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

[Joy Christian]

Joy uses geometric algebra, together with a new definition of correlation, and together with some magic sign switches, to get the a.b result. Read my paper http://arxiv.org/abs/1203.1504

Give up your slanderous lies Richard Gill: http://arxiv.org/abs/1203.2529. You are not going to intimidate me. If my work is too difficult for you to understand, then just ask and I will explain, as I did here: viewtopic.php?f=6&t=49&hilit=moronson&start=130#p2545.

[Gordon Watson]

Richard; thanks, but with respect: When we settle the World-Cup by computer, I'll switch my studies from real-life to gaming. Until then, I trust that you are happy to deal with the real world and real experiments? Knowing, as you do, that two correlated footballs have nothing like the correlations associated with two entangled particles?
***
So, Richard, seriously, how about we quit the word games and let our maths do the talking. I moved first, in my essay. Your move next, in reply, via some maths?

Too bad Gordon, you've had my very serious and careful reply. You can take it seriously or you can forget it, just as you like.

Richard, I take all serious replies seriously, but please understand: I have no clue as to the error that you think exists in my essay.

I have no Paragraph numbers, no Equation numbers. Are you referring to the issues that Harry is working with?

If you want to see some maths read my paper http://arxiv.org/abs/1207.5103. Theorem 1 is rather relevant to this discussion.

Please explain the significance/purpose of η (eta) in your theorem; also its relevance to this discussion.

Thanks: Gordon

[Gordon Watson]

Hi Gordon,
I replied first to minkwe and next to you on p.14 (=in the sequence of replies to my earlier reply to you).

Sorry; I missed it. So how about this: until the <subscribe> feature is again available here, send me a PM/email if you think I've missed one of your postings.

For, be assured, I'm keen to learn from and reply to all serious critiques and questions.

Thanks; Gordon

[gill1109]

Richard; thanks, but with respect: When we settle the World-Cup by computer, I'll switch my studies from real-life to gaming. Until then, I trust that you are happy to deal with the real world and real experiments? Knowing, as you do, that two correlated footballs have nothing like the correlations associated with two entangled particles?
***
So, Richard, seriously, how about we quit the word games and let our maths do the talking. I moved first, in my essay. Your move next, in reply, via some maths?

Too bad Gordon, you've had my very serious and careful reply. You can take it seriously or you can forget it, just as you like.

Richard, I take all serious replies seriously, but please understand: I have no clue as to the error that you think exists in my essay.

I have no Paragraph numbers, no Equation numbers. Are you referring to the issues that Harry is working with?

If you want to see some maths read my paper http://arxiv.org/abs/1207.5103. Theorem 1 is rather relevant to this discussion.

Please explain the significance/purpose of η (eta) in your theorem; also its relevance to this discussion.

Thanks: Gordon

I know you have no clue as to the error which I think exists (and it is indeed the same as that identified by Harry, and by others). That's why I'd like you to think seriously about the computer set-up which I describe. Call it a game, if you like. We learn by playing games. It's a safe environment where we all perfectly understand everything, no disagreements, and where (believe it or not) we can explore Bell's logic. Where we can refresh our memory of Statistics 101 and see how it might be relevant.

The relevance of eta in my theorem? Try substituting eta = 0.1 and N = 100 000 in my formula (3). I think you might find that it says something interesting. Something meaningful and non-trivial.

Does that have relevance to *this* discussion? Well, my paper also has a proof of a Bell-like theorem and I think it improves in many respects on Bell's result. It might even be easier to understand, while at the same time it is more powerful. It takes account of the facts (a) that in the good experiments, settings are chosen at random, and (b) that N is finite hence we must take account of statistical errors.

Ever heard of evidence based medicine? Ever heard of double blind randomized clinical trials? Randomization is an incredibly powerful tool in science, but little appreciated by physicists. Their training in probability and statistics is very defective. My theorem supplies an *easier* proof of a *stronger* result than Bell's (Bell's is a corollary) through the device of being explicit about the randomization. Bell's theorem has been around for 50 years now. We understand it better now than Bell himself did, 50 years ago.

You could start a new thread on "Gill's Theorem refuted: Gill's 2015 (3) is false" but then you should start explaining where you see the error. We already started talking about it and you already announced that my work as much a failure as Bell's but you never followed up your claim.

