Joy Christian, "Disproof of Bell's Theorem"

[bcrowell]

This showed up on the arxiv blog today: Joy Christian, "Disproof of Bell's Theorem," http://arxiv.org/abs/1103.1879

I'm not enough of a specialist to be able to judge the correctness or significance of the result.

Comments?

[naima]

A(a,lambda) seems to depend only on Lambda according to (1).
my Joy remains.

[Nabeshin]

I'm not familiar enough to judge either, but i just find it interesting that the only references for the paper, besides Bell's original paper, are Christian's own papers...

[ThomasT]

I'm not knowledgeable enough to judge/comment definitively either. But here's my two cents in lieu of some experts chiming in.

Christian apparently became convinced some years ago that there's nothing special about Bell's theorem or quantum entanglement. Since then he's presented a number of nonrealistic counterexamples to Bell's theorem. This is the latest. My guess, not having worked through all of it, is that all his math is probably correct, but that his result will probably be regarded as insignificant in that it's a consequence of assumptions/definitions that seem even more clearly nonrealistic than his previous attempts.

[Fredrik]

I tried to read one of Christian's "disproof" articles once, and it was a bunch of incoherent nonsense. It was impossible to make sense of what he was saying. I decided then to not let him waste any of my time again.

There are several other threads about his articles by the way. In one of them, I got an infraction for posting a link to the article I alluded to above. A bit excessive perhaps, but I do agree that discussions about articles that the authors have been unable to get published don't really belong in this forum.

[bobbytkc]

His paper is interesting, but I have heard a convincing explanation for why it is probably not significant:

Assuming that all his mathematics are correct, he still assumes that the measurement outcomes follow some weird algebra which when combined together, to give a desired value which he designed to replicate quantum experiments. However, measurement outcomes are defined by clicks on detectors, and it is the experimentalist, not the experiment itself, who assigns the values to the outcomes and combines the values of the outcomes to get the correlations. The experimentalist combines the values in such a way that it follows NORMAL algebra, and yet it still violates Bell's inequality. You just need to see Ekert's cryptographical protocol to see that this is true. In that protocol, two experiementalists randomly performs independent measurements and assigns +1 or -1 to the outcomes, then compares them using simple multiplication to violate Bell's inequality, no special algebra required.

Therefore, in a sense, Joy Christian is missing the point. What is required, is an explanation of why it is that when 2 experimentalists perform independent measurements and assigns real values to them, and thereafter combine them using ONLY normal algebra, the resulting correlations STILL violate Bell's inequality. So even though he found an interesting algebra which is local with hidden variables and is able to reproduce certain quantum results when you combine them, it still does not explain why when experimentalists apply only normal algebra to their measured outcomes, Bell's inequality is still violated. So his 'disproof' is probably incorrect.

[DrChinese]

This showed up on the arxiv blog today: Joy Christian, "Disproof of Bell's Theorem," http://arxiv.org/abs/1103.1879

I'm not enough of a specialist to be able to judge the correctness or significance of the result.

Comments?

His "proof" gives values for A and B, along with joint probabilities for A & B. But a realistic proof should give a value of C as well, such that various joint probabilities for A, B and C sum to 1 and none are negative. It is no surprise that you can derive a Bell Inequality violation without the realistic test applied.

Don't hold your breath on this one.

[yoda jedi]

So even though he found an interesting algebra which is local with hidden variables.

Thats goes back to Bohm and Hiley.

[bobbytkc]

Thats goes back to Bohm and Hiley.

You are talking about Bohmian mechanics?

Bohmian mechanics has hidden variables (in that particles have definite position and momentum, but still obeys Schrodinger's equations), however, the cost is that it is distinctively non local, so it still falls under the umbrella of Bell's theorem, which states that quantum mechanics is non-local and/or has no hidden variable. So in that respect, you are mistaken. What Joy Christian purports to have found is something more significant, that a local AND hidden variable theory is possible and matches the predictions of quantum mechancs. Unfortunately, it is probably not the right way to approach it.

[bobbytkc]

His "proof" gives values for A and B, along with joint probabilities for A & B. But a realistic proof should give a value of C as well, such that various joint probabilities for A, B and C sum to 1 and none are negative. It is no surprise that you can derive a Bell Inequality violation without the realistic test applied.

Don't hold your breath on this one.

What C? I believe Bell's theorem is only bipartite,no?

[ThomasT]

His paper is interesting, but I have heard a convincing explanation for why it is probably not significant:

Assuming that all his mathematics are correct, he still assumes that the measurement outcomes follow some weird algebra which when combined together, to give a desired value which he designed to replicate quantum experiments. However, measurement outcomes are defined by clicks on detectors, and it is the experimentalist, not the experiment itself, who assigns the values to the outcomes and combines the values of the outcomes to get the correlations. The experimentalist combines the values in such a way that it follows NORMAL algebra, and yet it still violates Bell's inequality. You just need to see Ekert's cryptographical protocol to see that this is true. In that protocol, two experiementalists randomly performs independent measurements and assigns +1 or -1 to the outcomes, then compares them using simple multiplication to violate Bell's inequality, no special algebra required.

Therefore, in a sense, Joy Christian is missing the point. What is required, is an explanation of why it is that when 2 experimentalists perform independent measurements and assigns real values to them, and thereafter combine them using ONLY normal algebra, the resulting correlations STILL violate Bell's inequality. So even though he found an interesting algebra which is local with hidden variables and is able to reproduce certain quantum results when you combine them, it still does not explain why when experimentalists apply only normal algebra to their measured outcomes, Bell's inequality is still violated. So his 'disproof' is probably incorrect.I agree. Your post is enlightening and points to the reason why Christian's purported LR models of entanglement are not regarded as LR models of entanglement -- which results, ultimately, from a qualitative assessment of how the purported local realism is encoded in the formulation(s).

What Joy Christian purports to have found is something more significant, that a local AND hidden variable theory is possible and matches the predictions of quantum mechancs.Yes. Obviously, proposing a LR formulation that doesn't reproduce qm expectation values is a non-starter.

Unfortunately, it is probably not the right way to approach it.If the aim is to produce an LR theory of entanglement, then it's the only way to approach it. Explicit, clearly LR models a la Bell have been definitively ruled out. Christian's LR offerings fail the quantitative test of this (which is what DrC is talking about). So we know that Christian's models are not Bell LR.

However, in the absence of a logical proof that Bell LR is the only possible LR, then it remains to assess each purported LR model qualitatively. Christian's λ fail the realism test by any qualitative standard that I'm aware of.

If the aim is to understand why LR models of entanglement are impossible (even in a world that obeys the principle of locality and the light speed limit), then I agree with you that Christian is missing the point and taking the wrong approach. But it's still fun to check out the stuff that he comes up with.

[DrChinese]

What C? I believe Bell's theorem is only bipartite,no?

