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

[minkwe]

Sorry, I do not see a good faith effort on your part to discuss these issues, that is why I can infer motives. When presented with a clear argument, you bob and weave and avoid the issue. That speaks to motive. Yet you are the first to accuse other of not knowing how to relate mathematics to physics. Why do you find the need to spread BS when ever you get stuck in an argument and don't know what to say. That is your MO. You don't have to engage but when you do, be honest and straight-forward, don't pretend to be arguing and then introduce all kinds of irrelevant rabbit trails. Don't say things about other people's work when you have not studied them. I am free to judge your actions as you are of mine. But I do not yet see a gentleman on the other side with whom to have a CLEAR discussion of what the issues are with respect to Bell.

[Xray]

"Fantastic sophisticated forum software. If you write BS out in full (eight letters), it converts that to "s, triple asterisk". It has an automatic BS detector.

The forum software is an "author detector". If a bull did not write BS in full (eight letters) it politely calls what you write what it is.

[Xray]

Sorry, I do not see a good faith effort on your part to discuss these issues, that is why I can infer motives. When presented with a clear argument, you bob and weave and avoid the issue. That speaks to motive. Yet you are the first to accuse other of not knowing how to relate mathematics to physics. Why do you find the need to spread BS when ever you get stuck in an argument and don't know what to say. That is your MO. You don't have to engage but when you do, be honest and straight-forward, don't pretend to be arguing and then introduce all kinds of irrelevant rabbit trails. Don't say things about other people's work when you have not studied them. I am free to judge your actions as you are of mine. But I do not yet see a gentleman on the other side with whom to have a CLEAR discussion of what the issues are with respect to Bell. emph.added

Gordon, your three page vixra pdf starts with:

Generalizing Bell 1964:(15) to realizable experiments, CHSH (1969) coined the term “Bell’s theorem”. Since the results of such experiments (eg, see Aspect 2002) contradict Bell’s theorem: at least one step in his supposedly commonsense analysis must be false.

CHSH coined the term "Bell's theorem" but by that term they did not mean the CHSH inequality.
So the first sentence exposes a major misunderstanding of the writer.
The second sentence further confirms that the writer doesn't know what he is writing about.

We had earlier tried your approach of going through your argument step by step and we earlier found out exactly where it derails.

Gill and minkwe and Joy Christian - you are three of the best here so take on board this unity attempt.

Gill - You mentioned an age difference recently. So I give you two the benefit of the doubt. Take a good look at minkwe's piece and take it on board as a young person's honest but abrupt appraisal - here is what I see between you two.

Watson - Generalizing Bell 1964:(15) to realizable experiments, CHSH (1969) coined the term “Bell’s theorem”.
Gill - CHSH coined the term "Bell's theorem" but by that term they did not mean the CHSH inequality.
Xray - This looks like bad faith and nasty propaganda because Gill agrees with Watson on one fact then Gill inserts an unrelated fact into the discussion making it look like Watson did not know something or made a mistake.


Watson - Since the results of such experiments (eg, see Aspect 2002) contradict Bell’s theorem: at least one step in his supposedly commonsense analysis must be false.
Gill - The second sentence further confirms that the writer does not know what he is writing about.
Xray - This looks like bad faith or nasty propaganda of the worst kind because Gill piles on to the first propaganda and compounds it.

Watson - viewtopic.php?f=6&t=62#p2612
(1): The essay for discussion here is just 2 pages of text and equations: each equation [(1, 2, …)] and paragraph [#1, #2, …] is numbered; plus 1 page of Acks and Refs.

(2): The focus of the essay is Bell 1964: (15) --- and Bell's (1964) paper is available online (see the essay).

(3): Please note that the essay is based on undergrad maths and logic. So it should be possible for almost all of the discussion to begin with: RE eqn (1), or RE para #1. That way we might more easily track the common issues -- for the benefit of all.

Gill - We had earlier tried your approach of going through your argument step by step and we earlier found out exactly where it derails.
Xray - Without a link this looks like bad faith or nasty propaganda so please guide me to the where any of you who make up the WE have quoted paragraph and equation numbers as Watson wanted - as stated in his step by step approach.

I disagree with both Gordon Watson and Richard Gill here.