You could also withdraw your claim and forget the whole thing. Fine by me.

[Gordon Watson]

Hi Harry; starting to catch up; more to come:

After I commented on your original illustration, you now have the Carpenter in a small room where he cannot put the timber "head-to-tail"! WtF.
But he'd already done the job without needing a larger room!?
I suggest that we focus on the simple and real experiments available; ie, let's stay real, OK?

I hope that my preceding reply to minkwe was clear enough; in view of the same arguments I'll not comment on everything here. Bell grouped the terms of integration according to the same effective lambda's, which is possible in a calculation but not in an experiment. Therefore I told you, and I hope that you follow it now: Bell's integral is not over over λ. Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ.

To group the lambdas by their effectiveness is NOT to keep " λ constant over each integration step". I presume you mean that lambdas may be grouped by there ontic state? Which, for Alice (and any mathematician) means just two groups: |A+> and |A->. So, quite simply: Alice as experimenter can use exactly the same classification system as the mathematician. Right?

In EPRB, if one does the same experiment [SAME TEST SETTINGS] again one reproduces the same outcome [SEQUENCE] for n->infinite.

Totally FALSE (unless you again change your wording, to be clearer re what you really mean). Do you NOT YET see why?

Think of drawing numbers Xi, at random, from the real line: -oo < Xi < +oo. Let your experiment report on the SIGN of the number: Infinite inputs, two outputs; the Probability that any two numbers (= any two lambdas) are the same is ZERO!

Equally: The Probability that two infinite sequences ++-+-+--+ (= EPRB outcome-sequences) are the same is equally zero!

Do we agree?
...

[gill1109]

Hi Harry; starting to catch up; more to come:

After I commented on your original illustration, you now have the Carpenter in a small room where he cannot put the timber "head-to-tail"! WtF.
But he'd already done the job without needing a larger room!?
I suggest that we focus on the simple and real experiments available; ie, let's stay real, OK?

I hope that my preceding reply to minkwe was clear enough; in view of the same arguments I'll not comment on everything here. Bell grouped the terms of integration according to the same effective lambda's, which is possible in a calculation but not in an experiment. Therefore I told you, and I hope that you follow it now: Bell's integral is not over over λ. Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ.

To group the lambdas by their effectiveness is NOT to keep " λ constant over each integration step". I presume you mean that lambdas may be grouped by there ontic state? Which, for Alice (and any mathematician) means just two groups: |A+> and |A->. So, quite simply: Alice as experimenter can use exactly the same classification system as the mathematician. Right?

In EPRB, if one does the same experiment [SAME TEST SETTINGS] again one reproduces the same outcome [SEQUENCE] for n->infinite.

Totally FALSE (unless you again change your wording, to be clearer re what you really mean). Do you NOT YET see why?

Think of drawing numbers Xi, at random, from the real line: -oo < Xi < +oo. Let your experiment report on the SIGN of the number: Infinite inputs, two outputs; the Probability that any two numbers (= any two lambdas) are the same is ZERO!

Equally: The Probability that two infinite sequences ++-+-+--+ (= EPRB outcome-sequences) are the same is equally zero!

Do we agree?
...

If you do the same experiment with infinitely many outcomes again, the long run averages will converge to the same result.

By the square root N law we know a lot about how close they tend to be when N is large and finite.

You guys both need a refresher Statistics 101.

[Gordon Watson]

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

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

No typo! (14a) corresponds to an impossible experiment, but your answer that it is experimentally valid allows me to reply your question. If Bell's first equation is experimentally valid, then so are his following equations if we accept his arguments.

NOT a TYPO? Impossible experiment?

The experimental results on the LHS of (14a) can be compared to (and they will CERTAINLY agree with) the calculations done on the RHS of (14a)!

(14a) is experimentally valid.

The experimental results on the LHS of (14a) can be compared to (and they will NOT agree with) the calculations done on the RHS of (14b)!

(14b) is experimentally FALSE.

If Bell's first equation is experimentally valid, then so are his following equations if we accept his arguments.

Your logic here is beyond me. Why would we accept anyone's experimentally-false arguments?

