Commonsense local realism refutes Bell's theorem

[minkwe]

So let me get this straight. You say the three expectation values in Bell's inequality represent separate measurements on three different sets of particles. This is clearly what Watson has done. He shows that within the weakly objective interpretation, which is the one applicable to performable experiments, Bell's inequalities can not be derived. This is also what Adenier showed more than 10 years ago.

Not only that, I've already shown you elsewhere and you agreed that the upper bound for the weakly objective inequality is not the same as that for the strongly objective one, due to different degrees of freedom in the two. Yet you say Adenier is confused. Do you now see that it is you who is confused?

[gill1109]

So let me get this straight. You say the three expectation values in Bell's inequality represent separate measurements on three different sets of particles. This is clearly what Watson has done. He shows that within the weakly objective interpretation, which is the one applicable to performable experiments, Bell's inequalities can not be derived. This is also what Adenier showed more than 10 years ago.

Not only that, I've already shown you elsewhere and you agreed that the upper bound for the weakly objective inequality is not the same as that for the strongly objective one, due to different degrees of freedom in the two. Yet you say Adenier is confused. Do you now see that it is you who is confused?

Watson is wrong, as we already explained. Bell's derivation has got nothing whatsoever to do with what experiments can and can not be done, but about the mathematical models which may or may not "explain" what is observed in experiments which can be done.

It seems to me that you are still confused! So perhaps we should leave it there ...

You think that Einstein Podolsky and Rosen were totally nuts?

I'll ask Adenier next week where he now stands. From his recent work I get the impression he has "moved on" from the misconceptions of his youth.

[minkwe]

Yes.

See

https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Instrumentalist_interpretation

It's just the usual frequentist interpretation of probability. It works pretty well in science. See "Introduction to mathematical statistics and data analysis" by John A Rice. Excellent text book with practical introduction to probability theory and then to statistics.

Surely you must understand that the the frequentist interpretation of probability applies to both "strongly objective" and weakly objective interpretations so I wonder why you would even bring that up in this discussion at all.

Secondly, since you have now committed that you are relying on the "weakly objective" interpretation of those expectation values, could you please explain how "counterfactual definiteness" is relevant to Bell's inequalities. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".

Remember I asked you if you were sure and you said yes, so there is no turning back now.

[minkwe]

Watson is wrong, as we already explained. Bell's derivation has got nothing whatsoever to do with what experiments can and can not be done, but about the mathematical models which may or may not "explain" what is observed in experiments which can be done.

But I'm explaining to you why it is you who has not understood the issue. The issue is about an interpretation of what the expectation value terms mean. You have picked the "weakly objective" interpretation. Within that interpretation, the inequalities can not be derived. Within that interpretation, there are no counterfactual expectation values.

Do you now want to change your mind? You are free to do that too. All I ask is that whatever you pick, you should be consistent with it and I'll make sure I hold your feet to the fire that you are being consistent.

[gill1109]

Could you please explain how "counterfactual definiteness" is relevant to the discussion. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".

A local hidden variables model allows us to mathematically entertain all outcomes of all conceivable measurements simultaneously. The model says that there is a set Lambda and a probability distribution rho(lambda) on it. For any lambda, all A(a, lambda) and all B(b, lambda) are well defined random variables, for all a and b simultaneously. I can mathematically study their joint probability distribution, their expectation values, whatever I like ...

There is no experiment. I am not modelling an experiment. I am doing mathematics. I derive a relation between A(a, b), A(a, b'), A(a', b), A(a', b') which must hold because these four *mathematical* objects have certain *mathematical* representations: A(a, b) = int A(a, lambda) B(b, lambda) rho(lambda) d lambda.

So if the A(a, b) etc which we "observe" in experiment have as an underlying explanation a hidden variables model, then the same relations must hold between them. And if those relations fail to hold, then obviously the underlying explanation which we had in mind, must have been false.

[minkwe]

Could you please explain how "counterfactual definiteness" is relevant to the discussion. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".

A local hidden variables model allows us to mathematically entertain all outcomes of all conceivable measurements simultaneously. The model says that there is a set Lambda and a probability distribution rho(lambda) on it. For any lambda, all A(a, lambda) and all B(b, lambda) are well defined random variables, for all a and b simultaneously. I can mathematically study their joint probability distribution, their expectation values, whatever I like ...

