Bell’s Theorem Refuted: Bell’s 1964:(15) is False

[minkwe]

Gordon should be happy with that idea, but Michel is certainly not. He's only interested in showing that experiments done to date (i.e. in the past) can be explained by LHV theories.

Contrary to the lie above, I am interested in all physically performable experiments, and simulations thereof. Neither your challenge nor QRC are relevant to physics as has been shown over and over again. The experiment you call "perfect" will never be performed because it is impossible to perform. It is impossible to force nature to choose the exact same probability distribution of lambda. Unless you resort to using Bertlmann's socks as your particles.

It is silly to insist on random selection of angles while at the same time assuming that Nature selects exactly the same set of lambda everytime. That statisticians and mathematicians make this error is even more startling. The point which Gordon is making is similar to the point which I have been making all along, and which many others have made previously in various different ways:

* For EPRB experiments, S <= 2 can not be derived without making a naive realism (Bertlmann's socks) assumption, an assumption which is very silly wrt EPRB, and can be rejected immediately without any fuss.
* Assuming that S <= 2 is a correct inequality, the experiment which it prescribes is impossible to perform because it requires either: (1) measuring the same set of particles more than once, or (2), forcing nature to select the EXACT same distribution of lambda every time. Anyone who might be tempted to argue against these should check:
- http://arxiv.org/pdf/quant-ph/0604124v2.pdf, which shows that not only does nature have to produce the same distribution of lambda every time, it MUST also produce them in the same sequence for the derivation to proceed. (This is related to Gordon's argument concerning AiAj =/= +1, The only way AiAj = +1 is true is if Nature produces the exact same set of lambdas in the exact same sequence every time, ie i=j, --- an impossibility). It is also similar to my "degrees of freedom" argument.
- http://arxiv.org/ftp/arxiv/papers/1305/1305.2948.pdf -- "Three classical examples and two variations on the GHZ construction are analyzed to demonstrate that combined counter factual results of non-commuting operations are in general logically inconsistent with performable measurement sequences that take non-commutation into account."

It is an utter waste of time then to even entertain challenges such as QRC or Gill's. Produce experimental results which can not be explained by LHV and we will be interested in it.

[Heinera]

It is silly to insist on random selection of angles while at the same time assuming that Nature selects exactly the same set of lambda everytime.

In the QRC, one is free to assume whatever set of lambdas one wishes. You can even keep track of them to ensure that a particular value of lambda is never emitted more than once. The only thing that is forbidden about the lambdas, is that the generation of the lambdas depends on the detector settings, since that information is not available to the source in a LHV model.

Of course, you could make a model where generation of the lambdas took advantage of information about the detector settings, but that would just replace QM theory with something even more weird, and you could no longer call it a LHV model.

[minkwe]

It is an utter waste of time then to even entertain challenges such as QRC or Gill's. Produce experimental results which can not be explained by LHV and we will be interested in it.

Enough said.

Or if you like, simulate experimental results using QM which can not be simulated by LHV and we will talk. If as some claim, a "perfect" experiment is imminent which will prove beyond any doubt that QM can do what LHV cannot, then they would produce the simulation using QM of what results such an experiment will purportedly show when it is done.

[Heinera]

It is an utter waste of time then to even entertain challenges such as QRC or Gill's. Produce experimental results which can not be explained by LHV and we will be interested in it.

Enough said.

http://arxiv.org/pdf/1306.5772
http://www.researchgate.net/publication ... 0ecce4.pdf

[minkwe]

It is an utter waste of time then to even entertain challenges such as QRC or Gill's. Produce experimental results which can not be explained by LHV and we will be interested in it.

Enough said.

http://arxiv.org/pdf/1306.5772
http://www.researchgate.net/publication ... 0ecce4.pdf

What does this mean? Are you afraid to place your foot in your mouth by actually stating what you imply? Let me repeat. There is no experiment that has ever been done that can not be explained by LHV. If anybody thinks otherwise they should clearly say so.

