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

[gill1109]

NB: Even IF Bell was not rusty using integration -- his results are experimentally INVALID: such results tend to confuse.

For the question then arises: Was it a false assumption or just a maths error?

Bell's assumptions have been discussed and disputed for fifty years, but not many people find a math error in his calculus, given his assumptions. Some people find hidden extra assumptions (Geurdes, Pitowsky), and other people think that the overt assumptions are not justified (Christian, if I understand his position correctly; Sanctuary; possibly also Adenauer).

You say that Bell's results are experimentally invalid, and you say this because you believe (but you are wrong, IMHO) that Bell's inequality has been violated by experiments.

But Bell was very excited and happy that they were violated, almost, up to some annoying details (loopholes!) by experiment! He did not say "oh dear I must have made a slip-up in the maths". No. He gave a list of four different conclusions which might be drawn and later admitted he had missed at least one other important one.

[Gordon Watson]

Please note that the essay is based on undergrad maths and logic.

In order to decode Bell's analysis, you also need (undergraduate?) probability and statistics - a good deal more than is typically included in undergraduate physics courses. You need undergraduate probability and statistics corresponding to fields where these topics are taken seriously. You need it at at least master's level. Econometricians and psychometricians understand Bell's analysis perfectly well, unfortunately most physicists simply don't have the training. This was already lamented by A. Fine in a landmark paper in the field 40 or so years ago. Caroline Thompson was both a physicist and a statistician. Her work was ignored and worse by the physics community for years, and she sadly died young of cancer, but nowadays experimentalists are actually adopting her ideas and recommendations. They are getting close to getting the experiment right, at last; there is intense competition, so now they all keep a very critical eye on one another. About time too.

Please clarify what your claims are here please:In your essay I noticed an incorrect interpretation of the meaning of probabilistic calculations, and no accounting for statistical aspects.

Please clarify what your claims are here:

At one stage, did Caroline Thompson believe that Bell's equations were correct and that the experiments had been falsified?

Did she change her opinion?

You say they are close to getting the experiment right. Does that mean that Bell's numbers will be proven right or wrong?

You noticed an incorrect interpretation of the meaning of probabilistic calculations in my essay: so what are the Eqn and Para numbers please; and your corresponding remarks, please?

[Gordon Watson]

To repeat: I need NO loopholes (as explained earlier).

I know, great. But I point out what appeared to me to be a failure of logic in the first sentence of your posting as well as a what seemed to me to be a major misconception as to what Bell actually was trying to do. You also make what seemed to me a hidden assumption and also seemed not to know the difference between Bell's theorem and Bell's inequality. So if we are going to have a sensible discussion about where Bell went wrong it might be good to clear the air of misconceptions at the start, as to what we are talking about. For instance, if we knew where Bell was headed that might change our understanding of what is going on in formula N or sentence X. You know, the context might provide some further clues.

Just an idea... maybe I am the one who is confused.
But I see now that your terminology is rather non-standard. You say "Bell's theorem = formula so and so from Bell 1964". That is not what the rest of the world called Bell's theorem. CHSH created endless confusion by writing down a slogan and giving it a name "Bell's theorem". On wikipedia you can see what most people nowadays understand by the words "Bell's theorem" but you won't find anything like that anywhere in Bell (1964) and if you look elsewhere in Bell's work you'll find rather more complex and subtle assertions.

On the other hand, one can do these things bottom up rather than top down. You want us to start with Bell (1964) formula (15) and work upwards and outwards ... ! Not a bad idea.

I understand that you want us to talk about what is usually called "Bell's three correlation inequality" or "Bell's original inequality".

Having studied these remarks seriously, and trying to be helpful here: You are definitely confused.

Anyway, please elaborate on:

A: what appeared to you to be a failure of logic in the first sentence of my posting.

B: what seemed to you to be my major misconception as to what Bell actually was trying to do.

C: what seemed to you to be my hidden assumption.

D: how it seemed to you that I did not to know the difference between Bell's theorem and Bell's inequality

E: Bell's three correlation inequality? Bell's original inequality? Bell-CHSH inequality? Bring them on; let's get sorted. Why not start with my Eqn (12)?

F: Define BT however you like: BUT mathematically! I correctly attributed the first use of the term to CHSH.