With 2 entangled photons, you can measure coincidence at 2 angle settings (say A and B, which will follow the cos^2 rule for AB). The third, C, is hypothetical in a realistic universe because the realist asserts it exists. However it cannot be measured. QM makes no statement about its existence, so no problem there. But the realist does. Bell pointed out that the values of coincidence for AC and BC will not both follow the QM predictions (if C existed). See his (14) where C is introduced.

So a local realistic model without a prediction for C is not truly "realistic" after all. In other words, A and B are not truly independent of each other for if they were, there would also be C, D, E... values possible which would all follow the QM expectation values when considered with A or B. Many "disproofs" of Bell conveniently skip this requirement.

[yoda jedi]

You are talking ..............?


So even though he found an interesting algebra which is local with hidden variables

Clifford Algebra.
(goes back to Bohm and Hiley).

[DrChinese]

Just to add to what I said above:

a) It is a requirement that 1 >= f(A,B) >= f(A,B,C) >= 0 where f() is a correlation function. This is the realism requirement. Using the logic of Bell, this is shown to be false if C is assumed to exist. (See also "Bell's Theorem and Negative Probabilities".)

b) It is a requirement that f(A,A)=f(B,B)=1 (or 0 depending on your basis). This is the requirement for perfect correlations. This is sometimes overlooked, but is actually the reason someone might think there are hidden variables in the first place. However, it is really a consequence of the cos^2 rule since:

f(A,A) = cos^2(A,A) = cos^2(A-A) = cos^2(0) = 1

[ThomasT]

With 2 entangled photons, you can measure coincidence at 2 angle settings (say A and B, which will follow the cos^2 rule for AB).What might be confusing for some is that what you're denoting as A,B and C are unit vectors associated with spin analyzer settings, and are usually denoted by bolded lower case letters (eg., a, b, c, etc.).

The third, C, is hypothetical in a realistic universe because the realist asserts it exists. However it cannot be measured.This might be confusing because (a,b), (a,c), and (b,c) are denotations of different dual analyzer settings, ie., different θ, or angular differences (a-b), in 3D, Euclidean space, and therefore realistic, and all follow the cos2 rule.

So, in what sense is c not realistic?

QM makes no statement about its existence, so no problem there.The qm (a,b) refers to any combination of analyzer settings, any θ, wrt the dual, joint analysis of bipartite systems. Since a can take on any value from the set of all possible analyzer settings, and so can b, then it isn't clear what you mean that qm makes no statement about the existence of a certain possible analyzer setting.

[...]

So a local realistic model without a prediction for C is not truly "realistic" after all.But all purported LR models make a prediction for any individual analyzer setting, as well as any θ. So does qm.

In other words, A and B are not truly independent of each other ...Well, obviously the analyzer settings aren't independent wrt the measurement of any given pair since together they're the global measurement parameter, θ. Is that what you mean? If not, then what?

... for if they were, there would also be C, D, E... values possible which would all follow the QM expectation values when considered with A or B. Many "disproofs" of Bell conveniently skip this requirement.It's not clear to me what you're saying or how you got there.

[DrChinese]

But all purported LR models make a prediction for any individual analyzer setting, as well as any θ. So does qm.


Joy's doesn't, and it should if it is realistic.

Where a=0, b=67.5, c=45:

The QM prediction for f(a, b)=.1464
There is no QM prediction for either f(a, b, c) or f(a, b, ~c). QM is not realistic. Note: the ~c means Not(c) which is the same as saying you would get the opposite result. I.e. a plus instead of minus, or vice versa.

The LR prediction for f(a, b)=.1464. OK so far.
But if any LR is truly realistic, then it has a prediction for both f(a, b, c) and f(a, b, ~c). For the angles above, what is that value? When you run the math, the value for f(a, b, ~c) comes out -.1036 which is impossible as it is less than zero.

[ThomasT]

Joy's doesn't, and it should if it is realistic.Sure it does. We're talking about analyzing bipartite systems with dual analyzers. ab, ac, and bc are the only possible analyzer settings for a given run.

There is no QM prediction for either f(a, b, c) or f(a, b, ~c).Why would there be? The bipartite system is generating data via dual, not triple, analyzers.

But if any LR is truly realistic, then it has a prediction for both f(a, b, c) and f(a, b, ~c).Why, if a model is intended to describe a bipartite system that's generating data via dual, not triple, analyzers? Seems like an unrealistic requirement.

[yoda jedi]

This showed up on the arxiv blog today: Joy Christian, "Disproof of Bell's Theorem," http://arxiv.org/abs/1103.1879

I'm not enough of a specialist to be able to judge the correctness or significance of the result.

Comments?

There is a book edited by him and myrvold.

Quantum reality, relativistic causality, and closing the epistemic circle. (Springer).

http://books.google.co.ve/books?id=TaM1Nv09hJAC&printsec=frontcover&dq=Quantum+reality,+relativistic+causality,+and+cl osing+the+epistemic+circle.&source=bl&ots=qo7AmhGgch&sig=F9zPdckpGsTfgNF4W3mEZBGAsEg&hl=es&ei=LimJTd6jD-iE0QG79InzDQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CCsQ6AEwAg#v=onepage&q&f=false

http://www.springerlink.com/content/u64316/?p=ff067ba37c4e409cbbebeeaef650fda1&pi=0#section=23120&page=1&locus=71

[DrChinese]

Why, if a model is intended to describe a bipartite system that's generating data via dual, not triple, analyzers? Seems like an unrealistic requirement.

What else would realism be except the requirement that unmeasured c exists alongside measured a and b?

[ThomasT]

What else would realism be except the requirement that unmeasured c exists alongside measured a and b?Realism is made explicit in Bell's equation (1), where he defines the functions A (operating at S1) and B (operating at S2),
A(a,λ) = ± 1, B(b,λ) = ± 1 ,
where the spin analyzer settings are described as unit vectors in 3D Euclidean space and denoted as a and b, and where λ denotes arbitrary hidden parameters (determining individual detection) carried by the particles from the source and is, in his equation (2), associated with the particles via probability density ρ.

Locality is made explicit via his equation (2),
P(a,b) = ∫dλρ(λ)A(a,λ)B(b,λ)

In Bell's (14) c isn't unmeasured. It represents an analyzer setting that produces a third individual ± 1 datastream. There are only two analyzers, one at S1 and one at S2, which produce the three joint datastreams, ab, ac, and bc necessary for the inequality, Bell's (15).

I still don't understand what you're getting at (at one point I thought I did, but now I see that I don't). But since we're assessing Christian's model as unrealistic for different reasons, then it seems ok to continue the discussion regarding your 'realistic dataset requirement".