NB: His following equations, after (14a), change form progressively; thus:

(14a) experimentally valid. (14b) experimentally false. (14c) experimentally false. (15) experimentally false.

However, I still suspect that at least one of his arguments is wrong, as his final inequality leads to an extremely unlikely conclusion.

Harry says: "Bell's final inequality -- his (15) --leads to an extremely unlikely conclusion."

Unlikely? Or just plain FALSE?

Harry, surely you've been reading too much Bellian double-speak? His (15) = his final inequality = experimentally false.

Can you yet focus your suspicions on the guilty party? HINT!
.

[gill1109]

Harry, surely you've been reading too much Bellian double-speak? His (15) = his final inequality = experimentally false.

Gordon, you have still not reviewed your Statistics 101. There is no Bellian double-speak. There is common-sense statistical insight, which Bell took for granted in his readers. Unfortunately.

[harry]

Hi Harry; starting to catch up; more to come:

After I commented on your original illustration, you now have the Carpenter in a small room where he cannot put the timber "head-to-tail"! WtF.
But he'd already done the job without needing a larger room!?
I suggest that we focus on the simple and real experiments available; ie, let's stay real, OK?

Hi Gordon, your suggestion is no good: you still don't know what I showed you with my simple illustration and want to drop it, but almost everything I wrote next to minkwe and you is based on the assumption that it was understood - that understanding is the basis for further discussion. So, it's useless to go on if not understood!

Last try: I calculated as if the carpenter put the rods head to tail. He never did that. We can even imagine a situation where it is impossible for him to do that experiment. As he used a different method to find the average length than I did in my calculation, my calculation was "experimentally false" in that sense. Is every such "experimentally false" calculation faulty, or not?
I can't be clearer than that, sorry!

Your following message to me is due to a total non-understanding of this simple matter; it's useless for me to reply that if you don't follow this. OTOH, when you follow this you can mostly reply your next message to me yourself!

Some unrelated things:

I hope that my preceding reply to minkwe was clear enough; in view of the same arguments I'll not comment on everything here. Bell grouped the terms of integration according to the same effective lambda's, which is possible in a calculation but not in an experiment. Therefore I told you, and I hope that you follow it now: Bell's integral is not over over λ. Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ.

To group the lambdas by their effectiveness is NOT to keep " λ constant over each integration step". I presume you mean that lambdas may be grouped by there ontic state? Which, for Alice (and any mathematician) means just two groups: |A+> and |A->. So, quite simply: Alice as experimenter can use exactly the same classification system as the mathematician. Right?

Note that something went wrong in your citation. I wrote: " Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step"

Lambda was introduced by Einstein to accomplish a certain outcome for a certain particle at certain detector settings. A lambda that accomplishes the same as another lambda is for all practical purposes the same - that's what I meant with "the same effective lambda". Lambda's that do the same are the same for Bell's calculation, even if they have a different cosmic registration number or astral colour.

In EPRB, if one does the same experiment [SAME TEST SETTINGS] again one reproduces the same outcome [SEQUENCE] for n->infinite.

[..]

No, your second insertion is obviously not what I meant - the outcome of a Bell experiment is a statistical result, and for n->infinite that result is perfectly reproduced (except for measurement inaccuracies). What can NEVER be reproduced for n->infinite is the sequence, and security firms like to use that feature.

[harry]

If you do the same experiment with infinitely many outcomes again, the long run averages will converge to the same result.
By the square root N law we know a lot about how close they tend to be when N is large and finite.
You guys both need a refresher Statistics 101.

Huh? I need advanced statistics, and if I spend less time on such forums then I can advance with studying the book of Jaynes.

[Gordon Watson]

Hi Harry; starting to catch up; more to come:

After I commented on your original illustration, you now have the Carpenter in a small room where he cannot put the timber "head-to-tail"! WtF.
But he'd already done the job without needing a larger room!?
I suggest that we focus on the simple and real experiments available; ie, let's stay real, OK?

Hi Gordon, your suggestion is no good: you still don't know what I showed you with my simple illustration and want to drop it, but almost everything I wrote next to minkwe and you is based on the assumption that it was understood - that understanding is the basis for further discussion. So, it's useless to go on if not understood!