However, a REMINDER: As per the OP, I want to talk about specific EQUATIONS and PARAGRAPHS in my essay.

So, if comments, etc., stray too far from that specification, I may have to out them aside for now. FOR there's little point in discussing matters unrelated to my essay here, now: in this narrowly-defined thread, seeking to be highly focussed.
.

[Gordon Watson]

NB: Even IF Bell was not rusty using integration -- his results are experimentally INVALID: such results tend to confuse.

For the question then arises: Was it a false assumption or just a maths error?

Bell's assumptions have been discussed and disputed for fifty years, but not many people find a math error in his calculus, given his assumptions. Some people find hidden extra assumptions (Geurdes, Pitowsky), and other people think that the overt assumptions are not justified (Christian, if I understand his position correctly; Sanctuary; possibly also Adenauer).

You say that Bell's results are experimentally invalid, and you say this because you believe (but you are wrong, IMHO) that Bell's inequality has been violated by experiments.

But Bell was very excited and happy that they were violated, almost, up to some annoying details (loopholes!) by experiment! He did not say "oh dear I must have made a slip-up in the maths". No. He gave a list of four different conclusions which might be drawn and later admitted he had missed at least one other important one.

I find one elementary mathematical error. It reinstates Einstein's worldview : to this point, that error is not seriously challenged by you.

In 1990; 26 years after launching "his theorem", Bell:

A: is still engaged in repetitive doublethink about action-at-a-distance.

B: offers 4 or 5 different "conclusions".

C: still expects and hopes for a solution like mine; simple, constructive, maybe harsh!

I rest my case!
.

[Gordon Watson]

"experimentally valid" is not a relevant criterion

After genius Bohm put the maths together for his EPRB experiment, Bohm's calculations were proven to be "experimentally valid."

After Bell put the maths together for Bohm's brilliant EPRB experiment, Bell's calculations were proven to be "experimentally invalid."

Take your pick if you wish: but whether building airplanes or putting maths together, BOTH are relevant criteria.

Gordon, I thought you were concerned about logical errors internal to a piece of mathematics.

A recent discussion in another thread has brought to my attention that Bell did indeed think he proved a mathematical theorem. His mathematical theorem (simplest form) might be the following.

Theorem. Let A and B be two functions from the product of a set of settings (a, b ...) and a set of values (lambda ....) of a so-called hidden variable to the set {-1, +1}. Let P be a probability measure on the space of values of lambda and let E denote expectation with respect to this probability distribution. Denote A(a), B(b) etc fas the random variables defined by the maps lambda -> A(a, lambda) etc etc. Then for any a, b, a', b'

E(A(a)B(b)) - E(A(a)B(b')) + E(A(a')B(b)) + E(A(a')B(b')) <= 2

Remark. We neglect measurability issues here.

Proof: Since all random variables here are bounded there are no issues in exchanging expectation values and summation. By elementary algebra we see that

A(a)B(b) - A(a)B(b') + A(a')B(b) + A(a')B(b') <= 2

Take the expectation left and right, and write expectation of a sum (and difference) of four terms as sum and difference of four expectation values.

QED.

According to Bell (as far as I can see) this is a prototypical statement and proof of Bell's theorem in a little bit more modern language than Bell used 50 years ago.

What's the problem with it? I mean, is there an internal problem? Do you just have problems with the applicability, ie the relevance, or do you believe that the tautology is wrong? It would be good to get that out of the way.

Bell like most sensible physicists was not bothered by technical mathematical niceties concerned with what exactly do we mean by a function, what exactly do we mean by integration, and so on. He could integrate anything he came across, no problem. Gerard 't Hooft has a very low opinion of mathematicians because when he did a course on measure theoretic integration he found out that mathematicians forbid him to integrate many things which he knew perfectly well how to integrate. Well who needs mathematicians then.


PS see http://arxiv.org/abs/1402.1972 for another mathematician's version of the theorem.

Richard, please see Eqn (12) in my essay. It is a simple and complete refutation of the maths above!

PS: You do know that:

A: the equations you give above are experimentally invalidated?

B: that my Eqn (12) shows why?
.