There is no point in being concerned about Bell’s theorem without simultaneous being concerned about both spacetime and the physical space. The concept of local causality is at the heart of both Bell’s theorem and Einstein’s position. What is the point of talking about Bell’s theorem without also talking about local causality?

The strong quantum correlations are observed in nature all the time, in many areas of physics, not only in the EPRB type experiments. They are observed in solid state physics, and they are observed in elementary particle physics. To be sure, they are not subjected to the same scrutiny in these areas as they are in the context of the EPRB experiments. But that does not change the fact that they are observed in Nature, period. This fact cries out for explanation, whether you are a local realist or an adherent of the orthodox quantum ideology.

It is therefore pointless to simply argue that Bell’s theorem is wrong. So what if it is? That still does not explain why we see the strong correlations in Nature.

The only plausible explanation for their existence (at least in my opinion) is that they are properties of the physical space itself. This brings us back to spacetime (of which the physical space is naturally a part), and to the concerns of local causality of Einstein and Bell.

That is the real topic. Not a supposed error in Bell’s paper (which is flawed in my opinion too, but the error in that paper is much more subtle than what Gordon thinks it is).

Joy Christian -
"What is the point of talking about Bell’s theorem without also talking about local causality?"
Implying that Watson equation (1) is not locally causal? Doesn't Watson link to another essay that talks about local casualty?

"It is therefore pointless to simply argue that Bell’s theorem is wrong."
Doesn't Watson link to another essay that builds on the one here for debate?

"Not a supposed error in Bell's paper."
Implying that the Watson claimed error is not correct?

Report card - In my opinion Gill and Joy Christian can do better and minkwe's frustration is showing like mine.

And if you want to object to what I have written in anger and disappointment start a new topic.

[gill1109]

X-ray, thanks for your careful and honest and frank attempt to get us back on track. You wrote "Take a good look at minkwe's piece and take it on board as a young person's honest but abrupt appraisal - here is what I see between you two." That is indeed how I take Michel: he is very honest and he's doing his best. I'm doing my best to explain to him why I think he is a bit mixed up. He says he writes clearly, but that I "bob and weave". I say that what he writes looks clear but isn't, because he doesn't make important distinctions. Well: maybe I'm older and wiser and know important stuff which might be useful for him, or maybe I'm senile. Too bad. But no excuse for accusations of evil motives.

Now you Xray are doing just the same. I explain that (I think that) Gordon is mixed up, I explain why, and if you accept my good faith, you must believe that I think this is rather important. Instead you call it "propaganda".

So if young people don't understand what the old people say, then the old people are just trotting out "propaganda" or blatantly trying to mislead, by hiding the fact that they are obviously wrong behind a smokescreen of verbiage.

Well: according to the rules of good behaviour on this forum, even if this is what you think, you shouldn't say it.

Get me right: you can say that (you think) I'm wrong. But you should not tell the world what you think are my motives for writing what I write. Always make the "good faith" assumption. Always know that you might be mistaken about almost anything. Live well. Have fun. Science is a collective enterprise.

[gill1109]

PS I have set up a dropbox with some of the key papers. Send me an email if you'ld like to join it. Consider it "our" private archive / library / reading room. The forum is great. We are making progress. Rome was not built in a day. Agree to differ, be thoughtful, relax, enjoy, play, learn.

PPS: how about this for propaganda: Gordon Watson sets up a new topic called "Gill's theorem refuted (GTR)" when he does not even know what my theorem is. Well, I take that as a joke (which it is, in fact). No hard feelings!

[Xray]

X-ray, thanks for your careful and honest and frank attempt to get us back on track. You wrote "Take a good look at minkwe's piece and take it on board as a young person's honest but abrupt appraisal - here is what I see between you two." That is indeed how I take Michel: he is very honest and he's doing his best. I'm doing my best to explain to him why I think he is a bit mixed up. He says he writes clearly, but that I "bob and weave". I say that what he writes looks clear but isn't, because he doesn't make important distinctions. Well: maybe I'm older and wiser and know important stuff which might be useful for him, or maybe I'm senile. Too bad. But no excuse for accusations of evil motives.