There is no experiment. I am not modelling an experiment. I am doing mathematics. I derive a relation between A(a, b), A(a, b'), A(a', b), A(a', b') which must hold because these four *mathematical* objects have certain *mathematical* representations: A(a, b) = int A(a, lambda) B(b, lambda) rho(lambda) d lambda.

So if the A(a, b) etc which we "observe" in experiment have as an underlying explanation a hidden variables model, then the same relations must hold between them. And if those relations fail to hold, then obviously the underlying explanation which we had in mind, must have been false.

So now you are picking the strongly "objective interpretation". Do you now see that it is you who is confused? Do you want to switch to the "strongly objective view", as implied by your "explanation" above?

[gill1109]

Watson is wrong, as we already explained. Bell's derivation has got nothing whatsoever to do with what experiments can and can not be done, but about the mathematical models which may or may not "explain" what is observed in experiments which can be done.

But I'm explaining to you why it is you who has not understood the issue. The issue is about an interpretation of what the expectation value terms mean. You have picked the "weakly objective" interpretation. Within that interpretation, the inequalities can not be derived. Within that interpretation, there are no counterfactual expectation values.

Do you now want to change your mind? You are free to do that too. All I ask is that whatever you pick, you should be consistent with it and I'll make sure I hold your feet to the fire that you are being consistent.

Thank you. Do please remain critical and sharp.

I disagree with you. Within the weakly objective interpretation, the inequalities can be derived. Bell derived them, so did I. Watson was confused. He thought that the lambdas in Bell's famous expression had to be numbered 1, 2, ... and were subsequent lambdas occuring in one run after another of the experiment. But he was wrong. As we already extensively discussed.

[gill1109]

Could you please explain how "counterfactual definiteness" is relevant to the discussion. Surely you must understand that there are no counterfactual terms in the "weakly objective" interpretation as opposed to the "strongly objective" one. So since your recent paper spends a lot of ink talking about counterfactual definiteness, please explain how it arises in the "weakly objective view".

A local hidden variables model allows us to mathematically entertain all outcomes of all conceivable measurements simultaneously. The model says that there is a set Lambda and a probability distribution rho(lambda) on it. For any lambda, all A(a, lambda) and all B(b, lambda) are well defined random variables, for all a and b simultaneously. I can mathematically study their joint probability distribution, their expectation values, whatever I like ...

There is no experiment. I am not modelling an experiment. I am doing mathematics. I derive a relation between A(a, b), A(a, b'), A(a', b), A(a', b') which must hold because these four *mathematical* objects have certain *mathematical* representations: A(a, b) = int A(a, lambda) B(b, lambda) rho(lambda) d lambda.

So if the A(a, b) etc which we "observe" in experiment have as an underlying explanation a hidden variables model, then the same relations must hold between them. And if those relations fail to hold, then obviously the underlying explanation which we had in mind, must have been false.

So now you are picking the strongly "objective interpretation". Do you now see that it is you who is confused? Do you want to switch to the "strongly objective view", as implied by your "explanation" above?

I am weakly objective as far as the connection between theory and experiment is concerned. Within theory, I just use mathematics. Within theory, interpretation is irrelevant.

Actually I think this is the root cause of all endless discussions here. We must distinguish between doing calculus and set theory within a mathematical framework, and interpreting what goes into that, and what comes out of that, by some interpretation of the physical meaning of probability.

Michel, I think this could be a Eureka moment ...

[minkwe]

But the inequalities can not be derived in the weakly objective view. This is what Adenier showed. This is what Watson has shown. This is what I have shown here on multiple threads. In fact, even your very own LG paper, relies on this fact. The fact that the ensembles must be the same to obtain the inequalities. Do you want me to quote your own paper to you.

See for example this thread: viewtopic.php?f=6&t=39

I've previously explained and you agreed that the number of degrees of freedom in the "weakly objective" interpretation is different from the "strongly objective" one. Are you now denying this?

[minkwe]

I am weakly objective as far as the connection between theory and experiment is concerned. Within theory, I just use mathematics. Within theory, interpretation is irrelevant.