[Ben6993]

Hi Gordon

My point about your paper was a very narrow one: that there is no error in dropping AA from the function being integrated.

Turning the problem from an integration into a discrete summation does not change this issue. λ must be held constant within the function until you are ready to do the discrete summation just as it should be held constant doing an integration.

Richard has referred to some points in Bell's paper requiring post-graduate mathematics or statistics, but this narrow issue is not one of them, it is much more basic than that.

Think of a calculation of the area under a curve given by function F. At point x = xi the area of a vertical strip under the curve is Fi times Δx. Where Fi is the value of F when x = xi. The integration is a sum of many such strips. Fi must be calculated at the point xi. When you are playing around with the form of Fi it should still be applicable only at point x=xi. It should not be a mix of what F is at x= xi and x=xj simultaneously. When you have a suitable form for Fi at x = xi, then you re-label Fi as F and xi as x and integrate Fdx.

In the broader issue of Bell's Inequality, I tend to side with Joy
.

[Gordon Watson]

Bell (1964) formula (15) is the famous three correlation inequality:

1 + P(b, c) >= |P(a, b) - P(a, c)|

He has previously made a number of definitions and assumptions.

We have to realize that an expression like P(a, b) can refer to at least three different things. His assumptions makes those two of these things equal, and the third likely to be close to equal to the other two.

On the side one thinks of P(a, b) as something accessible through experiment. We imagine repeatedly creating pairs of particles in a particular way, measuring them in a particular way depending on a and b, accuring a huge amount of data - two synchronized streams of numbers +/- 1, and then calculating the limit of their product as N goes to infinity. We imagine that that limit does exist and we call it the correlation.

On the another side we have a mathematical model for what goes on in one run of that experiment. It is a local hidden variables model. It is a probabilistic model. An element lambda is chosen by Nature at random from some mathematical set Lambda. It is chosen according to a probability distribution. Bell writes formulas in 60's physics style by sort of pretending that Lambda is a nice subset of R^p for some p and the probability distribution has a probability density rho(lambda) with respect to Lebesgue measure, so that the expectation value of some real function f of lambda can be calculated as int f(lambda) rho(lambda) d lambda. The model goes on to suppose that lambda gets carried by two particles to two measurement stations where what happens is that the experimenter gets to see the value of a function A(a, lambda) and the one station and B(b, lambda) at the other measurement station. The value if always +/- 1. Here, a and b are settings which the experimenter chose freely.

According to conventional probability theory, the expectation value of the product of A and B over many many independent runs all done exactly the same way would converge to the integral int A(a, lambda) B(b, lambda) rho(lambda) d lambda. We call it the correlation. (Actually, we shouldn't: it is an uncentered product moment. Another source of confusion.)

On the third side ... if we only do N runs and average the product we see something random, but if N is large, it will be close to the expectation value, with large probability. We call it the correlation.

It seems to me that Gordon has a problem with conventional probabilty theory, which is what (in my humble opinion) Bell is certainly using in his derivation of (15). In this part of the paper, we are doing mathematical physics. We have a mathematical model for some physical system. Our model is probabilistic. We are not doing an experiment. We are not talking about real experiments. We are talking perhaps about a conceptual experiment where the same thing is done infinitely many times ... quite a Gedankenexperiment, you see.

BTW I imagine that Bell was a frequentist and had a conventional frequentist understanding of "what probability means". Jaynes was a Bayesian and had a completely different understanding of "what probability means". If we are to discuss whether or not (15) is correct we might need to take account of what Bell's understanding of probability likely was.

Richard,

After studying my essay, why not go directly to the central issue:

A: Bell's 1964:(15) IS 1 + P(b, c) |P(a, b) - P(a, c)|. It IS derived by Bell from his general analysis of EPRB.

B: Bell's 1964:(15) IS NOT experimentally valid in many EPRB settings.

C: Bell's 1964:(14a) IS mathematically and experimentally valid.

D: One option [.] to be eliminated from E by the examinee; but proceed to F and G and H for now.

E: Bell's 1964:(14b) is [IS] [IS NOT] experimentally valid.

F: Bell's 1964:(14c) IS NOT experimentally valid -- because it equals his 1964:(15).

G: Bell's 1964:(15) IS NOT experimentally valid in many EPRB settings (replicated for emphasis).