I had the impression that you changed the illustration after I analysed it. Did you?

Was their something wrong with my analysis?

From the examples given by me, is it not clear that, by "experimentally false", I mean the derived result is proven false by experiment?

Thus Bell's (14a) is OK; his string (14b)-(15) is not.

Last try: I calculated as if the carpenter put the rods head to tail. He never did that. We can even imagine a situation where it is impossible for him to do that experiment. As he used a different method to find the average length than I did in my calculation, my calculation was "experimentally false" in that sense. Is every such "experimentally false" calculation faulty, or not?
I can't be clearer than that, sorry!

I thought it was MY definition of "experimentally false" that was under discussion. Now it turns out that your definition is polar-opposite to mine?

What's worse, as I read it, your definition makes no sense: You appear to imply that results which agree with each other, AND with experiment, are experimentally false (or not) based on the method or theory used to derive them.

Because, originally: Wouldn't you and the carpenter have agreed on the average length: the experimental average? But, alas, he was interrupted by your shout?

Yet you claim that it his result that is experimentally false, right?

PS: As I recall, wasn't your argument already in trouble when this definitional issue arose? To help me, could you please point to the equation in my essay that is the sticking point here? Thanks.

NB; in my terms: Every calculation that is proven to be false by a relevant experiment is "experimentally false". Can I be any clearer than that? Bell's string of equations from (14b) to (15) is experimentally false!

Your following message to me is due to a total non-understanding of this simple matter; it's useless for me to reply that if you don't follow this. OTOH, when you follow this you can mostly reply your next message to me yourself!

I'm missing your point here.

Some unrelated things:

I hope that my preceding reply to minkwe was clear enough; in view of the same arguments I'll not comment on everything here. Bell grouped the terms of integration according to the same effective lambda's, which is possible in a calculation but not in an experiment. Therefore I told you, and I hope that you follow it now: Bell's integral is not over over λ. Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ.

To group the lambdas by their effectiveness is NOT to keep " λ constant over each integration step". I presume you mean that lambdas may be grouped by there ontic state? Which, for Alice (and any mathematician) means just two groups: |A+> and |A->. So, quite simply: Alice as experimenter can use exactly the same classification system as the mathematician. Right?

Note that something went wrong in your citation. I wrote: " Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step"

I'm missing your point here. Is it something to do with me not using this intro: "Bell's integral is not over N or t, but over λ"?

Further, you say: "Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ."

How then does he obtain an expectation if one line contains, for example, only A+, B+, C+ and not the mix A±, B±, C±?

For, as I understand your meaning: one single λ delivers a single result at settings a,b,c?

Further: What was the purpose or point in Bell so doing?

PS: It just occurs to me that we need to be sure that we agree on these points:

A:- "NO final Bellian calculation/inequality agrees with EXPERIMENT."

Which, it seems to me is the same as saying:

B:- "ALL final Bellian calculations/inequalities are EXPERIMENTALLY FALSE; including Bell (15), CHSH, etc."

Are we agreed on points A and B?

Or do you rely on loopholes to support your view -- and thus not agree?

NB: I do not require any loopholes in my own theory because all loopholes are closed via my theory being based on commonsense local realism (CLR).

Lambda was introduced by Einstein to accomplish a certain outcome for a certain particle at certain detector settings. A lambda that accomplishes the same as another lambda is for all practical purposes the same - that's what I meant with "the same effective lambda". Lambda's that do the same are the same for Bell's calculation, even if they have a different cosmic registration number or astral colour.

Strange use of language to me: There is no way of knowing if lambda-i is doing the same as lambda-j. So, under your doctrine, Bell is wrong to treat them as doing the same; and we seem to agree. For how else did Bell's (14b) become experimentally false?

In EPRB, if one does the same experiment [SAME TEST SETTINGS] again one reproduces the same outcome [SEQUENCE] for n->infinite.

[..]
No, your second insertion is obviously not what I meant - the outcome of a Bell experiment is a statistical result, and for n->infinite that result is perfectly reproduced (except for measurement inaccuracies). What can NEVER be reproduced for n->infinite is the sequence, and security firms like to use that feature.

OK, good; we now clearly agree on this point.