[DrChinese]

Realism is made explicit in Bell's equation (1), where he defines the functions A (operating at S1) and B (operating at S2),
A(a,λ) = ± 1, B(b,λ) = ± 1 ,
where the spin analyzer settings are described as unit vectors in 3D Euclidean space and denoted as a and b, and where λ denotes arbitrary hidden parameters (determining individual detection) carried by the particles from the source and is, in his equation (2), associated with the particles via probability density ρ.

...

In Bell's (14) c isn't unmeasured. It represents an analyzer setting that produces a third individual ± 1 datastream. There are only two analyzers, one at S1 and one at S2, which produce the three joint datastreams, ab, ac, and bc necessary for the inequality, Bell's (15).


If you can measure it (c), then you don't have a realism assumption. And you specifically say that the analyzers are S1 and S2 for a and b (actually any 2 of a, b, c). The whole idea of Bell is that when you measure ab, there are no datasets for an additional assumed c which is itself consistent as to ac and bc - even though the third is not measured. This is very straightforward, see his (14) and after.

[ThomasT]

If you can measure it (c), then you don't have a realism assumption. And you specifically say that the analyzers are S1 and S2 for a and b (actually any 2 of a, b, c). The whole idea of Bell is that when you measure ab, there are no datasets for an additional assumed c which is itself consistent as to ac and bc - even though the third is not measured. This is very straightforward, see his (14) and after.Realism is assumed and explicated by Bell via the functions A and B defined in his equation (1).

Bell's inequality has nothing to do with not being able to generate an abc dataset. Obviously, it's physically impossible to generate an abc dataset using dual analyzers, and it's not clear to me why you think that that has anything to do with Bell's realism assumption.

[DrChinese]

Realism is assumed and explicated by Bell via the functions A and B defined in his equation (1).

Bell's inequality has nothing to do with not being able to generate an abc dataset. Obviously, it's physically impossible to generate an abc dataset using dual analyzers, and it's not clear to me why you think that that has anything to do with Bell's realism assumption.


Your mistake is a common one. :biggrin:

Bell's (1) leads to nothing inconsistent with QM. You would actually expect perfect correlations from that, and of course we see that experimentally. But Bell's (14+) is required to see the fallacy of (1). Once you try to fit a, b and c into things, it all falls apart. And certainly not before (14).

[DrChinese]

For those reading along, allow me to add the following. When you have 2 entangled particles that are essentially clones of each other, you would expect that if they were independent (locality holds) then any measurement on Alice (say) would yield the same result as an identical measurement on Bob. Therefore, you would expect that the result of ANY measurement on either Alice or Bob is actually predetermined. How else to explain the results? This idea - that the results of any measurement is predetermined - can be considered to be the assumption of Realism. Realism is the idea that ALL particle properties are independent of an actual measurement.

Of course, the Heisenberg Uncertainty Principle essentially says the opposite: a measurement of one property makes its non-commuting partner completely uncertain.

So if Realism AND Locality hold, particle properties are predetermined. So presumably the unmeasured properties have values. For polarization of photons, that means that you could expect either a + or - result and that such result would occur with a frequency of somewhere between 0 and 100% of the time. That's reasonable, right?

Ah, reasonable but wrong (says Bell)! Turns out you cannot construct a dataset in which the QM expectation value holds for many a, b and c settings. And yet we said those were predetermined if the entangled particles were really clones and if locality holds.

[ThomasT]

Your mistake is a common one. :biggrin:What mistake?

Bell's (1) leads to nothing inconsistent with QM. Agreed. Bell's (1) has to do with spin properties carried by particles produced at a common source which produce individual results. All consistent with the qm model and application of the conservation law.

But Bell's (14+) is required to see the fallacy of (1). What fallacy? Don't we agree that Bell's (1) is consistent with qm, as per Bell himself?

Bell's (14) is a revision of Bell's (2) in view of Bell's (12) and (13). Bell's (2) makes explicit the locality assumption, which is necessary because Bell's (1) doesn't explicate locality wrt joint detections.

Once you try to fit a, b and c into things, it all falls apart. And certainly not before (14).Bell shows that the form of Bell's (2) is incompatible with qm. The incompatibility is due to the locality assumption embodied in the form (2), which converted to (14) and evaluated wrt expectation values for three distinct joint analyzer settings (ab, ac, and bc) gives Bell's inequality.

[DrChinese]

What fallacy? Don't we agree that Bell's (1) is consistent with qm, as per Bell himself?

...

The issue is that there was no APPARENT flaw in (1) prior to Bell. Bell then showed how this innocent looking formula is wrong. Which it is. We now know that it cannot account at all for the observed behavior.

[ThomasT]

The issue is that there was no APPARENT flaw in (1) prior to Bell. Bell then showed how this innocent looking formula is wrong.Bell didn't show this. In fact, he showed that the functions (1) that determine individual detection, are compatible with qm. Which is not to say that standard qm can be interpreted as being realistic. It can't. It's nonrealistic and acausal.

What Bell did show was that the separable form of (2), the embodiment of his locality condition, is incompatible with qm.

Which it is.The functions A and B in (1) can't be said to be wrong, because they're compatible with qm and experiment. They determine individual detection. Period.

We now know that it cannot account at all for the observed behavior.What we know is that the separable form of (2) skews and reduces the range of the the predictions. This is because what's being measured by the analyzers in the joint context is a nonseparable parameter, unchanging from entangled pair to entangled pair (as opposed to what's being measured by the individual analyzers, which varies from particle to particle). Unfortunately for diehard local realists, there's no known way to make a realistic theory local without something akin to Bell's locality condition, which results in a separable form, which skews the predictions.

[DrChinese]

...This is because what's being measured by the analyzers in the joint context is a nonseparable parameter, unchanging from entangled pair to entangled pair (as opposed to what's being measured by the individual analyzers, which varies from particle to particle). Unfortunately for diehard local realists, there's no known way to make a realistic theory local without something akin to Bell's locality condition, which results in a separable form, which skews the predictions.

Presumably, if it is nonseparable it is also nonlocal. That is consistent with accepted interpretations of QM.

Now Bell's (1) is essentially A(a)={+1,-1}, B(b)={+1,-1}

Bell later effectively says that realism implies simultaneously C(c)={+1,-1}. This assumption is wrong if QM is correct.

[ThomasT]

Presumably, if it is nonseparable it is also nonlocal. That is consistent with accepted interpretations of QM.Yes, I agree, given certain definitions of the terms nonseparable and nonlocal. Due to ambiguous connotations of those terms it takes a bit of sorting out. In the case of standard qm nonlocal doesn't mean what it means wrt 3D classical physics, the assumed locality of which, vis SR, is compatible with quantum nonlocality. The nonlocality and nonseparability of entanglement can be taken as referring to essentially the same thing, with nonseparability ultimately tracing back to parameter (not ontological) nonseparability due to the experimental analysis of relationships between particles, which entails the dependence of measured particle properties and why the entangled system can be more completely described than it's subsystems.

Now Bell's (1) is essentially A(a)={+1,-1}, B(b)={+1,-1}Ok.