H: Please eliminate one option [.] from E above. Give reasons for your answer.

HINT: What error brings the change from [IS] to [IS NOT]?
.

[Gordon Watson]

Hi Gordon

My point about your paper was a very narrow one: that there is no error in dropping AA from the function being integrated.

Turning the problem from an integration into a discrete summation does not change this issue. λ must be held constant within the function until you are ready to do the discrete summation just as it should be held constant doing an integration.
….

[Ben's example], title added by GW: "Think of a calculation of the area under a curve given by function F. At point x = xi the area of a vertical strip under the curve is Fi times Δx. Where Fi is the value of F when x = xi. The integration is a sum of many such strips. Fi must be calculated at the point xi. When you are playing around with the form of Fi it should still be applicable only at point x=xi. It should not be a mix of what F is at x= xi and x=xj simultaneously. When you have a suitable form for Fi at x = xi, then you re-label Fi as F and xi as x and integrate Fdx."

In the broader issue of Bell's Inequality, I tend to side with Joy
.

Thanks Ben; it's good to see that:

A: in siding with Joy, you are open to answering "where did Bell (1964) go wrong?"

B: your focus in this post is a very narrow one: "that there is no error in dropping AA from the function being integrated."

C: as we'll see, you are close to making my point: AiAj ≠ 1 in general; and thus rejecting your assertion in B above.

To see why I've written C above, let's consider "Ben's example" (per my underlined edit above): and let's edit it as underlined below (for clarity, small obvious edits are not identified by underlining).

(Scene in Peru): Think of a calculation by a Peruvian physicist of the area under a curve given by some function F whose domain is [a,b]. At point x = xi the area of a vertical strip under the curve is Fi times Δx. Where Fi is the value of F when x = xi. The integration is a sum of many such strips Ai = FiΔx as i goes to infinity. Fi must be calculated at the point xi. When you are playing around with the form of Fi it should still be applicable only at point x=xi. It should not be a mix of what F is at x= xi and x=xj simultaneously. When you have a suitable form for Fi at x = xi [say, F(x) = 0.99999x], then you re-label Fi as F(x) and xi as x and integrate F(x)dx over [a,b].

(Scene in Paris): Think of a calculation by a Parisian physicist of the area under a curve given by some function G whose domain is [a,b]. At point x = xj the area of a vertical strip under the curve is Gj times Δx. Where Gj is the value of G when x = xj. The integration is a sum of many such strips Aj = GjΔx as j goes to infinity. Gj must be calculated at the point xj. When you are playing around with the form of Gj it should still be applicable only at point x=xj. It should not be a mix of what G is at x= xi and x=xj simultaneously. When you have a suitable form for Gj at x = xj [say, G(x) = 1.00001x], then you re-label Gj as G(x) and xj as x and integrate G(x)dx over [a,b].

Moral of the story:

(i): Two independently generated particle-pairs, like two independently generated curves, need not be the same. Moreover, why would they be the same? Worse: why would anyone insist that they be the same? Worse still: why would anyone require them to be the same?

(ii): Why not set your analyses up (like I do in my essay) so that it is irrelevant whether two curves are the same or different?

(iii): Ben, please study and understand my Eqn (12). Do you there see, on LHS: that Bell and Peres and many others (with EIGHT subscripted s) require FOUR curves to be the same?

(iv): Ben, please: count what Bell, Peres, ++ require. Then think of Peru, Paris, Pisa, Pshaw!

Ben; are we there yet? At PSHAW?

With best regards; Gordon

[Gordon Watson]

NB: Even IF Bell was not rusty using integration -- his results are experimentally INVALID: such results tend to confuse.

For the question then arises: Was it a false assumption or just a maths error?

...
You say that Bell's results are experimentally invalid, and you say this because you believe (but you are wrong, IMHO) that Bell's inequality has been violated by experiments.
...

Richard, please make your position absolutely clear on this one simple point:

Will loop-hole free tests vindicate or repudiate Bell's inequality and the Bell-CHSH inequality?

I'm concerned that you are unwittingly leaving yourself too much wriggle-room to be taken seriously (and I don't want that).

Please reply with a short answer from something like {Vindicate, Repudiate, Don't know, No opinion, Don't care} before expanding on your views.