That is precisely your problem. You are not being consistent. You use strongly objective interpretation (whether you recognize it or not) in your theoretical calculations, as evidenced by your post above, and your discussion of counterfactual definiteness in your paper, yet when it comes to comparing with QM predictions and experimental results, you use the weakly objective interpretations. That is the root of your misunderstanding (and Bell's), and the source of the paradoxes. It is precisely what Adenier wrote about 10 years ago. Now might be the time to review his paper again.

http://arxiv.org/abs/quant-ph/0006014

Bell's Theorem was developed on the basis of considerations involving a linear combination of spin correlation functions, each of which has a distinct pair of arguments. The simultaneous presence of these different pairs of arguments in the same equation can be understood in two radically different ways: either as `strongly objective,' that is, all correlation functions pertain to the same set of particle pairs, or as `weakly objective,' that is, each correlation function pertains to a different set of particle pairs.
It is demonstrated that once this meaning is determined, no discrepancy appears between local realistic theories and quantum mechanics: the discrepancy in Bell's Theorem is due only to a meaningless comparison between a local realistic inequality written within the strongly objective interpretation (thus relevant to a single set of particle pairs) and a quantum mechanical prediction derived from a weakly objective interpretation (thus relevant to several different sets of particle pairs).

Michel, I think this could be a Eureka moment ...

I hope the last 30 minutes has been an Eureka moment for you. That is why I said your answer picking "weakly objective" was opening Pandora's box.

[harry]

[..]
Ultimately, the point stands. In the EPRB experiment being discussed by Bell, in his derivation of his original inequalities, the particles can not be measured more than once, therefore Watson's analysis of Bell's original paper is correct. Bell made a fatal error which invalidates his proof. Bell's original highly acclaimed 1964 paper is wrong! [..]

As we discussed at length, Bell surely didn't suggest to measure the same particles twice or mix up lambda's. Apparently you overlooked, among other things, the simple illustration that I gave you a few days ago:

[..] A carpenter determines the average length of two similar beams as follows: He places them on top of each other, puts a mark halfway between the ends of the two beams as follows:

-------------- . . . . x
---------------------------------

Next he measures the length upto the mark of the top beam. I see him do that, and happen to know the lengths of the two beams.

So I calculate (230+240) / 2 = 235 cm and shout out that number to him. He shouts back: "Right - how did you know?"

My calculation should in theory give the same result as the measurement, despite the fact that there is not a 1-to-1 correspondence between the two.
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, but it does mean that Bell did not make the striking mistake that Watson ascribes (or ascribed) to Bell.

[Ben6993]

Gill1109 wrote on Sat May 31, 2014

Ben6993 wrote:
In other words, why cannot the hidden variables hide with the particle, wherever the particle is.

Because of Bell? Because, if you were right, then there would exist functions A(a, lambda) and ... and hence ... and hence your model
could not reproduce the singlet correlations.

But maybe you don't believe in the singlet correlations.

Or maybe it is OK by you that Alice's choice of a influences not only the lambda of her particle but also that of the other particke.

As I see it, Joy's analytic papers show the same cosine correlation as does QM. And in the those papers there is no influence of Alice on Bob or vice versa. The simulations, though, are different, and the meaning of zero outcomes has no consensus at present. If I understand it correctly, there is no loophole-free experimental evidence that the Bell experiment actually produces a cosine correlation? So, as yet, the cosine relationships of both QM and Joy are only achieved theoretically?

In a different strand, Joy has used or wanted to use, in one sum in a simulation, two left-handed bases and two right-handed bases. I am not an expert on geometric algebra but I believe this is a similar issue to one point that was raised by others against his analytic papers. I saw nothing wrong with his using both handednesses in one formula in his papers because of the need to take into account the double cover of spacetime which I believe geometrical algebra is said to represent. I presume that the use of only one handedness at a time could maybe give a match to spacetime i.e. to the laboratory space of observable outcomes?

I am not sure if Joy's cosine correlation inhabits the laboratory space or inhabits only the geometric algebra space. I assumed the latter. If that is true, there is no hope of obtaining that relationship in a table of observables. It could be that using dual handedness in the simulation calculation is turning a laboratory correlation into a geometrical algebra correlation, i.e. making an unobservable correlation. But I may be completely wrong and no doubt will need to be corrected.