Now you Xray are doing just the same. I explain that (I think that) Gordon is mixed up, I explain why, and if you accept my good faith, you must believe that I think this is rather important. Instead you call it "propaganda".

So if young people don't understand what the old people say, then the old people are just trotting out "propaganda" or blatantly trying to mislead, by hiding the fact that they are obviously wrong behind a smokescreen of verbiage.

Well: according to the rules of good behaviour on this forum, even if this is what you think, you shouldn't say it.

Get me right: you can say that (you think) I'm wrong. But you should not tell the world what you think are my motives for writing what I write. Always make the "good faith" assumption. Always know that you might be mistaken about almost anything. Live well. Have fun. Science is a collective enterprise.

Thank you gill1109 for taking my comment in a good spirit. I wrote hastily and I wanted to avoid making judgements by giving the REASON that some contributions LOOK LIKE bad faith and nasty propaganda but I should have said COULD GIVE THE IMPRESSION and I should have added that IMHO you and Joy Christian are very important writers on this website and that I admire your work AND added the hope that you focus on just facts as you see them in the future.

I mean specifically as a message to everyone that longwinded opinions expressed on this website without facts to base them on are not much use to anyone. This website is entitled to better than that from and for all of us.

Xray

[Ben6993]

Well, I think that everybody on this site is thinking hard and long on the problems and I have great respect for all of them.

Richard is giving a talk on Wednesday at Vaxjo on: 'Learning from experience: lessons from engagement with quantum c****pot'.
I am glad that does not identify me a "quantum c****pot" as I am sure Richard has learned nothing from me!
There have been so many opinions exchanged here that no-one should need a transcript/audio/video of Richard's talk, though it would be appreciated.

P.S.
Oh dear, I have just realised that I was assuming that he means learning 'physics', but as a statistician he could be meaning learning wrt c****pot psychology.
Maybe I do need that transcript, please.

[gill1109]

Ben I have learnt from you, too. I learn from everyone. And have fun (occasionally at other peoples' expense). Learning is fun, and sharing what you have learnt with others is fun, too. I honestly think that this is what we really are here on Earth for. What being a human being is all about. (As opposed to, say, being a cockroach).

Xray I really appreciate your unity attempt. We made yet again a lot more progress.

[Xray]

Xray I really appreciate your unity attempt. We made yet again a lot more progress.

gill1109 thank you

now you and I and everyone can set an example like this to make a lot more progress

Reference Watson's equation (12) - To ALL - specially laureate minkwe, Gordon Watson, gill1109

Equation (12) has a question mark in it but what if we did the LHS of (12) as a thought experiment - what would you say about (12) then ?

and because LHS of Equation (12) is all over the place in text-books and papers - so is Bell 1964 based on LHS of (12) as a thought experiment?

If the answer is yes - why would they do that ?

because no actually real experiment could check it could they ?

Xray

[gill1109]

Watson's (12), in context, with additional reference labels [A] and [B], is:

#15. To be clear: Using our compact notation (see #4 above), here’s an example of the easy corrective power of (11) — ie, of EPRB’s fact. Compare Peres 1995:(6.29)

Aj Bj +Bj Cj +Cj Dj −Dj Aj ≡ ±2(?) [A]

with

−4 ≤ AiBi + Bj Cj +Ck Dk −Dl Al ≤ +4 [B] : (12)

ie, Bell-Peres (with eight subscripted js) and the Bell-CHSH bounds of ±2 are false: exceeded experimentally and theoretically. Our bounds of ±4 are true: and never exceeded. QED.

What is the context? Certainly it includes the requirement that Ai Bj etc etc all take the values +/- 1.

Now it is a true fact of arithmetic / algebra / logic that if Aj, Bj, Cj, Dj are four elements of {-1, +1} then Aj Bj +Bj Cj +Cj Dj −Dj Aj takes values in {-2, +2} and that both values -2 and +2 do occur.

It is another true fact of arithmetic/ algebra / logic that Ai, Bi, ... Dl, Al are sixteen elements of {-1, +1} then AiBi + Bj Cj +Ck Dk −Dl Al takes values in {-4, -3, ... , +4} and all 9 values do occur

Neither of these statements is "about" experiments, whether real or imaginary. They are statements in combinatorial theory (discrete mathematics, logic, ...).