PS: It would be helpful if you included your understanding of (and your position in relation to) Caroline Thompson's views re the same question; thanks.

NB: To be clear about what I say: Bell's results are experimentally invalid, contrary to QM, and contrary to my own analysis. Bell's inequality -- starting with the erroneous Bell 1964:(14b) = Bell 1964:(14a) -- has been violated via many sound experiments by reputable experimentalists. In the face of these substantial facts, it is certain that Bell's work will continue to be invalidated when loop-hole-free tests begin!
.

[gill1109]

NB: Even IF Bell was not rusty using integration -- his results are experimentally INVALID: such results tend to confuse.

For the question then arises: Was it a false assumption or just a maths error?

...
You say that Bell's results are experimentally invalid, and you say this because you believe (but you are wrong, IMHO) that Bell's inequality has been violated by experiments.
...

Richard, please make your position absolutely clear on this one simple point:

Will loop-hole free tests vindicate or repudiate Bell's inequality and the Bell-CHSH inequality?

I'm concerned that you are unwittingly leaving yourself too much wriggle-room to be taken seriously (and I don't want that).

Please reply with a short answer from something like {Vindicate, Repudiate, Don't know, No opinion, Don't care} before expanding on your views.

PS: It would be helpful if you included your understanding of (and your position in relation to) Caroline Thompson's views re the same question; thanks.

NB: To be clear about what I say: Bell's results are experimentally invalid, contrary to QM, and contrary to my own analysis. Bell's inequality -- starting with the erroneous Bell 1964:(14b) = Bell 1964:(14a) -- has been violated via many sound experiments by reputable experimentalists. In the face of these substantial facts, it is certain that Bell's work will continue to be invalidated when loop-hole-free tests begin!
.

How can I know if there will ever be a test which is both successful and loophole free? The experimentalists expect one in five years. If they succeed that will definitely be a Nobel prize.

Caroline Thompson would have predicted that it will never happen.

If you want to know my views please read one of my papers for instance http://arxiv.org/abs/1207.5103, "Statistics, Causality and Bell's Theorem", invited paper for special issue of "Statistial Science" on causality, probably coming out in 2015. It has gone through five revisions; it has been refereed multiple times in excruciating detail by mathematicians, statisticians and physicists, and many colleagues around the world both pro and contra Bell and with very different views on QM have given me comments. There is a section on the quantum Randi challenge and the paper is dedicated to my anti-Bell friends Christian, Geurdes, and Sanctuary, but I could also have thanked Diether, Hess, de Raedt, Fodje since discussions with them too influenced the paper.

Regarding your many other very long reactions to my too many too long posts, I think it would be helpful now if you tried to study my work a bit. Starting with the just mentioned paper. All your issues are resolved. All of them. I could answer you by copy pasting my whole paper.

To be clear: you have not found an error in Bell's paper. Here is a small data set of a CHSH experiment with N = 4. The format is setting Alice, setting Bob, outcome Alice, outcome Bob

1, 1, +1, +1
1, 2, +1, -1
2, 1, -1, -1
2, 2, -1, -1

The four empirical correlations are +1, -1, +1, +1
CHSH: S = 4

I have a LHV model (detection loophole) which gives exactly these 4 correlations however large N.

My point: the existence of data-sets violating CHSH does not prove Bell's logic is wrong.

Yet that is exactly what you are saying ("experimental violation proves there must be an error")

I conclude that your logic is not mine. Hence I will not study your paper in detail. There's no point in it, for me.

[Gordon Watson]

...
You say that Bell's results are experimentally invalid, and you say this because you believe (but you are wrong, IMHO) that Bell's inequality has been violated by experiments.
...

Richard, please make your position absolutely clear on this one simple point:

Will loop-hole free tests vindicate or repudiate Bell's inequality and the Bell-CHSH inequality?

I'm concerned that you are unwittingly leaving yourself too much wriggle-room to be taken seriously (and I don't want that).

Please reply with a short answer from something like {Vindicate, Repudiate, Don't know, No opinion, Don't care} before expanding on your views.

PS: It would be helpful if you included your understanding of (and your position in relation to) Caroline Thompson's views re the same question; thanks.