[Heinera]

It is an utter waste of time then to even entertain challenges such as QRC or Gill's. Produce experimental results which can not be explained by LHV and we will be interested in it.

http://arxiv.org/pdf/1306.5772
http://www.researchgate.net/publication ... 0ecce4.pdf

What does this mean? Are you afraid to place your foot in your mouth by actually stating what you imply? Let me repeat. There is no experiment that has ever been done that can not be explained by LHV. If anybody thinks otherwise they should clearly say so.

Didn't you ask for experimetal results that could not be explained by LHV? Didn't I give you references to two such results?

[gill1109]

Exactly. The Christensen et al. experiment http://arxiv.org/abs/1306.5772
And there is the Giustina et al. experiment http://arxiv.org/abs/1309.0712

2013 was a miraculous year. Till last year there was no experiment done which could not be explained by LHV. However, things have changed that last year. The detection loophole was at long last overcome for experiments with photons.

Actually in those experiments there is still a "locality" loohole because the two detectors were not far enough apart. In principle, the setting used in one arm of the experiment could be communicated to the other before the measurement in the other arm is concluded. However, there are other photon experiments with no locality loophole. There does not seem to be any reason why there won't be an experiment in a year or two (at Växjö the experts predicted within a year from now) which overcomes both loopholes. As Jan de Raedt agreed, there will be no longer a LHV explanation of that experiment, if it is succesful. Michielsen (his wife) believes that that experiment won't be succesful. She believes in LHV. de Raedt however has an open mind.

[Joy Christian]

As Jan de Raedt agreed, there will be no longer a LHV explanation of that experiment, if it is successful.

If this is indeed what de Raedt believes (and I have no reason to trust a single word Richard Gill ever says), then I disagree with de Raedt.

A completely coherent and comprehensive local-realistic framework reproducing ALL quantum correlations already exists which does not exploit any loophole but simply does the physics correctly by recognizing and correcting the elementary topological error Bell made in the very first equation of his famous paper:

(1) http://arxiv.org/abs/1405.2355

(2) http://libertesphilosophica.info/blog/

(3) http://arxiv.org/abs/1301.1653

(4) http://arxiv.org/abs/1211.0784

(5) http://rpubs.com/jjc/16567

(6) http://rpubs.com/jjc/19298

[gill1109]

Gordon, perhaps you can explain to me what you don't understand about my Theorem 1 in Section 2 of http://arxiv.org/abs/1207.5103.

Note: the theorem is a little pure math thing. it's about a simple probability game you can play on a computer with an N x 4 spreadsheet of numbers A, A', B, B'. For each row of the spreadsheet you pick randomly either A or A', and either B or B' ...

Try substituting N = 100 000 and eta = 0.1 in the expression on the right hand side. Do you understand its meaning?

Have you tried testing the theorem by computer simulation?

I want to separate the math from the physics. There is a little bit of pure math I'd like you to understand. Once you have understood it, I think this might open your eyes to understanding of the role of random setting choices in EPRB experiments. Anyway, if you both understand and believe this little bit of pure math (ie pure logic), then we will have a basis of common understanding on which we can build further.

Just a suggestion.

Despite appearances, I do believe that this is "on topic". You think that Bell's 1964 (15) is false, but I think that's because you are missing something. What I think you are missing is a bit of probability intuition. A number of people tried to explain this to you in different ways but made no progress. So we need to take a fresh approach. This is an approach from a completely new direction to the same obstruction.

But if you think it is off topic, we can start a new thread (I think we already did make a start but it got forgotten. That's why I would like to draw your attention to it again).

[Gordon Watson]

Gordon, perhaps you can explain to me what you don't understand about my Theorem 1 in Section 2 of http://arxiv.org/abs/1207.5103.