PS: If there are specific points in your reply to minkwe that I should still answer, please let me know; thanks.
..

[Gordon Watson]

Harry, here's you as the source of much confusion. I trust that this particular confusion is now gone?

I've underlined and added identifiers [.]-- to some parts that had me confused; then added suggested corrections at the end.

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

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

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

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

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

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

Attempted clarifications/corrections of Harry's statements:

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

It is NOT a hollow argument to say that the same lambda NEVER comes back. And it is poor logic for you to confuse "the same effective lambda" with the need for "lambda_2438 = lambda_215, etc".

(a). For, allowing the lambdas to be vectors drawn from the continuum of 3-space, the Probability that any two lambdas are the same is ZERO (as previously illustrated with -oo < Xi < +oo and the SIGN function as output).

(b). In EPRB, from Alice's point of view (as previously illustrated with -oo < Xi < +oo and the SIGN function as output), there are just two classes of "effective lambda". Those that are members of the ontic state |A+>; those that are members of the ontic state |A->.

BUT two such classes do NOT require a "return of the same lambdas where for the experimental outcomes one must have lambda_2438 = lambda_215, etc." Nor are they required "ELSE NO RESULTS REOCCUR …."

For, in that you are surely not implying that there are just two lambdas (ie, to match the two ontic states): why require any lambdas to be the same?

[B]-- In EPRB, if one does the same experiment again one reproduces the same [NOT outcomes in the plural BUT] EXPECTATION [in the singular] for n->infinite.

HTH; Gordon

[gill1109]

Bell assumes that Nature picks from the same set of lambda every time, according to the same probability distribution.

Loophole-free experiments (delayed random choice of settings, no detection loophole, no locality loophole) are experiments which "enforce" that the set of lambda and the probability distribution of lambda was not influenced by the choice of settings.

However, obviously, the set of lambda and the probability distribution of lambda might change in time.

Fortunately, it is easy to strengthen Bell's proof. In my own work I have shown that it doesn't matter if the probability distribution of lambda changes with time, as long as all the other experimental precautions are in place.

I think it might be an enormous waste of time to be discussing a 50 years old proof which has since been improved and strengthened by many orders of magnitude. All the loopholes in this ancient piece of informal mathematics have been closed by now. All ambiguities resolved.

Bell (1964) makes more assumptions than are necessary in order to get his result. He does not explicitly address a number of important issues.

[harry]

[..] I had the impression that you changed the illustration after I analysed it. Did you?

I don't think so; I did add a possible detail to enhance the clarification.

Was their something wrong with my analysis?

Yes, it totally missed the point, as I clarified here below.

From the examples given by me, is it not clear that, by "experimentally false", I mean the derived result is proven false by experiment?
[rearrange]:
NB; in my terms: Every calculation that is proven to be false by a relevant experiment is "experimentally false". Can I be any clearer than that? Bell's string of equations from (14b) to (15) is experimentally false!

No, that was not clear, and doesn't make any sense to me: as far as I know, quantum experiments cannot prove Bell's derivation false! If you know of an experiment that proves 14a correct and 14b wrong, please cite it.

Thus Bell's (14a) is OK; his string (14b)-(15) is not.

Instead, Bell's (14a) is according to Bell's theoretical considerations equivalent to Bell's (14b) and you did not prove that wrong. As I explained and illustrated, contrary to your interpretation on which you based your argument, neither Bell's (14a) nor (14b) corresponds to the experimental procedure - just as my average calculation didn't correspond to the doings of the carpenter. As the below was my last try, I will leave it at that.

Last try: I calculated as if the carpenter put the rods head to tail. He never did that. We can even imagine a situation where it is impossible for him to do that experiment. As he used a different method to find the average length than I did in my calculation, my calculation was "experimentally false" in that sense. Is every such "experimentally false" calculation faulty, or not?
I can't be clearer than that, sorry!

I thought it was MY definition of "experimentally false" that was under discussion. Now it turns out that your definition is polar-opposite to mine?
What's worse, as I read it, your definition makes no sense: You appear to imply that results which agree with each other, AND with experiment, are experimentally false (or not) based on the method or theory used to derive them.