NB: To be clear about what I say: Bell's results are experimentally invalid, contrary to QM, and contrary to my own analysis. Bell's inequality -- starting with the erroneous Bell 1964:(14b) = Bell 1964:(14a) -- has been violated via many sound experiments by reputable experimentalists. In the face of these substantial facts, it is certain that Bell's work will continue to be invalidated when loop-hole-free tests begin!
.

How can I know if there will ever be a test which is both successful and loophole free? The experimentalists expect one in five years. If they succeed that will definitely be a Nobel prize.

Dear Richard,
I asked (and had hoped) for a direct answer from you: before you embarked on an expansion of your views. Here you have given neither!

The question asks you to expose your philosophical position: so that I might better understand the context that accompanies your views. Such positions generally capture the essence of a body of work to which you are committed. Regrettably, given what you've written here, I'm still guessing!

Caroline Thompson would have predicted that it will never happen.

Dear brave Caroline was ballsy enough to have the courage of her convictions: if only more had such; or at least honoured her name by not hiding behind it.

If you want to know my views please read one of my papers for instance http://arxiv.org/abs/1207.5103, "Statistics, Causality and Bell's Theorem", invited paper for special issue of "Statistial Science" on causality, probably coming out in 2015. It has gone through five revisions; it has been refereed multiple times in excruciating detail by mathematicians, statisticians and physicists, and many colleagues around the world both pro and contra Bell and with very different views on QM have given me comments. There is a section on the quantum Randi challenge and the paper is dedicated to my anti-Bell friends Christian, Geurdes, and Sanctuary, but I could also have thanked Diether, Hess, de Raedt, Fodje since discussions with them too influenced the paper.

Please confirm: That this paper has been formally accepted for publication?

Regarding your many other very long reactions to my too many too long posts, I think it would be helpful now if you tried to study my work a bit. Starting with the just mentioned paper. All your issues are resolved. All of them.

Please: could you match a few key Paragraphs and Equations (from my 2-pages of text) to the same in your 25-page work? (Preferably Equations, because I like my maths to do the talking.) That way I could quickly outline (to you) the basis of my foreseen rebuttal.

I could answer you by copy pasting my whole paper.

Why would you do that? In this day and age? Your affiliation allows you ready access to publish on arXiv, so I already have a copy of your last revision. I simply need to know that your submission is already accepted for publication: before I write a rebuttal. PS: If it is not yet accepted; please let me know when it is: you have my email address.

To be clear: you have not found an error in Bell's paper.

The OP emphasises: that every Paragraph and Equation is numbered; that this thread is for focussed critiques and questions; etc. I could be mistaken, but I don't, at this moment, recall one Para # or one Eqn (.) cited by you?

Here is a small data set of a CHSH experiment with N = 4. The format is setting Alice, setting Bob, outcome Alice, outcome Bob

1, 1, +1, +1
1, 2, +1, -1
2, 1, -1, -1
2, 2, -1, -1

The four empirical correlations are +1, -1, +1, +1
CHSH: S = 4

I have a LHV model (detection loophole) which gives exactly these 4 correlations however large N.

With a detection loophole? @%$

My point: the existence of data-sets violating CHSH does not prove Bell's logic is wrong.

Yet that is exactly what you are saying ("experimental violation proves there must be an error")

I trust you mean "experimental data sets" -- and not loophole-based variants? And understand that science advances via both theory and practice working together?

I conclude that your logic is not mine.

A quoted Paragraph number # or Equation (.) from my 2-page-text would be still welcomed by me: with a direct response assured.

Hence I will not study your paper in detail. There's no point in it, for me.

That's a pity, especially for me; but OK, fair enough. With sincere thanks for the ride; Gordon
.

[gill1109]

Gordon I gave you a concise and short answer to your short explicit questions.

I do not hide behind Caroline's views, and moreover I have many times published my own, I don't hide behind anyone's.

I have been promoting and defending Caroline's views about the loophole issues for many years even though they were very unfashionable. In fact I did that because though very unfashionable they are very valuable. However, she believes unreservedly in local realism so she thinks a loophole free successful experiment *cannot* be done. I do not have that "prejudice". I tend to believe that we have to abandon some prejudices which we have gained from evolution in a mainly classical world. Our "embodied cognition", our "systems of core knowledge" prevent us from ever being able to "understand" some things. Fortunately we have mathematics and can get by perfectly well even if we don't have a cozy picture in our head of what is going on.