However I can tell you a thought experiment in which formula [A] could be very relevant and indeed useful. It would concern an EPR-B type experiment in which we imagine Nature choosing a hidden variable lambda and sending it, within two particles, to two measurement stations, where Alice and Bob each independently pick either to choose a setting a or a setting a' (b or b') on some measurement devices. The outcomes of measuring a or a' are thought to be A(a, lambda) and A(a', lambda), respectively, and the outcomes of measuring b or b' are thought to be B(b, lambda) and B(b', lambda) respectively, where A and B are two functions taking values in the set {-1, +1}.

Does anyone have difficulties imagining the four numbers A = A(a, lambda), A' = A(a', lambda), B = B(b, lambda), B' = B(b', lambda)?

And what is wrong with saying "If Alice chose setting a and Bob chose setting b, then the outcomes they would observe are A and B, while if in fact Alice chose a' she would have observed A' ..."?

Dirac said we should forget all the words, w should not read the sentences, we should just study the formulas. Perhaps it would help if we stopped trying to imagine pictures conjured up in our imagination by long lists of difficult words and instead just remark that with the shorthand A = A(a, lambda), A' = A(a', lambda), B = B(b, lambda), B' = B(b', lambda) then AB - AB' +A'B + A'B' takes values in -2, +2.

[Gordon Watson]

Xray I really appreciate your unity attempt. We made yet again a lot more progress.

gill1109 thank you

now you and I and everyone can set an example like this to make a lot more progress

Reference Watson's equation (12) - To ALL - specially laureate minkwe, Gordon Watson, gill1109

Equation (12) has a question mark in it but what if we did the LHS of (12) as a thought experiment - what would you say about (12) then ?

"I'd say that it would deliver the Bell inequalities."

and because LHS of Equation (12) is all over the place in text-books and papers - so is Bell 1964 based on LHS of (12) as a thought experiment?

Who knows what excuses they'll invent for Bell's error? In my confident opinion: "No! It is based on sloppy maths!"

If the answer is yes - why would they do that ?

I answered No - so not applicable to me.

because no actually real experiment could check it could they ?

Correct! So, in that you do not expect any sensible physicist to test a physically unrealistic thought-experiment in any way (it's unphysical, remember): then they must have thought the maths was correct; independent of ANY thought or critical analysis -- but (no doubt) influenced by their training in quantum mysteries.

Hence my belief that Bell's theorem is based on "sloppy maths" --- with this added support for my view:

Bell was supposedly studying EPRB; YET nowhere in EPRB is there any clue that you can --

1. Test a single pristine particle-pair TWICE. (?)

2. Test a single pristine particle-pair THRICE: ie, to deliver Bell's theorem and his erroneous 1964:(15). (?)

3. Test a single pristine particle-pair FOUR TIMES: ie, to deliver Bell-CHSH-Peres and their erroneous LHS of my (12)! (?)

4. Further: EPR had no such crazy expectations either; yet Bell is supposedly modelling them too.(?)

I therefore conclude: Bell and his supporters continue to believe such fantasies as 1., 2., 3., due to their acceptance of "repeatedly sloppy maths"; either their own or that of others!

PS: Look at the names in Paragraph #14. Checkout some of the corresponding (appearing to be copycat) maths throughout the Bellian literature.
.

[minkwe]

Now it is a true fact of arithmetic / algebra / logic that if Aj, Bj, Cj, Dj are four elements of {-1, +1} then Aj Bj +Bj Cj +Cj Dj −Dj Aj takes values in {-2, +2} and that both values -2 and +2 do occur.

It is another true fact of arithmetic/ algebra / logic that Ai, Bi, ... Dl, Al are sixteen elements of {-1, +1} then AiBi + Bj Cj +Ck Dk −Dl Al takes values in {-4, -3, ... , +4} and all 9 values do occur

Neither of these statements is "about" experiments, whether real or imaginary. They are statements in combinatorial theory (discrete mathematics, logic, ...).

Neither of the statements requires any physical assumptions whatsoever to prove. Therefore their violations have nothing whatsoever to do with any physical reason such as non-realism/non-locality. Their violation simply points to mathematical confusion in which terms from the second are errorneously mixed into terms from the first.

