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations.

Is it really true that the reason they aren't using the original Bell's inequality is that they are not able to ensure perfect anti-correlation in experiments for the same settings?

@minkwe I hate to do this to you but it is because it is a piece of junk physics. Two streams of particles; 3 angles. How does that work? Back in those days, they would need 3 streams of "entangled" particles somehow. How?
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FrediFizzx wrote: 3 angles. How does that work?.

Simple. The source is the same, i.e., a singlet pair with the photons propagating in different directions to the detection stations. One station has its angle fixed, while the other station chooses between two angles. Concerns about different ensembles remain (weak versus strong objectivity).

Thank you for the interesting link, minkwe. Note that existing data sets for CHSH can be re-analysed for OB violation. It might be fun to try that.

I doubt that the lack of perfect anticorrelation is the key, because OB can be derived in other ways omitting that assumption.

FrediFizzx wrote:@minkwe I hate to do this to you but it is because it is a piece of junk physics. Two streams of particles; 3 angles. How does that work? Back in those days, they would need 3 streams of "entangled" particles somehow. How?
.

It is for sure but sometimes their reasoning helps us undo their "logic".

local wrote:

FrediFizzx wrote: 3 angles. How does that work?.

Simple. The source is the same, i.e., a singlet pair with the photons propagating in different directions to the detection stations. One station has its angle fixed, while the other station chooses between two angles. Concerns about different ensembles remain (weak versus strong objectivity).

Thank you for the interesting link, minkwe. Note that existing data sets for CHSH can be re-analysed for OB violation. It might be fun to try that.

I doubt that the lack of perfect anticorrelation is the key, because OB can be derived in other ways omitting that assumption.

You are welcome. Perhaps I should ask the question another way. Is any of you aware of any experiment which measured the particle pairs at the same setting on both sides and characterized perfect anti-correlation? This would seem like an excellent/obvious experiment to do as part of the myriad of experiments being done. I've been looking for such data and haven't found it after a long time of searching.

So I reduced my expectations and started looking for raw Malus law data for entangled particles. No luck there either. The Malus experiment is done in almost every undergraduate physics class, yet nobody ever reports the comparison of the intensity without polarizer to the maximum intensity with polarizer.

minkwe wrote:

local wrote:

FrediFizzx wrote: 3 angles. How does that work?.

Simple. The source is the same, i.e., a singlet pair with the photons propagating in different directions to the detection stations. One station has its angle fixed, while the other station chooses between two angles. Concerns about different ensembles remain (weak versus strong objectivity).

Thank you for the interesting link, minkwe. Note that existing data sets for CHSH can be re-analysed for OB violation. It might be fun to try that.

I doubt that the lack of perfect anticorrelation is the key, because OB can be derived in other ways omitting that assumption.

You are welcome. Perhaps I should ask the question another way. Is any of you aware of any experiment which measured the particle pairs at the same setting on both sides and characterized perfect anti-correlation? This would seem like an excellent/obvious experiment to do as part of the myriad of experiments being done. I've been looking for such data and haven't found it after a long time of searching. His inequality leaves enough room - enough distance between LR and QM. As long as QM is close to giving the right predictions (in the sense that the singlet correlations are close to true), you can use his methodology to reject local realism.

So I reduced my expectations and started looking for raw Malus law data for entangled particles. No luck there either. The Malus experiment is done in almost every undergraduate physics class, yet nobody ever reports the comparison of the intensity without polarizer to the maximum intensity with polarizer.

I believe that such experiments have been done, but without a big spatial separation between the two measurement stations. Indeed, one can use the data from experiments in which the whole negative cosine curve is measured. The important thing is that it is observed to be close to full amplitude.

In some experiments this has been seen after using the “fair sampling assumption” to dispose of the detection loophole.