I had always assumed that the QM correlations were in the laboratory space. But if they are then they should be found (eventually) in the laboratory ....
The lack of consensus on simulating a 4xN table showing the cosine correlation doesn't give me confidence that QM correlations are observables. Do they only exist in an abstract (Hilbert) space?

[minkwe]

...

Harry,
Unfortunately I think you do not yet understand the issue. Maybe if you answer the same question that Gill just did, you might begin to understand it:
What interpretation do you believe applies for the terms in Bell's inequality, strongly objective or weakly objective? What interpretation do you use for the terms from QM, strongly objective or weakly objective?

To remind you :

The set of values E(a,b), E(a,c) and E(b,c) does not tell you which interpretation to use. The "weakly objective" interpretation says the three expectation values represent separate measurements on three different sets of particles, The "strongly objective" view says they represent joint properties of a single set (aka population means).

So which interpretation do you use. Gill has already picked "weakly objective". Once you answer that, then we will discuss what the real issues are.

[harry]

[..]
So which interpretation do you use. Gill has already picked "weakly objective". Once you answer that, then we will discuss what the real issues are.

I think that you project your thinking about "what the issue is" on what Watson wrote. It is clear to me and Gill that, as he put it, "Watson thought that the lambdas in Bell's famous expression had to be numbered 1, 2, ... and were subsequent lambdas occuring in one run after another of the experiment."
If you disagree, please state what you think how Watson interpreted Bell's derivation (it definitely was how I meant it when I first elaborated on Watson's argument!). And then hopefully Watson will clarify who understood his argument correctly.

[gill1109]

As I see it, Joy's analytic papers show the same cosine correlation as does QM. And in the those papers there is no influence of Alice on Bob or vice versa. The simulations, though, are different, and the meaning of zero outcomes has no consensus at present. If I understand it correctly, there is no loophole-free experimental evidence that the Bell experiment actually produces a cosine correlation? So, as yet, the cosine relationships of both QM and Joy are only achieved theoretically?

...

I had always assumed that the QM correlations were in the laboratory space. But if they are then they should be found (eventually) in the laboratory ....
The lack of consensus on simulating a 4xN table showing the cosine correlation doesn't give me confidence that QM correlations are observables. Do they only exist in an abstract (Hilbert) space?

Ben, unfortunately, Joy's analytic papers contain (in the opinion of many readers) fatal errors. See for instance my http://arxiv.org/abs/1203.1504. So yes, he does get the cosine correlation, but he only gets it by using sloppy and ambiguous terminology and notation and changing definitions half-way through his derivation.

The QM correlations are the correlations between measurements of observables. Experimenters have succesfully measured them many times. They were not yet succesful in doing this in the frame-work of a delayed-choice, event-ready-detectors, experiment. This is jargon for an experiment where two particles are measured at two distant locations, rapidly, and according to randomly chosen settings. The measurement of particle 2 is completed before information could reach that location as to *how* particle 1 is being measured. Not only is the measurement completed but it is also always succesful. The outcome is +/- 1. No "non detections".

This has not quite been done yet, but nearly.... they say they will be there within five years (actually, they said that, three years ago...)

[gill1109]

Michel:

Bell's derivation does not assume that particles can be measured more than once. Bell shows that the assumption of a local hidden variables theory implies certain limits on correlations which can be observed in Nature, if Nature could be described by such a theory. There is no need to "rescue" his 1964 paper, but there certainly was possibility to remove ambiguities and sharpen the results. Bell's 1980 (?) "Bertlmann" paper already improves and sharpens Bell (1964) in numerous respects.

My own recent work is a further *strengthening* of Bell's. Bell's 1980 results, which improve on those from 1964, are a *corollary* of mine. I derive finite N probability bounds, but Bell only has infinite N limits.

A local hidden variables *theory* implies the mathematical existence, simultaneously, within the theory, of outcomes of different potential measurements. The measurements don't need to be *done*. They aren't *done* within the derivation of the famous inequalities.