However I can tell you a thought experiment in which formula [A] could be very relevant and indeed useful. It would concern an EPR-B type experiment in which we imagine Nature choosing a hidden variable lambda and sending it, within two particles, to two measurement stations, where Alice and Bob each independently pick either to choose a setting a or a setting a' (b or b') on some measurement devices. The outcomes of measuring a or a' are thought to be A(a, lambda) and A(a', lambda), respectively, and the outcomes of measuring b or b' are thought to be B(b, lambda) and B(b', lambda) respectively, where A and B are two functions taking values in the set {-1, +1}.

Indeed we can unhinge our imagination and imagine all kinds of impossible things. For example, in the above "thought-experiment", Nature somehow knows what Alice and Bob are going to do, such that nature makes sure it sends the same hidden variable lambda to Alice, every time it knows Alice is going to pick angle "a", and exactly the same hidden variable lambda to Bob every time it knows in advance that Bob will pick angle "b". This way A(a, lambda_i) = A(a, lambda_j) because lambda_i = lambda_j. Indeed in this situation, we can easily imagine without any difficulties having four numbers A = A(a, lambda), A' = A(a', lambda), B = B(b, lambda), B' = B(b', lambda), since we can effectively ignore all subscripts, and formula [A] is very relevant and indeed useful for such a conspiratorial and incredibly mystical "Nature". Indeed if nature worked like this, formula [A] would be the correct one and the results of such an experiment should never exceed the bounds [-2,+2].

And what is wrong with saying "If Alice chose setting a and Bob chose setting b, then the outcomes they would observe are A and B, while if in fact Alice chose a' she would have observed A' ..."?

There is absolutely nothing wrong with saying that. The problem only arises when it is naively assumed that such a thought can ever be tested experimentally, in a situation in which the act of measurement changes the particles or destroys them, such as in the EPRB experiment. The problem only arises when it is naively assumed that such results can be compared to QM predictions which only deal with results of doable experiments.

Dirac said we should forget all the words, w should not read the sentences, we should just study the formulas. Perhaps it would help if we stopped trying to imagine pictures conjured up in our imagination by long lists of difficult words and instead just remark that with the shorthand A = A(a, lambda), A' = A(a', lambda), B = B(b, lambda), B' = B(b', lambda) then AB - AB' +A'B + A'B' takes values in -2, +2.

This is the trend. The inequalities do not make sense when explained in the context of the physical experiments, so let us forget about the inequalities. The experiment does not make sense when we try to understand it in terms of the inequalities, so let us forget about the experiments and just calculate. What else have we forgotten about:

Where does CFD come in? Well forget CFD for just a moment

Forget about physics for the moment.

Forget Bell's first paper on Bell's inequality.

But let's forget about the challenge.

I suggest we forget altogether about inequalities. Let's talk instead of the relation between theory and experiment

Let's forget the word "bound" and the word "inequality". They lead to endless misunderstanding.

Let's forget about interpretations. Let's discuss the maths.

At this rate, we'll all soon have amnesia, sorry I can't forget the sloppy Bell maths and its irrelevance to any physics, it reeks, and no amount of duct-tape (aka new papers which purport to "strenghten" Bell), however noble the attempt, can keep the stench in.

[Heinera]

Neither of the statements requires any physical assumptions whatsoever to prove. Therefore their violations have nothing whatsoever to do with any physical reason such as non-realism/non-locality.

The term "local" in "local hidden variable model" (aka a computer simulation) has a perfectly well defined algorithmic meaning independent of any physical reason. It means that the output variable for Alice should not depend, directly or indirectly, on Bob's setting, and vice versa. Whether a model is local or not can thus be deduced by analyzing its code.

I'm not quite certain of what your position actually is here. Do you think it is possible to write a local hidden variable computer simulation with outcomes in {-1, 1} that produces the strong correlations? Or do you mean that it is impossible, but irrelevant to physics? If the former is the case, it is purely a question of mathematics and algorithms, so there is no need to involve any physical reasons. If the latter is the case, I won't get into any argument, since relevance, like beauty, is in the eyes of the beholder.