Already, at the end of his famous paper, Bell mentioned that one could never expect to observe *perfect* anti-correlation because of inevitable experimental errors. He showed how to modify his inequality to make it experimentally useful. You must show (up to some acceptable statistical uncertainty) that the negative correlation at equal settings is stronger than -1 + epsilon, where epsilon is a small positive number, you may choose it yourself; and you must show that his inequality holds (again, up to some acceptable statistical error), but sharpened by an amount delta; he shows how to compute delta from epsilon. The smaller is epsilon, the smaller delta will be. His original inequality is, in a good sense, robust to imperfect measurement.

local wrote:

FrediFizzx wrote: 3 angles. How does that work?.

Simple. The source is the same, i.e., a singlet pair with the photons propagating in different directions to the detection stations. One station has its angle fixed, while the other station chooses between two angles. Concerns about different ensembles remain (weak versus strong objectivity). ...

Thus allowing the CHSH type cheating.
.

minkwe wrote:Simple question: Why has the original Bell inequality not been tested experimentally? There have been tons of tests focused on the CHSH but not a single on the original Bell inequality. The answer must be very revealing.

In this paper, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512796/ Andrei Khrennikov argues that testing the original Bell inequality should provide an even bigger deviation from classically since the ratio of the RHS between QM and classical is bigger than for CHSH. He also hints at the reason why the original Bell inequality is often ignored

Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations.

Is it really true that the reason they aren't using the original Bell's inequality is that they are not able to ensure perfect anti-correlation in experiments for the same settings?

I believe that your question minkwe is a very good one. According to what CHSH said in their 1969 paper, they criticize the assumption of perfect correlations. However, that is not very convincing to me. The final result only contains correlations of the form P(a,b) with , you do not need to measure perfect correlations, i.e., results of experiments measured in the same direction are discarded. I suppose I am missing something.

Justo wrote:I believe that your question minkwe is a very good one. According to what CHSH said in their 1969 paper, they criticize the assumption of perfect correlations. However, that is not very convincing to me. The final result only contains correlations of the form P(a,b) with , you do not need to measure perfect correlations, i.e., results of experiments measured in the same direction are discarded. I suppose I am missing something.

Yes, you are sort of right that you don't need to measure perfect correlations but you don't have to discard a = b and a = -b either. In fact, if you are doing a proper simulation you want everything so that you can see that you are in fact having perfect anti-correlation and perfect correlation.
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FrediFizzx wrote: In fact, if you are doing a proper simulation you want everything so that you can see that you are in fact having perfect anti-correlation and perfect correlation.

Yes. For example, Weihs et al tested the entire cosine curve, so you can consider that experiment to have tested for perfect anti-correlation and perfect correlation. Unfortunately, it's easy to show that the Weihs et al experiment is simply demonstrating the detection "loophole".

minkwe wrote:So I reduced my expectations and started looking for raw Malus law data for entangled particles. No luck there either. The Malus experiment is done in almost every undergraduate physics class, yet nobody ever reports the comparison of the intensity without polarizer to the maximum intensity with polarizer.

All real polarizers have some light loss even when perfectly aligned. You can find this loss in the specifications for the polarizer.

Justo wrote:I believe that your question minkwe is a very good one. According to what CHSH said in their 1969 paper, they criticize the assumption of perfect correlations. However, that is not very convincing to me. The final result only contains correlations of the form P(a,b) with , you do not need to measure perfect correlations, i.e., results of experiments measured in the same direction are discarded. I suppose I am missing something.

Discarded because there is no perfect correlation? So if there is no perfect correlation, then what does that tell you about expectations placed on for explaining the experiment? The QM prediction is perfect anti-correlation so claims that QM explains the experiment without that agreement there is suspect. When you do experiments, you have to include controls to verify the internal consistency of your data. This is one of them.

local wrote:

minkwe wrote:So I reduced my expectations and started looking for raw Malus law data for entangled particles. No luck there either. The Malus experiment is done in almost every undergraduate physics class, yet nobody ever reports the comparison of the intensity without polarizer to the maximum intensity with polarizer.

All real polarizers have some light loss even when perfectly aligned. You can find this loss in the specifications for the polarizer.