Note: the theorem is a little pure math thing. it's about a simple probability game you can play on a computer with an N x 4 spreadsheet of numbers A, A', B, B'. For each row of the spreadsheet you pick randomly either A or A', and either B or B' ...

Try substituting N = 100 000 and eta = 0.1 in the expression on the right hand side. Do you understand its meaning?

Have you tried testing the theorem by computer simulation?

I want to separate the math from the physics. There is a little bit of pure math I'd like you to understand. Once you have understood it, I think this might open your eyes to understanding of the role of random setting choices in EPRB experiments. Anyway, if you both understand and believe this little bit of pure math (ie pure logic), then we will have a basis of common understanding on which we can build further.

Just a suggestion.

Despite appearances, I do believe that this is "on topic". You think that Bell's 1964 (15) is false, but I think that's because you are missing something. What I think you are missing is a bit of probability intuition. A number of people tried to explain this to you in different ways but made no progress. So we need to take a fresh approach. This is an approach from a completely new direction to the same obstruction.

But if you think it is off topic, we can start a new thread (I think we already did make a start but it got forgotten. That's why I would like to draw your attention to it again).

Richard,

Your proposal is fine here; and I'm more convinced than ever that Bell 1964:(15) is false. So I'll happily deal with it AND your theorem here.

But first I need to find the references that you say are here, pointing to specific Paragraphs and Equations and errors in my essay.

PS: If you can help in this latter regard, that would be great. After all, it's you that says that they are here.

With best regards; Gordon

[harry]

Once more: no, the above detailed reconstruction does not correctly reproduce Bell. We overlooked the fact that of course he held lambda constant when he integrated over lambda (it's an unforgettable sin not to do so). And because of that he had to include the relative frequency (probability) of each lambda - something that is glaringly missing in the above reconstruction, because that reconstruction ignores what he really tried to do.

Harry,

Do you believe the following integrals misrepresent what Bell was trying to do?





Note that Bell did not specify a range for his definite integral. So we supply ranges for him, consistent with what he was doing, and with what makes sense, given the thought experiment he had in mind.

Yes, I'm sure that that misrepresents what Bell did, as I and others tried to explain several times. I'll do a last attempt to clarify it:

Once more, he had no thought experiment in mind! There are two ways to go at such a problem:

1. calculate according to theoretical assumptions. As I illustrated, such a calculation doesn't need to simulate an experiment at all.
2. do a simulation of an experiment.

Bell and others had been trying method 2 for a while without success, and many people are continuing that route. However, such simulations cannot prove that a successful simulation using unimagined parameters isn't possible. Therefore Bell next went for option 1. But if I understand it correctly, you and Gordon still think that Bell continued with option 2, just putting the simulation of an experiment in equations instead of in FOR-NEXT loops. But then he could not achieve what he claimed to achieve, as indeed:

[..] in such experiments we have no control over lambda,

Thus instead, in his theoretical calculation based on probability theory he bunched together expected results for every lambda (as is also clear from the math).

[..] Now Watson's point is that with the sensible choice we just picked above, it is impossible to complete Bell's derivation, unless some rather unphysical and unreasonable assumptions are made about the integration range.

That "sensible choice" was a dead end that Bell did not attempt, or at least, did not publish; you're shooting at a strawman. What remains is what many other publications debate: if Bell's assumptions are warranted or not.

One of the other posters have suggested that we can assume that the three sets are the same since according to him "Nature is the one picking lambda, and we can assume that nature picks the same set of lambda everytime". Of course, such an assumption will allow the derivation to proceed but is such an assumption reasonable? Definitely not.

Why not?? According to observations and asserted by QM, nature delivers reproducible results. That means repeatable statistics. Repeatable statistics implies that the same statistical environment is present every time. It's the starting point for Bell's derivation.

There is nothing about local hidden variable theories that implies nature must pick the exact same set of lambdas every time -- none whatsoever.