Yes my paper
http://arxiv.org/abs/1207.5103 Statistics, Causality and Bell's Theorem
is accepted by the editors and right now it is on its way to the printers. Please give it a spin. I've read your paper, quickly. Now you read mine, quickly.

You want me also to expose my philosophical views? In long or short version? That's OT (off topic). If you want to know more about them we could start a new topic.

You can find summaries (but a few years old now) at

http://www.math.leidenuniv.nl/~gill/waveparticle.html The past is particles, the future is a wave
http://www.math.leidenuniv.nl/~gill/fifthposition.html Bell’s fifth position

You might like the following papers
http://arxiv.org/abs/0905.2723 Schrödinger's cat meets Occam's razor
http://arxiv.org/abs/quant-ph/0301059 Time, Finite Statistics, and Bell's Fifth Position

On my home page you can also find some links to slides of talks on these and many other topics
http://www.math.leidenuniv.nl/~gill/

[Gordon Watson]

Thank you Richard; some nice reading (and writing) ahead.

Before that (my own position being clear); I seek once more to clarify this one point:

In your opinion, given (ie, assuming) that a loophole-free experiment was run yesterday, has Bell's inequality and the Bell-CHSH inequality be vindicated or repudiated.

I know Caroline's position, and I now know that you differ (thank you) but a specific answer? …..

With thanks again; Gordon
.

[gill1109]

Thank you Richard; some nice reading (and writing) ahead.

Before that (my own position being clear); I seek once more to clarify this one point:

In your opinion, given (ie, assuming) that a loophole-free experiment was run yesterday, has Bell's inequality and the Bell-CHSH inequality be vindicated or repudiated.

I know Caroline's position, and I now know that you differ (thank you) but a specific answer? …..

With thanks again; Gordon.

You don't tell me if the experiment was not only loop-hole free but also violated the appropriate inequality to a high degree of statistical significance.

Actually I'd like to reserve judgement till I saw the experiment replicated in a few different labs, too.

But if the experiment gets done and the appropriate Bell-CHSH inequality is resounding violated then we must, in my opinion, abandon "realism" (but we can keep locality). It will be a paradigm shift.

Bell will have been vindicated.

[gill1109]

Thank you Richard; some nice reading (and writing) ahead.

Before that (my own position being clear); I seek once more to clarify this one point:

In your opinion, given (ie, assuming) that a loophole-free experiment was run yesterday, has Bell's inequality and the Bell-CHSH inequality be vindicated or repudiated.

I know Caroline's position, and I now know that you differ (thank you) but a specific answer? …..

With thanks again; Gordon.

You don't tell me if the experiment was not only loop-hole free but also violated the appropriate inequality to a high degree of statistical significance.

Actually I'd like to reserve judgement till I saw the experiment replicated in a few different labs, too.

But if the experiment gets done and the appropriate Bell-CHSH inequality is resounding violated then we must, in my opinion, abandon "realism" (but we can keep locality). It will be a paradigm shift.

Bell's logical analysis will have been vindicated, Bohr will have been proven right all along, Bell would not be happy because he is a realist by inclination.

One of the triple: realism, locality, no-conspiracy would have to go. Which of the three is metaphysics. Maybe you could even say a matter of taste or possibly even of semantics.

I will put two key chapters of "Speakable and Unspeakable" in the Dropbox. You need to read them too. Chapters 13 and 16.

[Ben6993]

Hi Gordon

Aha ... , now I think I see why you are trying to do what you are doing.

In my note about integration I used x instead of your λ. And my x is one dimension in Euclidean 3D space aka flatland. And I am sure that I am correct in flatland. Bell's Inequality is trivial to prove pictorally in flatland in a couple of lines based on a Venn diagram.

What you seem to be doing is having a multidimensional x (i.e. λ) axis. That is your way of getting more dimensions into your equations. QM gets more dimensions by using a different maths (in Hilbert space). Joy gets more dimensions by using Clifford Algebra. You are getting more dimensions by saying x is multi-valued at what is only one point in flatland.