[Xray]

Neither of the statements requires any physical assumptions whatsoever to prove. Therefore their violations have nothing whatsoever to do with any physical reason such as non-realism/non-locality.

The term "local" in "local hidden variable model" (aka a computer simulation) has a perfectly well defined algorithmic meaning independent of any physical reason. It means that the output variable for Alice should not depend, directly or indirectly, on Bob's setting, and vice versa. Whether a model is local or not can thus be deduced by analyzing its code.

I'm not quite certain of what your position actually is here. Do you think it is possible to write a local hidden variable computer simulation with outcomes in {-1, 1} that produces the strong correlations? Or do you mean that it is impossible, but irrelevant to physics? If the former is the case, it is purely a question of mathematics and algorithms, so there is no need to involve any physical reasons. If the latter is the case, I won't get into any argument, since relevance, like beauty, is in the eyes of the beholder.

Heinera, what is the [deleted] relevance of your comment to anything that mikwe said? Or to this thread?

Considering that from the opening post by Watson

(4): Please stay on topic: … no place in this thread for … computer models/simulations … .

Xray

[gill1109]

Neither of the statements requires any physical assumptions whatsoever to prove. Therefore their violations have nothing whatsoever to do with any physical reason such as non-realism/non-locality.

The term "local" in "local hidden variable model" (aka a computer simulation) has a perfectly well defined algorithmic meaning independent of any physical reason. It means that the output variable for Alice should not depend, directly or indirectly, on Bob's setting, and vice versa. Whether a model is local or not can thus be deduced by analyzing its code.

I'm not quite certain of what your position actually is here. Do you think it is possible to write a local hidden variable computer simulation with outcomes in {-1, 1} that produces the strong correlations? Or do you mean that it is impossible, but irrelevant to physics? If the former is the case, it is purely a question of mathematics and algorithms, so there is no need to involve any physical reasons. If the latter is the case, I won't get into any argument, since relevance, like beauty, is in the eyes of the beholder.

Heinera, what is the [deleted] relevance of your comment to anything that mikwe said? Or to this thread?

Considering that from the opening post by Watson

(4): Please stay on topic: … no place in this thread for … computer models/simulations … .

Xray

Xray, as has been patiently explained many times, neither Fodje nor Watson appreciate the difference between a mathematical model of reality, or a computer model of reality, and reality itself. Because Watson doesn't appreciate this difference, he does not understand Bell. Watson's "logic" might be impeccable but since one of his axioms is that apples equal pears, it is irrelevant. Strike a lot of words out of the vocabulary - and lose concepts. It's like "newspeak" in "1984".

Watson's admonishment to stay on topic ("no simulations ...") is a demand to wear the same blinkers which he has on; the ones which narrow the vision so strongly that you can't see you are headed over a cliff.

[minkwe]

Xray, as has been patiently explained many times, neither Fodje nor Watson appreciate the difference between a mathematical model of reality, or a computer model of reality, and reality itself.

Spoken by the person whose only responses to clear mathematical and physical arguments presented by Watson and Fodje are:
- "forget about physics",
- "forget about experiments",
- "forget about mathematics",
- "forget about inequalities", -
- "forget everything",
- "only focus on abstract non-physical simulations",
- "nature can see the future",
- "there is no bell's theorem but I have strengthened it and it shows that realism is false",
- "there are no counterfactual terms in my inequality but violation of my inequality proves that counterfactual definiteness is false.",
- "just trust me because I invented Bell's fifth postulate."

[gill1109]

Spoken by the person whose only responses to clear mathematical and physical arguments presented by Watson and Fodje are ...

IMHO, as far as those arguments were clear they were clearly incorrect. (But you already know that that is my opinion). Please let's stick to math and physics and not go on and on about persons.

[minkwe]

Xray, as has been patiently explained many times, neither Fodje nor Watson appreciate the difference between ...

Spoken by the person whose only responses to clear mathematical and physical arguments presented by Watson and Fodje are ...

IMHO, as far as those arguments were clear they were clearly incorrect. (But you already know that that is my opinion). Please let's stick to math and physics and not go on and on about persons.