Exactly, that is what I'm aware of as well. The point is that it appears nobody has ever measured a cosine curve then. A cosine curve goes from -1 to 1 not -0.9 to 0.9. Looking at the Aspect data, in this paper https://arxiv.org/pdf/quant-ph/0402001.pdf, their probabilities do not go from 0 to 0.5 as claimed. It goes from ~0.025 to ~.475 including error bars! Has any experiment done better in terms of reproducing the cosine curve? If so I'll be interested in seeing that paper. If not, why not?

The typical explanation has been that it is due to "experimental error" but what is the justification for that claim. How do they know that it is not due to a real physical phenomenon?

minkwe wrote:

local wrote:

minkwe wrote:So I reduced my expectations and started looking for raw Malus law data for entangled particles. No luck there either. The Malus experiment is done in almost every undergraduate physics class, yet nobody ever reports the comparison of the intensity without polarizer to the maximum intensity with polarizer.

All real polarizers have some light loss even when perfectly aligned. You can find this loss in the specifications for the polarizer.

Exactly, that is what I'm aware of as well. The point is that it appears nobody has ever measured a cosine curve then. A cosine curve goes from -1 to 1 not -0.9 to 0.9. Looking at the Aspect data, in this paper https://arxiv.org/pdf/quant-ph/0402001.pdf, their probabilities do not go from 0 to 0.5 as claimed. It goes from ~0.025 to ~.475 including error bars! Has any experiment done better in terms of reproducing the cosine curve? If so I'll be interested in seeing that paper. If not, why not?

The typical explanation has been that it is due to "experimental error" but what is the justification for that claim. How do they know that it is not due to a real physical phenomenon?

I think I remember seeing a crude -cosine curve from the Weihs, et al, experiment. I think you might have to dig through Weihs' thesis.
.

FrediFizzx wrote:

minkwe wrote:

local wrote:

minkwe wrote:So I reduced my expectations and started looking for raw Malus law data for entangled particles. No luck there either. The Malus experiment is done in almost every undergraduate physics class, yet nobody ever reports the comparison of the intensity without polarizer to the maximum intensity with polarizer.

All real polarizers have some light loss even when perfectly aligned. You can find this loss in the specifications for the polarizer.

Exactly, that is what I'm aware of as well. The point is that it appears nobody has ever measured a cosine curve then. A cosine curve goes from -1 to 1 not -0.9 to 0.9. Looking at the Aspect data, in this paper https://arxiv.org/pdf/quant-ph/0402001.pdf, their probabilities do not go from 0 to 0.5 as claimed. It goes from ~0.025 to ~.475 including error bars! Has any experiment done better in terms of reproducing the cosine curve? If so I'll be interested in seeing that paper. If not, why not?

The typical explanation has been that it is due to "experimental error" but what is the justification for that claim. How do they know that it is not due to a real physical phenomenon?

I think I remember seeing a crude -cosine curve from the Weihs, et al, experiment. I think you might have to dig through Weihs' thesis.
.

I've seen it as well and it definitely did not go from -1 to 1. It was hovering around ~0.95. I don't believe it is possible to perform a photonic experiment with imperfect polarizing beam splitters and obtain the cosine curve. Even the values already in Weihs and Aspect's experiments suggest they are already scaling the data. The highest efficiency polarizing beam splitters I can find are in the 80-90% maximum efficiency range. My interest in this is not for the purpose of evaluating error bars for "violating" the inequalities. I'm trying to understand the physical justification for claiming that any losses must be due to "experimental error".

Imperfection of physical detectors can be thought to be part of experimental error. “Experimental error” can have many components. There can be systematic deviations from an ideal theoretical result as well as completely random noise. Moreover, noise can effect the statistics of interest in a non-linear way, producing systematic errors in the final results.

producing systematic errors in the final results

Such as artifactual violations of Bell-like inequalities.

local wrote:

producing systematic errors in the final results

Such as artifactual violations of Bell-like inequalities.

.