When deriving the CHSH inequality we are not talking about measurements at all, and certainly not about multiple measurements on the same particles. We are talking about mathematical relations between functions A(a, lambda), B(b, lambda) and a probability distribution rho(lambda). The functions A and B only take the values -1 and +1. We determine that the functions E(a, b) = int A(a, lambda) B(b, lambda) rho(lambda) d lambda are not completely arbitrary but have to satisfy certain relations, in particular we find
E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 2


In quantum theory, correlations are computed in a different way using various Hillbert space objects (operators, states, ...). One can also work within quantum theory and assuming a product system, pairs of POVM measurements on each system with outcomes -1 and +1 only, and an arbitrary joint quantum state rho, prove the Tsirelson inequality
E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 2 sqrt 2.

If we only assume no action at a distance (at the surface level), one can only prove the PR inequality (Popescu-Rohrlich)
E(a, b) + E(a, b') + E(a', b) - E(a', b') <= 4

All of this theoretical work has got nothing whatsoever to do with actual experiments. The calculations do not presuppose some weird experiment during which all kinds of impossible things are done. They show that if you believe that a certain kind of theory underlies the correlation which we see in Nature, then those correlations will satisfy certain properties. They can't be just anything.

When we do experiments we get to learn something about E(a, b), up to statistical error, by many times doing a particular measurement on pairs of particles. We learn about E(a, b') by measuring other particles in a different way.

It's very hard for me to understand why this is so hard to understand ... but perhaps it would help to have some understanding of statistics and real experiments.

For instance if we are interested in whether people are getting more intelligent, we could take a sample of fathers and a sample of sons and look at the difference between the average IQ's of the fathers and of the sons. Alternatively we could take a sample of father-son pairs and look at the average of the differences. For given sample sizes, the second route is more accurate than the first route, but the first route is not invalid. Of course we do have to take care that our sample of fathers and our sample of sons are random samples from the same population as the sample of father-son pairs, otherwise things go wrong.

Exactly as in Bell-EPR experiments. If we measure a lot of time one pair of settings, and then another lot of time another pair of settings, maybe things have changed in the lab between the first batch and the second batch and the two samples of pairs of particles are not samples from the same population.

Or if we reject particles which arrive too early or too late at our detectors, maybe the particles which are left are not a random sample from all particles.

This is why good EPR-B experiments are done with delayed-choice settings and event-ready detectors. It's like the preference for a randomized double blind clinical trial above an observational study when testing new medications. We can't test both treatments on the same patient. We can only treat each single patient in one way. Yet we do clinical trials and tell the world that the new treatment is better than the old one.

Seems that Watson, Adenaur and now Fodje have no belief whatsoever in evidence based medicine. Because we can't both give a breast-cancer patient a mastectomy and a breast-preserving operation, we can never tell which treatment is better.

[Joy Christian]

Ben, unfortunately, Joy's analytic papers contain (in the opinion of many readers) fatal errors. See for instance my http://arxiv.org/abs/1203.1504. So yes, he does get the cosine correlation, but he only gets it by using sloppy and ambiguous terminology and notation and changing definitions half-way through his derivation.

Unfortunately Richard Gill is far too incompetent in elementary algebra (and mathematics in general) to see his own silly errors: http://arxiv.org/abs/1203.2529. His claim that my "analytic papers contain (in the opinion of many readers) fatal errors" is a slanderous lie---a calculated attempt to mislead the physics community.

It is actually quite amusing that he claims there are errors in my analytic papers. There are in fact no errors. The whole idea of "errors" was manufactured by him and other incompetent and uninformed individuals for social and political purposes. The so-called “errors” are simply made up. This has been obvious to a number of knowledgeable people, who are too polite to point out his own errors to him. In particular, my analytic equations have been checked in great detail by Lucien Hardy---an exceptionally competent and well known expert in foundations of quantum mechanics. He immediately spotted Gill’s silly mistake: “They didn’t understand that parity is the hidden variable in your model.” I have of course pointed this out to him, literally hundreds of times, most elaborately in the above paper. His error was also spotted at once---a long time ago---by Bill Schnieder. Here is what Bill Schnieder wrote on Physics Forums long time ago:

"Richard Gill's refutation is not a new critique. It is essentially the same as one of the critiques advanced by a certain Florin Moldoveanu in the fall last year to which Joy Christian has already replied. It originates from a misunderstanding of Joy's framework which admittedly is not very easy to understand, especially for those who have blinders of one kind or another.