Bell later effectively says that realism implies simultaneously C(c)={+1,-1}. This assumption is wrong if QM is correct.I understand how this is the basis for your dataset requirement and your 'negative probability' paper, ie., I think it does constitute an understandable insight. My only problems with it were 1) that I thought there might be a more thorough process for assessing proposed LR models, and 2) that I wasn't sure where/why you were reading this, apparently tacit (because I don't remember it being mentioned in Bell's paper), realization on Bell's part into Bell's development of his theorem. I was concerned with nailing down Bell's explicit realism assumption as a guide to evaluating the realism of LR models, and thought that your understanding of that might have been a bit off the mark. In any case, whether Bell was actually thinking along those lines or not is less important than the fact that it works as an evaluative tool.

Regarding Christian, my current opinion is that his LR program fails, and he's missing the point, for essentially the reason that bobbytkc gave in post #6. Christian, apparently, doesn't quite get what the LR program is about.

[Gordon Watson]

<SNIP>
Regarding Joy Christian, my current opinion is that his LR program fails, and he's missing the point, for essentially the reason that bobbytkc gave in post #6. Christian, apparently, doesn't quite get what the LR program is about. ["Joy" inserted above for clarity. GW]

1. The thread initiated by me -- http://www.physicsforums.com/showthread.php?t=475076 --

is an off-shoot from another thread discussing Joy Christian's work.


2. I make no claim as to whether Joy Christian does or does NOT understand the LR program. But I would be very surprised if he does not understand it exactly, precisely, whatever.

3. IMHO, it is not that difficult; unless I too am missing some extreme subtlety; or there is being inserted a requirement that goes beyond the Einstein and EPR program.

4. I would certainly expect that anyone, critically and carefully studying Bell's theorem, would be trying to ensure that their efforts did not breach the commonsense (the core Einstein and EPR principles) that attaches to the LR program.

5. However, in this widely rejected/neglected area of study (Einstein's baby, IMHO), slips are possible. So a better critique of JC's work, for those concerned by it, would be to identify JC's error specifically; my own critical opinion of JC's efforts not being relevant here.

6. The point that I would like to emphasize is this: The L*R program, discussed in the above thread (http://www.physicsforums.com/showthread.php?t=475076), is most certainly local and realistic, and in full accord with the Einstein and EPR program, as I understand it. (And I doubt that JC understands it any less than I do -- so why not help him find his slip -- IF slip there be. Because my "guess" is: it's fixable!)

[billschnieder]

Nonseparability has been mentioned but I doubt that it's impact to this discussion has been fully understood. In the the Gordon Watson's linked thread he mentioned "triangle inequality", I have a variation of it which may throw some light in a simple and common sense manner why "nonseparability" is so important to the issue being raised by Joy Christian. DrC may be interested in this because it blows the lid off his "negative probabilities" article.

A simple analogy is the x^2 + y^2 = z^2 relationship for right angled triangles, of sides, x, y and z. Consider a process which generates right angled triangles defined within a unit circle, where z is always = 1, x = cos(angle), y = sin(angle), where the angle is randomly chosen each time. Our goal is to measure the lengths of the sides x and y. But, assume that in the first experiment, we can only make a single measurement. So we run our experiment a gazzillion number of times and obtain the averages <x> and <y> averages. Do you think <x>^2 + <y>^2 will obey the relationship of being equal to 1. If you do, think again <x>^2 + <y>^2 converges to 0.8105... not 1, a violation. This is simply because x and y are non-separable in our relationship.

However we can imagine that in our experiment we also had corresponding values for both x and y for each individual measurement. So we might think that using our new dataset with all corresponding values included will result in <x>^2 + <y>^2 = 1, right? Wrong. We get exactly the same violation as before. The reason is separability. But there is one thing we can calculate in our second scenario which we could not in the first. We can calculate <x^2 + y^2> since we now have both points, and indeed we obtain 1 as the result which obeys the relationship.

In our first experiment, x and y do not commute therefore it is a mathematical error to use x and y in the same expression, that is why the violation was observed. In probability theory, an expectation value such as E(a,c) is undefined if A(a,lambda) and A(c,lambda) do not commute. Expectation values are only defined for E(a,c) if there is an underlying probability distribution P(a,c). But it is not possible to measure at angles "a" and "c" on the same particle pair therefore there is no P(a,c) probability distribution. The same is the case in Bell-test experiments and QM, in which it is possible to measure "a" and "b" but not "c" simultaneously so, the pairs measured in different runs do not correspond to each other, so we are left with calculating three different expectation values from three different probability distributions to plug into an inequality in which the terms are defined on the same probability distribution. This is a mathematical error.

Concerning negative probabilities, Dr C says:

X is determined by the angle between A and B, a difference of 67.5 degrees X = COS^2(67.5 degrees) = .1464 This prediction of quantum mechanics can be measured experimentally.*
Y is determined by the angle between A and C, a difference 45 degrees Y = SIN^2(45 degrees) = .5000 This prediction of quantum mechanics can be measured experimentally.*
Z is determined by the angle between B and C, a difference 22.5 degrees Z = COS^2(22.5 degrees) = .8536 This prediction of quantum mechanics can be measured experimentally.*

...

(X + Y - Z) / 2

Substituting values from g. above:

= (.1464 + .5000 - .8536)/2

= (-.2072)/2

= -.1036


Note how he defines X, Y and Z as being non commuting since only two of such angles can be measured at the same time, and yet he writes down an impossible equation which includes terms which can never be simultaneously valid. No doubt he obtains his result.

[ThomasT]

["Joy" inserted above for clarity. GW]

1. The thread initiated by me -- http://www.physicsforums.com/showthread.php?t=475076 --

is an off-shoot from another thread discussing Joy Christian's work.


2. I make no claim as to whether Joy Christian does or does NOT understand the LR program. But I would be very surprised if he does not understand it exactly, precisely, whatever.

3. IMHO, it is not that difficult; unless I too am missing some extreme subtlety; or there is being inserted a requirement that goes beyond the Einstein and EPR program.

4. I would certainly expect that anyone, critically and carefully studying Bell's theorem, would be trying to ensure that their efforts did not breach the commonsense (the core Einstein and EPR principles) that attaches to the LR program.

5. However, in this widely rejected/neglected area of study (Einstein's baby, IMHO), slips are possible. So a better critique of JC's work, for those concerned by it, would be to identify JC's error specifically; my own critical opinion of JC's efforts not being relevant here.