Then how can results be reproduced? I saw the argument that maybe the same lambda never comes back. That sounds good but is a hollow argument: the same effective lambda must come back to yield repeatability. Thus for example, for the experimental outcomes one must have lambda_2438 = lambda_215, etc, else no results reoccur in contradiction with QM theory (and also in contradiction with experience).

Some may be tempted at this point to invoke "law of large numbers". However, a deflating question to squash that thought is: How many particle pairs should be measured, to make sure that we have sampled enough distinct values of lambda to obtain the same probability distribution in each of the correlations? 100000, 1000000, .... ??? As soon as anyone tries to answer this question, they immediately realize that they will have to make an additional assumption about the number of distinct values of lambda which exist! More candidates for rejection when the inequality is violated.

As you hopefully now understand, Bell's calculation is an integral over the whole (assumed to be infinite) set of lambda's. Gordon's paper does not address that issue.

To pre-empt "non-replies" which claim contrary to fact that Bell was not talking about experiments, [...]

Such replies were just as imprecise as the allegations that those replies addressed; which is why I replied with more precision and with an example.

[Ben6993]

Q-reeus wrote on Tue Jul 01, 2014 1:54 am

Please supply relevant link(s)! [and assuming YouTube, the relevant time(s) into lecture(s)]

Leonard Susskind's autumn 2012 lecture 2 http://www.youtube.com/watch?v=-nBOCF0s ... 5MmILu1nBo on Supersymmetry & Grand Unification. He starts with the topic of 4pi rotations. Dirac's belt for the first 9 minutes. The next five minutes covers magnetic field rotations in a double slit experiment, and the following five minutes cover relevant questions from the audience. He did not say he had done the experiment himself (so I remembered that incorrectly), but that he and Aharonov suggested the experiment in 1967, and that the experiment has been done.

[Joy Christian]

Q-reeus wrote on Tue Jul 01, 2014 1:54 am

Please supply relevant link(s)! [and assuming YouTube, the relevant time(s) into lecture(s)]

Leonard Susskind's autumn 2012 lecture 2 http://www.youtube.com/watch?v=-nBOCF0s ... 5MmILu1nBo on Supersymmetry & Grand Unification. He starts with the topic of 4pi rotations. Dirac's belt for the first 9 minutes. The next five minutes covers magnetic field rotations in a double slit experiment, and the following five minutes cover relevant questions from the audience. He did not say he had done the experiment himself (so I remembered that incorrectly), but that he and Aharonov suggested the experiment in 1967, and that the experiment has been done.

Ben,

Several such experiments have been done. Please see references [6], [7], and [8] of this paper: http://arxiv.org/abs/1211.0784.

[harry]

Hello Gordon, I'm back.
[..]
OK. The point was not the ordering of the sequence (indeed you are free to change the order) but the sequence itself: the data. As I stressed next by means of an illustration, Bell did not calculate according to experimental data collection.

Harry; with a BIG welcome back!

Now, since experimental data can be collected any way you like, what do you mean: "Bell did not calculate according to experimental data collection"?

I hope that my preceding reply to minkwe was clear enough; in view of the same arguments I'll not comment on everything here. Bell grouped the terms of integration according to the same effective lambda's, which is possible in a calculation but not in an experiment. Therefore I told you, and I hope that you follow it now:

[..] Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ - and not a λi and a different λn+i which have different outcomes.

So let me follow your illustration IN THE CONTEXT of my essay! You are playing the bisexual role of Alice and Bob combined, right? For YOU know both measurement outcomes; A = 230 cm and B = 240 cm, right? So you THEN get the average as 235 cm, right? So bisexual you has been able to act as coincidence-counter and expectation/average calculator, right?

I'm afraid that you read too much in my simple example, the point I tried to make is much more basic, see next.

And here's your MATHS! (A + B)/2 = 235 cm.

But the carpenter is ALSO the (duplicate/backup) coincidence-counter (placing - NB my accuracy here - the short beam on top of the long; and think voltages), duplicating your effort. As well, the carpenter is also the (duplicate/backup) expectation/average calculator in his bi-role, too, right?