No definition of terms is "under discussion". Please read it again: "IN THAT SENSE". Terms can be used with opposite meanings in subsequent sentences. I discussed there the second possible meaning of "experimentally false". The first I already discussed earlier, also with no result. My average calculation may be called "experimentally false" because it doesn't match experiment, and in that sense Bell's 14a is also "experimentally false" . Earlier you appeared to clarify that you call a calculation that doesn't match experiment but according to theory gives the correct result "experimentally correct", which made both 14a and 14b possibly "experimentally correct" in that sense.

The two ways that I could imagine you meant "experimentally" yield no qualitative difference between (14a) and (14b). The way you now say that you meant it doesn't make sense to me, as Bell's equations don't predict the result of a quantum experiment. As now you give a meaning to your phrase of which I cannot make sense at all. I give up; thus I will drop anything with "experimentally false".

Because, originally: Wouldn't you and the carpenter have agreed on the average length: the experimental average? But, alas, he was interrupted by your shout? Yet you claim that it his result that is experimentally false, right?

No, and that was not the point, and I make no claims except that my calculation is correct despite it not corresponding to the experiment... anyway, I ended my efforts there too.

PS: [...] could you please point to the equation in my essay that is the sticking point here? Thanks.

Once more, the equation that was the sticking point here (and which is IMHO is the sticking point of this topic) is your version of Bell's 14a which is wrong (even the revised version) - as several people explained now on many pages here.

[..] To group the lambdas by their effectiveness is NOT to keep " λ constant over each integration step". I presume you mean that lambdas may be grouped by there ontic state? Which, for Alice (and any mathematician) means just two groups: |A+> and |A->. So, quite simply: Alice as experimenter can use exactly the same classification system as the mathematician. Right?

Note that something went wrong in your citation. I wrote: " Bell's integral is not over N or t, but over λ. Bell keeps λ constant over each integration step"

I'm missing your point here. Is it something to do with me not using this intro: "Bell's integral is not over N or t, but over λ"?

No, as you could see if you looked, your citation there was broken, muddled-up.

Further, you say: "Bell keeps λ constant over each integration step: on purpose one whole line corresponds to a single λ."

How then does he obtain an expectation if one line contains, for example, only A+, B+, C+ and not the mix A±, B±, C±?

For, as I understand your meaning: one single λ delivers a single result at settings a,b,c?

Further: What was the purpose or point in Bell so doing?

A result depends on λ and the angles a and b. Thus one integration step gives a determined result. The expected outcome (according to Bell) of an experiment with N->infinity is determined by integration over all possible λ for the used angles, taking in account the relative frequency of those λ ((and which your version omits) .
And the purpose of Bell was to predict possible outcomes for a theory as Einstein proposed, and to show therewith that Einstein's proposed solution cannot work.

PS: It just occurs to me that we need to be sure that we agree on these points:
A:- "NO final Bellian calculation/inequality agrees with EXPERIMENT." [..]

Who wrote that where? I cannot find anyone saying that in this thread (except for you here). I searched: "final Bellian calculation/inequality" and no results...

Lambda was introduced by Einstein to accomplish a certain outcome for a certain particle at certain detector settings. A lambda that accomplishes the same as another lambda is for all practical purposes the same - that's what I meant with "the same effective lambda". Lambda's that do the same are the same for Bell's calculation, even if they have a different cosmic registration number or astral colour.

Strange use of language to me: There is no way of knowing if lambda-i is doing the same as lambda-j. [..]

Lambda is a hypothetical entity introduced by Einstein; Bell puts it to the test. If no similarly acting lambda's occur in later experiments then how can you (or Einstein) produce reproducible experiments??

[..] the outcome of a Bell experiment is a statistical result, and for n->infinite that result is perfectly reproduced (except for measurement inaccuracies). [..]

OK, good; we now clearly agree on this point.

Surely everyone here always agreed on that.

[harry]

Attempted clarifications/corrections of Harry's statements:

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

It is NOT a hollow argument to say that the same lambda NEVER comes back. And it is poor logic for you to confuse "the same effective lambda" with the need for "lambda_2438 = lambda_215, etc" [..]

(a). For, allowing the lambdas to be vectors drawn from the continuum of 3-space, the Probability that any two lambdas are the same is ZERO (as previously illustrated with -oo < Xi < +oo and the SIGN function as output).[..] why require any lambdas to be the same? .