6. The point that I would like to emphasize is this: The L*R program, discussed in the above thread (http://www.physicsforums.com/showthread.php?t=475076), is most certainly local and realistic, and in full accord with the Einstein and EPR program, as I understand it. (And I doubt that JC understands it any less than I do -- so why not help him find his slip -- IF slip there be. Because my "guess" is: it's fixable!)See Carlos Castro's, There is no Einstein-Podolsky-Rosen Paradox in Clifford-Spaces (http://vixra.org/pdf/0908.0103v1.pdf) . In C-space, the particles can exchange signals encoding their spin measurement values across a null interval, which isn't the sort of locality required by the LR program. Or can it be translated into that because this is essentially the same as specifying a relationship produced via a common source? I don't know.

Because Christian is using tensors (http://en.wikipedia.org/wiki/Tensor) (in the papers using Clifford algebra and in the paper currently under discussion with the Kronecker Delta, Levi-Cevita algebra) to deal with a relationship (which is what Bell tests are actually measuring) between vectors, then maybe I was too quick to dismiss his stuff. Or maybe not. Again, I don't know.

These articles might also be relevant:

Bound entanglement and local realism (http://iftia9.univ.gda.pl/~pg/prace/2002PhRvA..65c2107K.pdf)

All the Bell Inequalities (http://arxiv.org/PS_cache/quant-ph/pdf/9807/9807017v2.pdf)

Clearly, we need some input from experts, or at least more knowledgeable, in the field.

[Gordon Watson]

Nonseparability has been mentioned but I doubt that it's impact to this discussion has been fully understood. In the the Gordon Watson's linked thread he mentioned "triangle inequality", I have a variation of it which may throw some light in a simple and common sense manner why "nonseparability" is so important to the issue being raised by Joy Christian. DrC may be interested in this because it blows the lid off his "negative probabilities" article.

A simple analogy is the x^2 + y^2 = z^2 relationship for right angled triangles, of sides, x, y and z. Consider a process which generates right angled triangles defined within a unit circle, where z is always = 1, x = cos(angle), y = sin(angle), where the angle is randomly chosen each time. Our goal is to measure the lengths of the sides x and y. But, assume that in the first experiment, we can only make a single measurement. So we run our experiment a gazzillion number of times and obtain the averages <x> and <y> averages. Do you think <x>^2 + <y>^2 will obey the relationship of being equal to 1. If you do, think again <x>^2 + <y>^2 converges to 0.8105... not 1, a violation. This is simply because x and y are non-separable in our relationship.

However we can imagine that in our experiment we also had corresponding values for both x and y for each individual measurement. So we might think that using our new dataset with all corresponding values included will result in <x>^2 + <y>^2 = 1, right? Wrong. We get exactly the same violation as before. The reason is separability. But there is one thing we can calculate in our second scenario which we could not in the first. We can calculate <x^2 + y^2> since we now have both points, and indeed we obtain 1 as the result which obeys the relationship.

In our first experiment, x and y do not commute therefore it is a mathematical error to use x and y in the same expression, that is why the violation was observed. In probability theory, an expectation value such as E(a,c) is undefined if A(a,lambda) and A(c,lambda) do not commute. Expectation values are only defined for E(a,c) if there is an underlying probability distribution P(a,c). But it is not possible to measure at angles "a" and "c" on the same particle pair therefore there is no P(a,c) probability distribution. The same is the case in Bell-test experiments and QM, in which it is possible to measure "a" and "b" but not "c" simultaneously so, the pairs measured in different runs do not correspond to each other, so we are left with calculating three different expectation values from three different probability distributions to plug into an inequality in which the terms are defined on the same probability distribution. This is a mathematical error.

Concerning negative probabilities, Dr C says:

---Quote---
X is determined by the angle between A and B, a difference of 67.5 degrees X = COS^2(67.5 degrees) = .1464 This prediction of quantum mechanics can be measured experimentally.*
Y is determined by the angle between A and C, a difference 45 degrees Y = SIN^2(45 degrees) = .5000 This prediction of quantum mechanics can be measured experimentally.*
Z is determined by the angle between B and C, a difference 22.5 degrees Z = COS^2(22.5 degrees) = .8536 This prediction of quantum mechanics can be measured experimentally.*

...

(X + Y - Z) / 2

Substituting values from g. above:

= (.1464 + .5000 - .8536)/2

= (-.2072)/2

= -.1036
---End Quote---

Note how he defines X, Y and Z as being non commuting since only two of such angles can be measured at the same time, and yet he writes down an impossible equation which includes terms which can never be simultaneously valid. No doubt he obtains his result.

Note how he defines X, Y and Z as being non commuting since only two of such angles can be measured at the same time, and yet he writes down an impossible equation which includes terms which can never be simultaneously valid. No doubt he obtains his result.

I, for one, will be very interested in studying this beautiful example. My current concern is to first show where BT fails. That for me will open the way for me (and others) to assess what I would presently call "analogies." For my job then would be to use examples such as yours; showing how they fit into a "more formal" disproof of BT.

Until that time, I can hear Bell's supporters discussing "loopholes" against you, ad nauseam.

(The boot will be on the other foot, as it were, for them then; considering all the loopholes that EPR-style supporters adduce to ignore BT and related experimental results. Me here wanting to be very clear that LOOPHOLES are not only unnecessary but unwarranted. And have never been considered valid or relevant by me.)

[ThomasT]

A simple analogy is the x^2 + y^2 = z^2 relationship for right angled triangles, of sides, x, y and z. Consider a process which generates right angled triangles defined within a unit circle, where z is always = 1, x = cos(angle), y = sin(angle), where the angle is randomly chosen each time. Our goal is to measure the lengths of the sides x and y. But, assume that in the first experiment, we can only make a single measurement. So we run our experiment a gazzillion number of times and obtain the averages <x> and <y> averages. Do you think <x>^2 + <y>^2 will obey the relationship of being equal to 1. If you do, think again <x>^2 + <y>^2 converges to 0.8105... not 1, a violation. This is simply because x and y are non-separable in our relationship.

However we can imagine that in our experiment we also had corresponding values for both x and y for each individual measurement. So we might think that using our new dataset with all corresponding values included will result in <x>^2 + <y>^2 = 1, right? Wrong. We get exactly the same violation as before. The reason is separability. But there is one thing we can calculate in our second scenario which we could not in the first. We can calculate <x^2 + y^2> since we now have both points, and indeed we obtain 1 as the result which obeys the relationship.You say you're varying θ randomly. So, <θ> = 45°, where <x> = cosθ = .707..., <y> = sinθ = .707... , (.707...)2 + (.707...)2 = 1. No violation.