So if I think of the multidimensions as a double cover (as I interpret it in Joy's model) at x, ie x1 and x2. A function which is apparently F in flatland is really an aggregate of F1 in cover 1 and an F2 in cover 2. And F1 and F2 can be quite different.

I see F1 and F2 as, in the total dimensionality, somehow contributing to the appropriate correlation, whereas F1 and F2 aggregate in flatland to an inappropriate correlation for particle behaviour.

I have only looked at a few equations in your paper (wrt AA = 1). Are you doing multidimensional calculations in flatland space?

Regards.

[Joy Christian]

But if the experiment gets done and the appropriate Bell-CHSH inequality is resounding violated then we must, in my opinion, abandon "realism" (but we can keep locality).

Hardly. The phrase "abandon "realism"" is a philosophical gobbledygook. Besides, a completely consistent, manifestly local-realistic framework for the strong quantum correlations already exists. The said experiments will simply confirm this framework. For details, see my latest paper (for example): http://arxiv.org/abs/1405.2355.

It will be a paradigm shift... Bell's analysis will have been vindicated, Bohr will have been proven right all along, Bell would not be happy because he is a realist by inclination.

You have a lot to learn. You can begin your first steps by reading and understanding what I have explained on my blog: http://libertesphilosophica.info/blog/.

The experiments will simply vindicate Einstein's local-realistic position.

Moreover, they will confirm the well known fact that our physical space naturally respects the SU(2), or spinorial symmetries.

[gill1109]

But if the experiment gets done and the appropriate Bell-CHSH inequality is resounding violated then we must, in my opinion, abandon "realism" (but we can keep locality).

Hardly. The phrase "abandon "realism"" is a philosophical gobbledygook. Besides, a completely consistent, manifestly local-realistic framework for the strong quantum correlations already exists. The said experiments will simply confirm this framework. For details, see my latest paper (for example): http://arxiv.org/abs/1405.2355.

It will be a paradigm shift... Bell's analysis will have been vindicated, Bohr will have been proven right all along, Bell would not be happy because he is a realist by inclination.

You have a lot to learn. You can begin your first steps by reading and understanding what I have explained on my blog: http://libertesphilosophica.info/blog/.

The experiments will simply vindicate Einstein's local-realistic position.

Moreover, they will confirm the well known fact that our physical space naturally respects the SU(2), or spinorial symmetries.

Of course, a slogan like "abandon realism" could mean anything or nothing. I mean something metaphysically precise with it, but if you already know Bell got it completely wrong and that Einstein is vindicated by your work then stick with your local realism, and don't try to read or understand anything else. It's a logically consistent position to take, given you know that your work is correct.

[Joy Christian]

Of course, a slogan like "abandon realism" could mean anything or nothing. I mean something metaphysically precise with it, but if you already know Bell got it completely wrong and that Einstein is vindicated by your work then stick with your local realism, and don't try to read or understand anything else. It's a logically consistent position to take, given you know that your work is correct.

Thank you.

But just that you know, I have been learning about this subject for the past 32 years, at the feet of the best of them all---Wigner, Bell, Shimony, and Penrose.

[gill1109]

Of course, a slogan like "abandon realism" could mean anything or nothing. I mean something metaphysically precise with it, but if you already know Bell got it completely wrong and that Einstein is vindicated by your work then stick with your local realism, and don't try to read or understand anything else. It's a logically consistent position to take, given you know that your work is correct.

Thank you.

But just that you know, I have been learning about this subject for the past 32 years, at the feet of the best of them all---Wigner, Bell, Shimony, and Penrose.

I know. I already knew. Wonderful for you. To be sure I have only been in this Bell business for about 20 years and obviously in many respects only as some kind of outsider.

I went up to Cambridge in 1970 at age 19 so you could say that I have been learning to be a scientist for close on 45 years now. I too certainly have had many wonderful teachers (including Hawking and Conway) and wonderful colleagues (including 't Hooft and Landsman), and I've worked with wonderful people such as Zeilinger, Weihs, Zukowski, Massar, Werner, Gisin. Wow it has been quite some ride. I hope you have noticed that I thank you, Bryan Sanctuary, and Han Geurdes in my causality paper.