If you assume to lambda to be a continuum, non-quantized, then you are technically (from a strict math viewpoint) correct I think! However, in practice (from physics viewpoint) it's a meaningless argument, for Bell assumed a probability distribution from which approximately the same lambda's must reoccur for those lambda's to reproduce experimental outcomes. If not, please explain how your lambda's cause reproducible experiments to happen? As Bell did not emulate experiments, for a theoretical prediction of those results he could therefore integrate over lambda times the probability of each to occur. In other words, that argument is not relevant for the discussion here of your paper. See also how Gill phrases it. Note also that Gill says to have achieved a derivation without that possible weakness in Bell's derivation, while still arriving at Bell's result.

[gill1109]

Attempted clarifications/corrections of Harry's statements:

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

It is NOT a hollow argument to say that the same lambda NEVER comes back. And it is poor logic for you to confuse "the same effective lambda" with the need for "lambda_2438 = lambda_215, etc" [..]

(a). For, allowing the lambdas to be vectors drawn from the continuum of 3-space, the Probability that any two lambdas are the same is ZERO (as previously illustrated with -oo < Xi < +oo and the SIGN function as output).[..] why require any lambdas to be the same? .

If you assume to lambda to be a continuum, non-quantized, then you are technically (from a strict math viewpoint) correct I think! However, in practice (from physics viewpoint) it's a meaningless argument, for Bell assumed that practically the same lambda's must reoccur for your lambda to reproduce experimental outcomes. See also how Gill phrases it. If not, please explain how your lambda's cause reproducible experiments to happen? Note however that Gill says to have achieved that, and still arriving at Bell's result.

Maybe Gordon would like to explain why he trusts evidence based medicine and double blind randomized clinical trials. The same patient never comes back again. No patient is treated with both the treatments which are to be compared. You can't give a breast cancer patient both a mastectomy and a breast-preservation treatment. The outcome of any patient (whether or not they are still alive five years later) depends on a myriad of variables which can't be measured, can't be observed, can't be "fixed". Even if you get to see infinitely many patients you'll never see two identical patients.

[Gordon Watson]

Attempted clarifications/corrections of Harry's statements:

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

It is NOT a hollow argument to say that the same lambda NEVER comes back. And it is poor logic for you to confuse "the same effective lambda" with the need for "lambda_2438 = lambda_215, etc" [..]

(a). For, allowing the lambdas to be vectors drawn from the continuum of 3-space, the Probability that any two lambdas are the same is ZERO (as previously illustrated with -oo < Xi < +oo and the SIGN function as output).[..] why require any lambdas to be the same? .

If you assume to lambda to be a continuum, non-quantized, then you are technically (from a strict math viewpoint) correct I think! However, in practice (from physics viewpoint) it's a meaningless argument, for Bell assumed that practically the same lambda's must reoccur for your lambda to reproduce experimental outcomes. See also how Gill phrases it. If not, please explain how your lambda's cause reproducible experiments to happen? Note however that Gill says to have achieved that, and still arriving at Bell's result.

Maybe Gordon would like to explain why he trusts evidence based medicine and double blind randomized clinical trials. The same patient never comes back again. No patient is treated with both the treatments which are to be compared. You can't give a breast cancer patient both a mastectomy and a breast-preservation treatment. The outcome of any patient (whether or not they are still alive five years later) depends on a myriad of variables which can't be measured, can't be observed, can't be "fixed". Even if you get to see infinitely many patients you'll never see two identical patients.

Thanks Richard, for making my point.

We seem to be in total agreement here, though I make the point that I'd rather be writing equations for QM than patients:

It's Probability zero that two patents are the same.

It's Probability zero that two lambdas are the same.

PS: I trust that these same points are now clear to Harry.

Gordon

[harry]

Maybe Gordon would like to explain why he trusts evidence based medicine and double blind randomized clinical trials. The same patient never comes back again. No patient is treated with both the treatments which are to be compared. You can't give a breast cancer patient both a mastectomy and a breast-preservation treatment. The outcome of any patient (whether or not they are still alive five years later) depends on a myriad of variables which can't be measured, can't be observed, can't be "fixed". Even if you get to see infinitely many patients you'll never see two identical patients.