In our first experiment, x and y do not commute therefore it is a mathematical error to use x and y in the same expression, that is why the violation was observed. In probability theory, an expectation value such as E(a,c) is undefined if A(a,lambda) and A(c,lambda) do not commute. Expectation values are only defined for E(a,c) if there is an underlying probability distribution P(a,c). But it is not possible to measure at angles "a" and "c" on the same particle pair therefore there is no P(a,c) probability distribution. The same is the case in Bell-test experiments and QM, in which it is possible to measure "a" and "b" but not "c" simultaneously so, the pairs measured in different runs do not correspond to each other, so we are left with calculating three different expectation values from three different probability distributions to plug into an inequality in which the terms are defined on the same probability distribution. This is a mathematical error.Bell's inequality is based on the fact that for x,y,z = ±1, you have |xz - yz| = 1 - xy. Substituting x = A(b,λ), y = A(c,λ), z = A(a,λ) and integrating wrt the measure ρ, you get 1 + P(b,c) ≥ |P(a,b) - P(a,c)| , (Bell's inequality), in view of Bell's (14), P(a,b) = - ∫dλρ(λ)A(a,λ)B(b,λ) . There's no mathematical error in Bell's stuff.

Note how he (DrC) defines X, Y and Z as being non commuting since only two of such angles can be measured at the same time, and yet he writes down an impossible equation which includes terms which can never be simultaneously valid. No doubt he obtains his result.I don't see any mathematical error in DrC's stuff either. It's an interesting numerical treatment based on Einstein realism which demonstrates the incompatibility with qm.

[billschnieder]

You say you're varying θ randomly. So, <θ> = 45°, where <x> = cosθ = .707, <y> = sinθ = .707 . (.707)2 + (.707)2 = 1. No violation.


This is inaccurate. Generating θ randomly around a circle gives us values in the range [0,360]. So how do you get <θ>=45 degrees shouldn't it be 180? Even if your 45 degrees were correct which it is not, <x> is not the same as Sin<θ>. You may be tempted to say Sin(180) = 0 and Cos(180) = 1 which still adds up to 1 but the error here is that you are assuming that information is present in the experiment which is is not. Remember that x is a length and our experimenter is measuring a length not an angle. He is never given an angle, just a triangle so he can not determine <θ>. He only has the length which is the absolute value of Sin(θ). Secondly, were you to suggest that the mean value for x which he measured were <x> = 0 (cf sin(180)), you will be suggesting that he actually measured negative lengths which is not possible.

In fact <x> is 0.6366.. NOT 0.707 as you stated. You can verify it with a simple calculation, the python code below does that
0.6366^2 + 0.6366^2 = 0.81056.. NOT 1

I hope you see that this simple example is not as stupid as you may have assumed at first. In fact your misunderstanding of this example highlights exactly the point I'm trying to make.


import numpy
# generate 1million angles from 0 to 360
thetas = numpy.linspace(0,2*numpy.pi, 1000000)

# calculating |sin(<theta>)|
x1 = numpy.abs(numpy.sin(thetas.mean()))
print "%0.4f" % x1
#Output: 0.0000

# calculating <|sin(theta)|>
x2 = numpy.abs(numpy.sin(thetas)).mean()
print "%0.4f" % x2
#Output 0.6366



Bell's inequality is based on the fact that for x,y,z = ±1, you have |xz - yz| = 1 - xy. Substituting x = A(b,λ), y = A(c,λ), z = A(a,λ) and integrating wrt the measure ρ, you get 1 + P(b,c) ≥ |P(a,b) - P(a,c)| , (Bell's inequality), in view of Bell's (14), P(a,b) = - ∫dλρ(λ)A(a,λ)B(b,λ) . There's no mathematical error in Bell's stuff.

That is not my point. For the valid inequality |xz - yz| = 1 - xy., all three terms xz, yz, and xy are defined within the same probability space. You can not take terms from three different probability spaces and substitute them in the above equation. The problem is not with the inequality. It is a question of whether bipartite experiments, and QM's predictions for expectation values for bipartite experiments (which do not commute with each other) can be used as legitimate sources of terms to be substituted into the equation for comparisons. I believe not.

I don't see any mathematical error in DrC's stuff either. It's an interesting numerical treatment based on Einstein realism which demonstrates the incompatibility with qm.
Given that you did not understand my original point, I did not expect that you will see the error either. The main point is simply that you can not combine expectation values for non-commuting observables into the same expression as is commonly done when comparing Bell's inequality with QM, and as DrC does in the text I quote. If anybody thinks it is a valid mathematical procedure, let them say so and we can discuss that in a new thread.

[ThomasT]

This is inaccurate. Generating θ randomly around a circle gives us values in the range [0,360]. So how do you get <θ>=45 degrees shouldn't it be 180?Just simplifying. Shouldn't varying θ from 0° to 90° be enough to demonstrate what you want to demonstrate?

Even if your 45 degrees were correct which it is not, <x> is not the same as Sin<θ>.You defined x = cosθ. I wrote <x> = cos<θ> because you said you're randomly varying θ. If instead you randomly vary x from 0 to 1, then <x> = <cosθ> = .5, but then you're not randomly varying θ, which is what you said you were doing. It was a little confusing. But I now understand what you're doing. Anyway, I don't think we need it, unless you want to contribute to the collection of illustrations showing that qm is incompatible with LR.

The problem is not with the inequality. It is a question of whether bipartite experiments, and QM's predictions for expectation values for bipartite experiments (which do not commute with each other) can be used as legitimate sources of terms to be substituted into the equation for comparisons. I believe not.Given what's being compared, it's legitimate. And the conclusion is that qm is incompatible with Bell's generalized LR form (2). You do agree with that, don't you?

The main point is simply that you can not combine expectation values for non-commuting observables into the same expression as is commonly done when comparing Bell's inequality with QM, and as DrC does in the text I quote.Bell is comparing his form (2) with qm. They're incompatible. DrC is comparing Einstein realism (via his numerical treatment) with qm. They're incompatible. Both comparisons are mathematically sound.

If your point is that this doesn't inform us about the underlying reality, then I agree with you. Joy Christian on the other hand is presenting so called LR models of entanglement that agree with qm predictions. Any ideas you have on Christian's offerings, and in particular the one presented in this thread, are most welcome.

[Gordon Watson]

..

DrC, ThomasT, billschnieder, and others.


Am I mistaken?

We have here, in the "triangles" and "negative probability" discussions, a chance to at least settle these issues with finality. Yes?

And, even if little else were to be resolved: That would be progress. Yes?

So shouldn't someone take the initiative and start a new thread -- leaving this one to the JC discussions, per the OP?

How about: Bell's theorem and negative probabilities versus triangle-inequalities?

??

With some of the discussion, already here, transferred to kick it off?

[billschnieder]

Just simplifying. Shouldn't varying θ from 0° to 90° be enough to demonstrate what you want to demonstrate? Why should it? Try to understand the point before you suggest what should be enough or not. The simple fact the <θ> in your "simplification" is different from <θ> in my original example 'should' tell you that it is not the same thing we are talking about.
You defined x = cosθ. I wrote <x> = cos<θ> because you said you're randomly varying θ. If instead you randomly vary x from 0 to 1, then <x> = <cosθ> = .5, but then you're not randomly varying θ, which is what you said you were doing. It was a little confusing.
I also mentioned that x was the length of one side of a triangle. I assumed it will be obvious to most that a length can not be negative which means you should take its absolute value. Which means <x> is not the same as cos<θ> for the same reason that |<v>| does not mean the same thing as <|v|>. You do not deny that randomly varying θ reaches the conclusion I reached so your response here is curious and very surprising.