Gill thinks Joy is using a convoluted more difficult method to do a calculation and prefers a different method which ultimately leads him to a different result, not realizing/understanding that the calculation method Joy used is demanded by his framework. This is hardly a serious critique, not unlike his failed critique of Hess and Phillip. He should at least have read Joy's response to Moldoveanu which he apparently did not, since he does not cite or mention it. It's been available since October 2011, one-month after Moldoveanu posted his critique.

I remember Florin came here to boast about his critique and I pointed out his misunderstanding at the time in this thread:

"... you are missing the point because Joy Christian is not using handedness as a convention but as the hidden variable itself."

This is the same error Gill has made. See section (II) of Joy's response to Moldoveanu."

The bottom line is that Richard Gill has simply failed to understand my local-realistic framework because of his own incompetence in elementary algebra. In fact the incompetence of Richard Gill is well known among the experts in foundations of quantum mechanics. Here is what Karl Hess has to say about him:

Dear Joy,

I am sorry to hear about your plight with Gill. He is a third rate mind and I had the following experience with him. After Walter and I wrote the PNAS paper about the role of time, Gill wrote a number of counter-papers with Zeilinger and others stating repeatedly that time was irrelevant and that our papers were non-local because our probability density depended on the settings of both sides but was not a product density. Then after three years of harassing us (I had to block his e-mails), he had turned himself into a complete pretzel and had to admit that time plaid a role after all. By choosing suitable delay times between the experiments with different settings one can easily get a violation. He wrote a paper with Larsson that repeated that our work was still non-local, because we had a setting dependent probability density. They did not need it because their parameters $\Lambda_{A, C}$ depended on the settings of both stations. They ignored that this were, of course, exactly our time and setting dependent equipment parameters that did the job, and stated after their equation 6 that their dependence was permitted because of the involvement of time delays, and one just needed to remember were their dependence on both settings came from. This is in the literature and can be read by anyone and I would say that most serious people who understand the text would conclude that Gill showed definitely dishonest behavior and just adopted our (more general ) idea, and made it their own and stated that we were wrong.

Gill also e-mailed Walter that he should not work with me, because I was just an ignorant engineer (I am actually a member of both the National Academy of Science and Engineering and Walter knew that, of course).

It is terrible that a third rater like Gill can do so much damage. Mermin wrote an e-mail to Walter saying in essence that Gill is a card holding probabilist and must therefore know what he says.

This whole story reminds me of Goethe's word:

Those who exclusively for truth have yearned
and then discovered it
Have been since ages crucified and burned.

One might like to add that there always were those like Gill that tried to make innocence and honesty suffer.

Best wishes,

Karl

There are other comments and details by Karl that are far more damaging for Gill. I will publish them here if Gill continues his unwarranted attacks on my work.

Dear Joy,

I fully agree with what you said below. Please also feel free to let anyone know what I think of Gill.

Best wishes, stay in touch,

Karl

[gill1109]

His claim that my "analytic papers contain (in the opinion of many readers) fatal errors" is a slanderous lie --- a calculated attempt to mislead the physics community.

I tried very hard to make a careful and true factual statement. Notice the qualification "in the opinion of many readers".

Obviously it is hurtful to Joy Christian: it is not nice when other people tell you you have made a mistake. However, it can be cruel to be kind; not saying it, would be lying by omission.

Here are some names of such readers: Scott Aaronson, Lucien Hardy, Florin Moldoveanu, Bryan Sanctuary, Han Geurdes, Adrian Kent, Abner Shimony, David Hestenes, Manfried Faber, Azhar Iqbal, Chantal Roth, Samson Abramsky, Reinhard Werner, James Weatherall, ...

Most of these people were not influenced by me in any way.

Thus Christian's claim that my statement is a "slanderous lie" (a calculated attempt to mislead) is a very slanderous lie.

I do not attempt to mislead. I mention my opinion, and I give support for it, and I mention that it is not just my own personal opinion, but one shared by almost anyone who took a serious look at Christian's papers. Anyone who wants to study the case can take a look at Christian's one page paper, my "refutation" of it, and Christian's "refutation" of mine.

http://arxiv.org/abs/1103.1879 Disproof of Bell's Theorem, Joy Christian (Oxford)
http://arxiv.org/abs/1203.1504 Simple refutation of Joy Christian's simple refutation of Bell's simple theorem, Richard D. Gill (Leiden)
http://arxiv.org/abs/1203.2529 Refutation of Richard Gill's Argument Against my Disproof of Bell's Theorem, Joy Christian (Oxford)

As to what Mr Hess says about me, I would very much like to see more of his writings. I see that he gave Christian express permission to spread them further. These are more slanderous lies which further damage the already badly damaged reputation of Karl Hess, as well as that of anyone who spreads these lies further. Hans de Raedt, who I know well, works together with Karl Hess nowadays, and I will be seeing him next week at Vaxjo.