Thanks Richard, for making my point.

We seem to be in total agreement here, though I make the point that I'd rather be writing equations for QM than patients:

It's Probability zero that two patents are the same.

It's Probability zero that two lambdas are the same.

PS: I trust that these same points are now clear to Harry.

Gordon

Gordon, as you saw in my answer (which I next elaborated slightly more before seeing this), that point was clear to me, and (as Richard hinted at) irrelevant with respect to Bell's statistical approach.

Once more: please explain how your lambda's enable reproducible experiments.

[Gordon Watson]

Attempted clarifications/corrections of Harry's statements:

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

It is NOT a hollow argument to say that the same lambda NEVER comes back. And it is poor logic for you to confuse "the same effective lambda" with the need for "lambda_2438 = lambda_215, etc" [..]

(a). For, allowing the lambdas to be vectors drawn from the continuum of 3-space, the Probability that any two lambdas are the same is ZERO (as previously illustrated with -oo < Xi < +oo and the SIGN function as output).[..] why require any lambdas to be the same? .

If you assume to lambda to be a continuum, non-quantized, then you are technically (from a strict math viewpoint) correct I think! However, in practice (from physics viewpoint) it's a meaningless argument, for Bell assumed a probability distribution from which approximately the same lambda's must reoccur for those lambda's to reproduce experimental outcomes. If not, please explain how your lambda's cause reproducible experiments to happen? As Bell did not emulate experiments, for a theoretical prediction of those results he could therefore integrate over lambda times the probability of each to occur. In other words, that argument is not relevant for the discussion here of your paper. See also how Gill phrases it. Note also that Gill says to have achieved a derivation without that possible weakness in Bell's derivation, while still arriving at Bell's result.

Harry, with respect and seeking to be helpful:

The highlighted pieces are seriously flawed at a very elementary level:

Harry says, "Bell assumed a probability distribution from which approximately the same lambda's must reoccur for those lambda's to reproduce experimental outcome."

Response: Alice's detector has just two outputs, +1 and -1. Are there just two lambdas, or 100, or … (say when).

Harry asks, "explain how your lambda's cause reproducible experiments to happen."

Response, presuming you mean "reproducible outputs (±1) from many repetitions of the same experiments": Alice's detector has just two outputs, +1 and -1. Are there just two lambdas, or 100, or ... (say when).

Please consider an aluminium-extruding machine with two dies producing just two profiles: + -. What limitation is there, then, on the orientation of the allowable billets (feed-stock)? Given N factories (N -> infinity), each producing the same outputs (= two profiles) from machines of their own design, what limit is there on the number and orientation of billets?

Harry, hoping this poor analogy helps, and with best regards; Gordon

PS: Please see my response to Richard above: re the similarity of patients and lambdas under experimentation; no two of them the same!
.

[Gordon Watson]

Maybe Gordon would like to explain why he trusts evidence based medicine and double blind randomized clinical trials. The same patient never comes back again. No patient is treated with both the treatments which are to be compared. You can't give a breast cancer patient both a mastectomy and a breast-preservation treatment. The outcome of any patient (whether or not they are still alive five years later) depends on a myriad of variables which can't be measured, can't be observed, can't be "fixed". Even if you get to see infinitely many patients you'll never see two identical patients.

Thanks Richard, for making my point.

We seem to be in total agreement here, though I make the point that I'd rather be writing equations for QM than patients:

It's Probability zero that two patents are the same.

It's Probability zero that two lambdas are the same.

PS: I trust that these same points are now clear to Harry.

Gordon

Gordon, as you saw in my answer (which I next elaborated slightly more before seeing this), that point was clear to me, and (as Richard hinted at) irrelevant with respect to Bell's statistical approach.

Once more: please explain how your lambda's enable reproducible experiments.

Harry, please: Ask minkwe, or Richard, or consider his medical example, or consider my extrusion machines, or see a text book.

For, please, how can you say that point was clear to you when you repeat the question but now with no two lambdas the same (I presume)?

And what was Richard's hint? (He and I, now, I believe, on the same page on this small matter. If we ever differed?)
.