But I now understand what you're doing. Anyway, I don't think we need it, unless you want to contribute to the collection of illustrations showing that qm is incompatible with LR.
I still do not think you understand it, otherwise you will not conclude that you do not need it.

And the conclusion is that qm is incompatible with Bell's generalized LR form (2). You do agree with that, don't you?
No I do not agree. I would instead say that, neither QM not Bell test experiments are legitimate sources of terms for the inequality 1 + P(b,c) ≥ |P(a,b) - P(a,c)|. Simply because all three terms are not defined within the same probability space neither QM nor in Bell test experiments. Non-locality and/or reality are completely peripheral here. There is no P(a,b,c) distribution from which you can extract the three terms, not in QM, not in Bell test experiments and that alone explains why you can not use QM nor Bell test experiments as sources for those three terms.

Bell is comparing his form (2) with qm. They're incompatible. DrC is comparing Einstein realism (via his numerical treatment) with qm. They're incompatible. Both comparisons are mathematically sound.
This is wrong. There is no conflict with QM until Bell introduces the third angle. Please check his original paper again to confirm that this is correct. I mentioned DrC article because the same error is made in which expectation values from three incompatible non-commuting measurements are combined in the same expression. Are you claiming hereby that it is sound mathematics to do that? This is the question you did not answer.

If your point is that this doesn't inform us about the underlying reality, then I agree with you.
I'm not just interested in stating that. I am explaining WHY any result so obtained can not inform us of anything other than the fact that a subtle mathematical error has been made, ie substituting incompatible expectation values within Bell's inequality.

Joy Christian on the other hand is presenting so called LR models of entanglement that agree with qm predictions. Any ideas you have on Christian's offerings, and in particular the one presented in this thread, are most welcome.
Did you read the one posted in this thread? You seemed to dismiss it earlier based on what you had heard about his other offerings. He presents in 1/2 a page, a LR model which violates Bell's inequality. You may ask how come his LR model could violate the inequallity, and the answer is for the same reasons I have already explained. -- the terms he used are not all defined within the same probability space. It is the same reason why QM violates the inequalities.


He concludes that:

Evidently, the variables A(a, λ) and B(b, λ) defined above respect both the remote parameter independence and the remote outcome independence (which has been checked rigorously [2][3][4][5][6][7]). This contradicts Bell’s theorem.


I haven't seen anybody here argue that his model presented in the above paper is not LR, nor have I seen any one argue that his model does not reproduce the QM result. All I have seen is discussion around his other papers.

[ThomasT]

Just simplifying. Shouldn't varying θ from 0° to 90° be enough to demonstrate what you want to demonstrate?
Why should it? Try to understand the point before you suggest what should be enough or not. The simple fact the <θ> in your "simplification" is different from <θ> in my original example 'should' tell you that it is not the same thing we are talking about.

I also mentioned that x was the length of one side of a triangle. I assumed it will be obvious to most that a length can not be negative which means you should take its absolute value. Which means <x> is not the same as cos<θ> for the same reason that |<v>| does not mean the same thing as <|v|>. You do not deny that randomly varying θ reaches the conclusion I reached so your response here is curious and very surprising.The values I input for 0° --> 90° give roughly <x>2 + <y>2 = .8, which corresponds with what you got. And <x2 + y2> = .975. So, isn't the net effect the same -- you get a contradiction between separable and nonseparable formulations?

I still do not think you understand it, otherwise you will not conclude that you do not need it.Only that we already have illustrations of the incompatibility between separable and nonseparable formulations. Bell's, for one.

And the conclusion is that qm is incompatible with Bell's generalized LR form (2). You do agree with that, don't you?

No I do not agree. I would instead say that, neither QM nor Bell test experiments are legitimate sources of terms for the inequality 1 + P(b,c) ≥ |P(a,b) - P(a,c)|. Simply because all three terms are not defined within the same probability space neither QM nor in Bell test experiments. Non-locality and/or reality are completely peripheral here.The inequality is based on Bell's LR form. Any model of entanglement taking that form must satisfy his inequality. The question concerns how locality and reality might be explicitly encoded in the same model, while remaining compatible with qm, and Bell shows that they can't be.

There is no P(a,b,c) distribution from which you can extract the three terms, not in QM, not in Bell test experiments and that alone explains why you can not use QM nor Bell test experiments as sources for those three terms.That's the point of DrC's illustration. (a,b,c) is the LR dataset, based on the idea that underlying predetermined particle parameters exist independent of measurement.
There is no such dataset in qm. Hence, the conflict.

Bell is comparing his form (2) with qm. They're incompatible. DrC is comparing Einstein realism (via his numerical treatment) with qm. They're incompatible. Both comparisons are mathematically sound.

This is wrong. There is no conflict with QM until Bell introduces the third angle. Please check his original paper again to confirm that this is correct.The results (10) and (11) are in conflict with qm. The unit vectors a and b in (2) can refer to any θ. The unit vector, c, is introduced after that, specifically to derive the inequality. The whole point of Bell's paper is that the generalized LR form (2) is incompatible with qm.

I mentioned DrC article because the same error is made in which expectation values from three incompatible non-commuting measurements are combined in the same expression. Are you claiming hereby that it is sound mathematics to do that? This is the question you did not answer.Yes, it's sound mathematics to do that given what he's trying to show. There are limits on how explicit LR models can be formulated. These limits are based on certain assumptions. Based on the assumption of realism, DrC has fashioned a numerical treatment that demonstrates a conflict between that assumption and qm.

If your point is that this doesn't inform us about the underlying reality, then I agree with you.

I'm not just interested in stating that. I am explaining WHY any result so obtained can not inform us of anything other than the fact that a subtle mathematical error has been made, ie. substituting incompatible expectation values within Bell's inequality.We sort of agree then. The results can't inform us of anything other than the fact that a certain mathematical form can't possibly agree with qm or experiment. But, what Bell did is not a mathematical error. Bell constructed a generalized LR form and compared it with qm. They're incompatible.

If you can present another form that an LR model can take, that meets the the requirements for an explicit LR model, and reproduces qm predictions, then that might be interesting.

Did you read the one posted in this thread?Sure, but I don't really understand what he did.

You seemed to dismiss it earlier based on what you had heard about his other offerings.I thought he might be doing essentially the same thing in both, ie., allowing a and b to communicate, but 'locally' in an imaginary space, which wouldn't be an LR model. Then I was wondering if there might be 'any' way to translate what he did into a realistic local view of the underlying mechanics. But, even if so, if it can't be made explicitly LR, that is with a clearly 3D classical LR encoded in the model, then it isn't an LR model.