People who publish nonsense, and deny it when it is kindly pointed out to them, only get into worse trouble. Hess' mathematical friend Phillip slipped up in a deep calculation with their local hidden variables model, published in PNAS, accidentally dropping one of three indices, and thereby forgetting to normalize a measure to a probability measure. Instead of publishing a correction note they now claim that this was deliberate. Jan-Ake Larsson and I pointed out that the re-normalization, which was needed on both sides of the experiment, effectively saved their model but turned it into a detection loophole model. We also were inspired by their work to think more closely about the coincidence loophole which till then had not even been thought of. Hess now claims that Larsson and I stole the idea of the coincidence loophole from him. Hess works with de Raedt implementing the coincidence loophole in their event-based local-realist simulation models of past experiments. Phillip died shortly after the publication of the PNAS paper. He had been suffering from a brain tumour for some years. I understand that Hess is not well either, Andrei Khrennikov said he had some heart problems. All very sad.

[gill1109]

Michel, I think I have a way to explain something to you. I need to run your epr-simple Python program with some slight modifications and I need to save the experimental results in a way so that I can do some simple data-processing with R of the results.

Here are my requests:

Alice's settings are *only* the famous 0 and 90 degrees
Bob's settings are *only* the famous 45 and 135 degrees

It will be fine just to have

NUM_ITERATIONS = 100000

so that there will be approximately 25 000 pairs of particles measured according to each of the pairs of settings. Even one tenth of these numbers would be fine: the statistical error in the correlations will only be of size approximately +/- 0.01

The outcome of measuring each particle is either +1 or -1 or "nothing" (no particle detected). For convenience, code this with a 0 (zero).

I would like to have the following data output: for each of the four pairs of settings, a 3 x 3 table of the numbers of each kind of outcome.
Alternatively, generate a 100 000 by four data matrix containing in each row:
Alice's setting (0 or 90), Bob's setting (45 or 135), Alice's outcome (-1, 0, or 1), Bob's outcome (-1, 0, or 1).

Your simulation is what I would call a simulation of a pulsed or clocked experiment: there will be exactly 100 000 pairs of particles generated and emitted from the source, we know how they are matched with one another; we also know when either or both particle is not detected. This is what is called a 2x2x3 experiment (two parties, two settings per party, three outcomes per setting per party).

The experiment generates, as I have explained, four 3x3 tables of counts (absolute frequencies). Convert to relative frequencies, per table, and we have four 3x3 tables of empirical probabilities. If we would let the sample size go to infinity these would stabilize at certain true probabilities. Four sets of nine probabilities adding up to +1, per set.

I would like to see the empirical probabilities (relative frequencies) for a reasonably large N, say 10 000 or 100 000. And I would like to compare them with the predictions of local realism for a 2x2x3 experiment, which are namely a whole bunch of CHSH inequalities got by grouping three outcomes to two in all possible different ways, together with a bunch of CGLMP inequalities.

My prediction is that all of these inequalities will be satisfied, up to statistical error of size roughly 1 divided by square root of N.

But my prediction might be wrong, and then I might have to withdraw some papers I have written ...

[minkwe]

[..]
So which interpretation do you use. Gill has already picked "weakly objective". Once you answer that, then we will discuss what the real issues are.

I think that you project your thinking about "what the issue is" on what Watson wrote. It is clear to me and Gill that, as he put it, "Watson thought that the lambdas in Bell's famous expression had to be numbered 1, 2, ... and were subsequent lambdas occuring in one run after another of the experiment."
If you disagree, please state what you think how Watson interpreted Bell's derivation (it definitely was how I meant it when I first elaborated on Watson's argument!). And then hopefully Watson will clarify who understood his argument correctly.

So you won't answer the question? Too bad. Its your loss, you will remain confused then.