So he goes, correctly, as programmed in trade-school: A + (B-A)/2 = (A + B)/2; in readiness for measurement.
[..]

Contrary to what you think, the LHS corresponds to an experimental procedure that a differs from the RHS! The carpenter was not duplicating my effort. The room in which he was working was perhaps not even long enough so that he could not lay the two beams head-to-tail. Theoretical considerations allowed me to calculate in a way that reflects an impossible experiment that nevertheless should give the same outcome as the actual one that was performed.
Bell did the same, or at least, he argued that he did.

What is the physical significance (when studying EPRB) of "Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ"?
[..]

As I stressed with my simple illustration with the possibly unphysical significance of my average length calculation (a+b)/2, in mathematics one can do what is impossible in physical experiments, and nevertheless expect to obtain a physically significant answer out of it. That is also what gill tried to explain to you and minkwe earlier.

[..]

Bell did similarly not stick to the experimental procedure for his derivation of what may be predicted as experimental outcomes. That doesn't mean that Bell didn't make a mistake of course; but he did not mix up the λ's.
[..]
Bell certainly matched his λ's, as can be seen from his math notation. Any criticism on Bell's derivation must start from that fact.

It is not clear (to me) what fact we must start from? Perhaps, if you told me where you'd like to start, then I could start there and get the same result: Bell's theorem refuted.

See my reply to minkwe.

Once more: no, the above detailed reconstruction does not correctly reproduce Bell. We overlooked the fact that of course he held λ constant when he integrated over λ (it's an unforgettable sin not to do so). And because of that he had to include the relative frequency (probability) of each λ - something that is glaringly missing in the above reconstruction, because that reconstruction ignores what he really tried to do.

How, exactly, does he hold λ constant when he integrates over it? Don't constants come out of the integral as constants?
What am I missing here, please?
Please explain this, which should not be beyond me but is: (it's an unforgettable sin not to do so). [..]

In an integral with λ, just as in an equation with x, if λ or x appears several times (without suffix) then it must be the same λ or x, else you make a fundamental blunder. For example to calculate y= x + 2x^2 you cannot plug in x=3 for the first appearance and x=8 for the second one.

[..] Please explain: How do λ recur in EPRB? Except by mistakenly thinking of them as being some beable to do with Bertlmann's finite number of socks?

See my repy to minkwe. In EPRB, if one does the same experiment again one reproduces the same outcomes for n->infinite.

Thus, your question about "experimentally valid" is too ambiguous. Compare once more: my average calculation about the carpenter's experiment gives the correct experimental result but does not match experiment. Do you call that "experimentally invalid"? Depending on your answer, in your wording we then get that Bell's 1964:(14a) IS / IS NOT experimentally valid. And the same for all what follows.

Harry, surely: There's a BIG misleading TYPO here!! [..]
Bell's (14a) is FINE! It IS experimentally valid! Surely we ALL agree on that?

No typo! (14a) corresponds to an impossible experiment, but your answer that it is experimentally valid allows me to reply your question. If Bell's first equation is experimentally valid, then so are his following equations if we accept his arguments. However, I still suspect that at least one of his arguments is wrong, as his final inequality leads to an extremely unlikely conclusion.

[gill1109]

If Bell's first equation is experimentally valid, then so are his following equations if we accept his arguments. However, I still suspect that at least one of his arguments is wrong, as his final inequality leads to an extremely unlikely conclusion.

What is unlikely about his conclusion?

Do you mean that you believe in LHV and QM hence cannot accept that Bell finds some kind of contradiction?

So far no experiment has been done for which there is not an explanation with LHV, because of the loophole issues. Some people believe that QM itself makes it impossible that an experiment can be done which does *not* have an LHV explanation. This is what I call "Bell's fifth position".