Richard, if you can't stand the heat, don't start a fire. As you should know by now, I won't take likely the rubbish that you keep dishing (underlined above) so be prepared the feel the maximum response everytime you peddle that kind of personal stuff. So dare you try to personally belittle me, and I will make sure you end up looking stupid, mark my words. Be respectful to me and I will be respectful to you.

[Xray]

Neither of the statements requires any physical assumptions whatsoever to prove. Therefore their violations have nothing whatsoever to do with any physical reason such as non-realism/non-locality.

Heinera, what is the [deleted] relevance of your comment to anything that mikwe said? Or to this thread?

Considering that from the opening post by Watson

(4): Please stay on topic: … no place in this thread for … computer models/simulations … .

Xray

Xray, as has been patiently explained many times, neither Fodje nor Watson appreciate the difference between a mathematical model of reality, or a computer model of reality, and reality itself. Because Watson doesn't appreciate this difference, he does not understand Bell. Watson's "logic" might be impeccable but since one of his axioms is that apples equal pears, it is irrelevant. Strike a lot of words out of the vocabulary - and lose concepts. It's like "newspeak" in "1984".

Watson's admonishment to stay on topic ("no simulations ...") is a demand to wear the same blinkers which he has on; the ones which narrow the vision so strongly that you can't see you are headed over a cliff.

Gill,

if I ignore your opinions this is left

gill1109 - "Watson's "logic" might be impeccable but since one of his axioms is that apples equal pears, it is irrelevant."

so that I can see this for myself please supply para.# or eqn.# for this next piece - which cannot be an opinion -- or can it

gill1109 - "one of Watson's axioms is that apples equal pears" - see para.#

Xray

oops - edit - or gill1109 - is this another erroneous opinion and if so when and how will ever we know when you are in your good-faith mode

is it too much to ask you signal your opinions your jokes your facts

Xray

[gill1109]

Let's get back on track. Gordon apparently believes that in order to derive the CHSH inequality you have to imagine "testing a single pristine particle-pair four times" and therefore CHSH is wrong. I say that you don't have to imagine anything at all in the real world. CHSH is calculus which you can do which tells you something useful to know. In order to derive CHSH you have to imagine three functions with certain properties.

IF we have functions

A : {settings} x { values of a "hidden variable lambda} -> {-1, +1}
B : {settings} x { values of a "hidden variable lambda} -> {-1, +1}

rho : { values of a "hidden variable lambda} -> [0, infty) such that integral rho = 1

THEN for any a, a', b, b'

S = integral [ A(a, lambda)B(b, lambda) - A(a, lambda)B(b', lambda) + A(a', lambda)B(b, lambda) + A(a', lambda)B(b', lambda) ] rho(lambda) d lambda

is less than or equal to 2

PROOF: the expression in square brackets is less than or equal to 2 because ... and therefore ...

This is just calculus. You can imagine that AB - AB' + A'B + A'B' stands for something nonsensical, or you can not imagine it stands for anything at all, or you can imagine it stands for what happens when we run Michel's programs with some lines added which calculate the expression in square brackets for each particle pair which the computer simulates, and average it over a large number of runs. (Note: adding some such lines to his program code needn't change the rest of the output. They don't correspond to something that happens in the real experiment but we can still imagine it added to his computer program).

A bit more calculus tells us that E(a, b) - E(a', b) + E(a, b') + E(a', b') is less than or equal to 2, where E(a, b) is defined to be integral A(a, lambda)B(b, lambda) rho(lambda) d lambda.

If we want to apply these calculus trivialities to physics (or to computer simulations) we need a bridge to the real world and to experiment (or computer simulation models). On the other side of the bridge there is also something which we sometimes write E(a, b) but it stands for something in the real world. In the mathematical world there are apples, in the real world there are pears. Some of the pears correspond to some of the apples. But not every mathematical feature has a real world counterpart, and vice versa.

This is one of the things I discussed in my talk http://www.slideshare.net/gill1109/vaxjo-2014

For instance: settings are elements of S^2 (unit vectors in R^3), "rho(lambda) d lambda" stands for integrating with respect to the uniform probability measure over S^2 ie rho(lambda) = 1 / 4 pi if I remember correctly and d lambda is surface measure on S^2. A(a, lambda) = sign(a . lambda) and B(b . lambda) = - sign(b . lambda).