If you read Bertlman's socks you'll find that Bell gives a list of four, not exhaustive, logically possible positions which one could take, having considered his arguments. Obviously he had a personal inclination (which actually seems to have changed over the years). But his work does not lead to a *conclusion*.

I am amazed that people keep suggesting that Bell's work leads to some kind of more or less impossible conclusion. It doesn't lead to a conclusion at all.

[Joy Christian]

If Bell's first equation is experimentally valid...

Bell's first equation is operationally valid but "functionally" and topologically invalid: http://libertesphilosophica.info/blog/d ... orem-book/.

Therefore Bell's so-called theorem is a non-starter: http://arxiv.org/abs/1405.2355.

[Q-reeus]

Leonard Susskind's autumn 2012 lecture 2 http://www.youtube.com/watch?v=-nBOCF0s ... 5MmILu1nBo on Supersymmetry & Grand Unification. He starts with the topic of 4pi rotations. Dirac's belt for the first 9 minutes. The next five minutes covers magnetic field rotations in a double slit experiment, and the following five minutes cover relevant questions from the audience. He did not say he had done the experiment himself (so I remembered that incorrectly), but that he and Aharonov suggested the experiment in 1967, and that the experiment has been done.

Thanks for the link and synopsis. At a stretch it could be argued he performed such an experiment 'by hand' right there between 0:52 and 1:28 with that crazy dance move demo version of Dirac belt trick. Of course a proper 4pi rotation with no sneaky back twists would have his arm ripped from shoulder . I recall but can't find an old Scientific American article that gave examples of practical classical physics applications. One was an optical 'rectifier' that via a series of prisms transformed a rotating reference frame view into a still. An article commenter also claimed at least some helicopters make use of Dirac belt trick in connecting wiring and/or hydraulic tubing between rotor hub and 'fixed' fuselage.

[minkwe]

Do you believe the following integrals misrepresent what Bell was trying to do?





Note that Bell did not specify a range for his definite integral. So we supply ranges for him, consistent with what he was doing, and with what makes sense, given the thought experiment he had in mind.

Yes, I'm sure that that misrepresents what Bell did, as I and others tried to explain several times. I'll do a last attempt to clarify it:

Once more, he had no thought experiment in mind!

You are sure I'm misrepresenting Bell but you do not specify how or what. Please state exactly why you believe any of the three expressions I wrote above misrepresent Bell. Can you or can you not elaborate on that point?

Have you read Bell's paper? Can you have measurements without having an experiment?

There are two ways to go at such a problem:

1. calculate according to theoretical assumptions. As I illustrated, such a calculation doesn't need to simulate an experiment at all.
2. do a simulation of an experiment.

Bell and others had been trying method 2 for a while without success, and many people are continuing that route. However, such simulations cannot prove that a successful simulation using unimagined parameters isn't possible. Therefore Bell next went for option 1. But if I understand it correctly, you and Gordon still think that Bell continued with option 2, just putting the simulation of an experiment in equations instead of in FOR-NEXT loops. But then he could not achieve what he claimed to achieve, as indeed:

You do not realize that it is possible to theorize about experiments. This is what physics is all about. So please state clearly where exactly any of the three expressions above misrepresent Bell, if you can.

That "sensible choice" was a dead end that Bell did not attempt, or at least, did not publish; you're shooting at a strawman. What remains is what many other publications debate: if Bell's assumptions are warranted or not.

I simply specified all the possibilities and none of them saves Bell. If you claim none of them is what Bell chose, then tell us the other option you believe he chose if his equations must continue to be valid?

Then how can results be reproduced?

What results? It is easy to make this mistake. Long running averages of correlations between A and B are reproduced, but the individual outcomes [+1, -1] are never reproduced. It is at this level that this discussion is focused. The factorization that happens inside the integral happens at this level. It is at this level that Gordon's argument about AiAj =/= 1 applies. Do not be fooled that because long running averages of correlations between A and B are conserved means the results of the experiments are reproduced. They are not. You can even take a look at my simulations which have reproducible correlations without the same distributions of lambda and without reproducible individual results.

Please read this paper: http://arxiv.org/pdf/quant-ph/0604124v2.pdf

I saw the argument that maybe the same lambda never comes back. That sounds good but is a hollow argument: the same effective lambda must come back to yield repeatability.

The question is not whether the same lambda never comes back. The question for you is: Can Bell's derivation proceed if just one of the lambdas does not come back? And what is the basis of your blatant proclamation that correlation will not be reproduced unless ALL the lambdas come back? My simulations proof you wrong. Read the above paper. The point being made which you apparently have failed to grasp is not about what correlations you get at the end, but what inequalities to compare the correlations you get.

Thus for example, for the experimental outcomes one must have lambda_2438 = lambda_215, etc, else no results reoccur in contradiction with QM theory (and also in contradiction with experience).

QM does not predict individual results, so you are confusing re-occurrence of lambda with reproducibility of long-running averages. The cosine correlations are not due to the relationship between one lambda and the next, but rather due to the relationship between one particle and it's twin for the same lambda. The different distribution of lambda prevents Bell from factorizing as he did within the integral. If you read the above article, you will understand that even if every lambda encountered for P(a,b) was also encountered for P(b,c) and for P(a,c), you will will not be able to do the factorization unless the sequence of the lambda's is exactly the same. In short, Bell's factorization can only be done if you start with a single spreadsheet with three columns a,b,c and recombine the columns in pairs. If you start with three 6 different columns, even if the same lambdas are in each one in different orders, you must in principle be able to resort them into 3 effective columns for the derivation to proceed. The above paper shows that the resortings required to achieve this are incompatible. In yet other words, the numbers of degrees of freedom for 6 columns is different for 3 columns and that is why the inequality must have a different upper bound for 6 columns, and that is why AiAj =/= 1 as Gordon argues.

[minkwe]

Exactly. The Christensen et al. experiment http://arxiv.org/abs/1306.5772
And there is the Giustina et al. experiment http://arxiv.org/abs/1309.0712

2013 was a miraculous year. Till last year there was no experiment done which could not be explained by LHV. However, things have changed that last year. The detection loophole was at long last overcome for experiments with photons.

Actually in those experiments there is still a "locality" loohole because the two detectors were not far enough apart. In principle, the setting used in one arm of the experiment could be communicated to the other before the measurement in the other arm is concluded. However, there are other photon experiments with no locality loophole. There does not seem to be any reason why there won't be an experiment in a year or two (at Växjö the experts predicted within a year from now) which overcomes both loopholes. As Jan de Raedt agreed, there will be no longer a LHV explanation of that experiment, if it is succesful. Michielsen (his wife) believes that that experiment won't be succesful. She believes in LHV. de Raedt however has an open mind.

So Heinera and Gill believe that the results of the Christensen and Giustina experiments can not be explained by LHV. Is that correct? Note that even the authors of those papers themselves do not believe that as if obvious if you actually read the papers.

[gill1109]

The different distribution of lambda prevents Bell from factorizing as he did within the integral.

The distribution of lambda is the same for each particle pair, *if* the settings are repeatedly chosen anew, at random.

This is called "randomization".

This is why in Evidence Based Medicine, we trust randomized double blind clinical trials.

To further ensure the benefits of randomization, in Evidence Based Medicine, we use the "intention to treat principle" to deal with non-compliance. We include an outcome from every patient even from those who refuse to take their medicine.

This is why the best CHSH experiments have "event-ready detectors" (no post-selection) and "delayed choice settings" (settings chosen at random "while" the particles are in flight). We use the CH or Eberhard inequality, or CHSH with "no-detection" treated as the outcome zero. This is why the best experiments are pulsed. This is why we avoid the coincidence loophole by defining a fixed system of coincidence windows, instead of coincidence windows determined by the particles themselves.