You may ask how come his LR model could violate the inequality, and the answer is for the same reasons I have already explained. -- the terms he used are not all defined within the same probability space. It is the same reason why QM violates the inequalities.I don't think this clarifies it fully enough.

The inequality is based on a generalized LR form, the salient feature of which is the separability of the underlying parameter determining coincidental detection. Standard qm and Christian's formalisms violate the inequality because those formalisms don't encode a feature that skews the underlying parameter nonseparability (ie., they don't skew the relationship between the particles) -- qm, 'nonlocally' via the projection, and Christian's Clifford algebraic models by allowing the particles to communicate 'locally' via a null interval in C-space. I'm not sure how Christian's paper in this thread does it.

I haven't seen anybody here argue that his model presented in the above paper is not LR, nor have I seen any one argue that his model does not reproduce the QM result. All I have seen is discussion around his other papers.Hence, my call for experts or at least more knowledgeable people than myself. Glad you showed up.

His model does reproduce the qm result. But it doesn't 'look' LR because of the bivectors and the algebra he employs. I'm just plodding along trying to learn as I go, so if you or anybody else has some insights into Christian's stuff to offer then that would be most appreciated. And thanks for your input so far. It's motivating me to think about this a little more and not just set it aside.

[DrChinese]

Concerning negative probabilities, Dr C says:

...

Note how he defines X, Y and Z as being non commuting since only two of such angles can be measured at the same time, and yet he writes down an impossible equation which includes terms which can never be simultaneously valid. No doubt he obtains his result.

I think that is precisely my point. The HUP should be applied literally, and that makes realism untenable. Experiment follows this in all respects.

[DrChinese]

Now Bell's (1) is essentially A(a)={+1,-1}, B(b)={+1,-1}

Bell later effectively says that realism implies simultaneously C(c)={+1,-1}. This assumption is wrong if QM is correct.

Just to drive the above home, here is a definition of realism from an experimental paper from the past few days:

"Reality": The state of any physical system is always well defined, i.e. the dichotomic variable Mi(t), which tells us whether (Mi(t) = 1) or not (Mi(t) = 0) the system is in state i, is, at any time, Mi(t) = {0, 1}.

This from Violation of a temporal Bell inequality for single spins in solid by over 50 standard deviations (http://arxiv.org/abs/1103.4949). And you could find similar definitions in hundreds of papers.

[billschnieder]

The inequality is based on Bell's LR form. Any model of entanglement taking that form must satisfy his inequality. The question concerns how locality and reality might be explicitly encoded in the same model, while remaining compatible with qm, and Bell shows that they can't be.
I have already shown elsewhere in another thread that you do not need LR or anything other than paired products of three variables to obtain Bell-like inequalities, irrespective of the physics behind the variables. It is a mathematical fact first established by Boole almost a hundred years before Bell, that paired products of three variables will obey Bell-like inequalities. Boole even concluded at the time that if in an experiment the data for three variables did not obey the inequality, it simply meant that those three variables could not possibly exist at the same time. He called them "conditions of possible experience".

That's the point of DrC's illustration. (a,b,c) is the LR dataset, based on the idea that underlying predetermined particle parameters exist independent of measurement.
There is no such dataset in qm. Hence, the conflict.
But there can never be such a dataset for the EPR scenario ever because it is impossible to measure two particles three times. Why would any sane individual expect a joint probability space of P(a,b,c) to exist? We do not need a thread discussing the idea that our inability to observe square circles in an experiment means nature is not real do we? We stop the discussion at the point where we realize that there is no such thing as a square circle.

All I am doing here is highlighting the fact that the lack of a P(a,b,c) in QM and in experiments is sufficient to make it impossible to apply Bell's inequalities to the EPR scenario. They are incompatible. So you can't even talk of a violation yet, because the laws of mathematics and logic prohibit you from using those terms from QM and experiments in the inequality. Find an experimental scenario for which P(a,b,c) is a valid probability distribution and you can discuss all you want about QM and experiments and Bell's inequality and LR etc. Until then such discussion is a waste of time and a weapon for increasing mutual confusion.


EDIT:
I thought the above was too complicated so I thought I should simplify.

Some choose to say: the fact that it is impossible to provide a dataset of triples which obeys Bell's inequality, implies that realism is false.

I say: Duh, in the statement of the problem, the impossibility of measuring two particles three times is almost explicitly recognized by any sane individual. Why then would any such individual expect two particles to actually be measured 3 times to obtain the dataset? It can not be done in QM, nor in any experiment, nor in any LR theory that anyone could cook up. Obviously, the fact that we can not measure two particles three times, says absolutely nothing about locality or realism.

[DrChinese]

But there can never be such a dataset for the EPR scenario ever because it is impossible to measure two particles three times. Why would any sane individual expect a joint probability space of P(a,b,c) to exist? We do not need a thread discussing the idea that our inability to observe square circles in an experiment means nature is not real do we? We stop the discussion at the point where we realize that there is no such thing as a square circle.


Well gosh darn, Bill. I have non-brown eyes, non-black hair and light skin. My friend has brown eyes, black hair and dark skin. Funny, groups of people have properties that seem to persist and follow Bell Inequalities all day long. I will gladly show you datasets of these, 3 properties for random pairs of persons (that would be 2). The only samples I know of that don't follow these inequalities are quantum particles that are well described by the HUP.

And that would be: any 2 measurements of 3 properties of 2 particles. Is that too hard for you to follow? I mean, really, when has anyone tried to measure 2 particles 3 times? Basically I am saying you are full of hot air, and I think I have said as much before in our prior discussions. Or perhaps you can provide some experimental support for your position. Perhaps a reputable source other than yourself? Otherwise, you are adding nothing of value here except confusion for folks who have no idea that your views are not standard science.

If you want to add here, please add normal scientific thought. Set up your own site for your personal views.

[ThomasT]

We've gotten a bit off topic. But all these considerations are connected. I'll tie it to Christian's stuff at the end.

We do not need a thread discussing the idea that our inability to observe square circles in an experiment means nature is not real do we?No. And it seems that the discussion here at PF has moved beyond that, and that the physics community at large is moving beyond that as well. We're concerned with the form that models of entanglement can take to be instrumentally viable, and why -- and the why of it has, effectively, only to do with a formalism's correspondence with experimental design and preparation. Realism and localism refer to certain formal requirements or limits.

Einstein thought, and others still think (now, in the face of overwhelming evidence to the contrary), that LR formalisms are possible. Opposing postulates associated with competing formalisms are the basis for theorems (Bell) and 'tautologies' (DrC) which are developed to show a quantitative difference between incompatible formalisms. Incompatibility between LR and qm/experiment doesn't imply that some form of nonlocality exists or that an underlying reality with specific properties doesn't -- in fact there's absolutely no empirical evidence that even suggests those notions. It's unfortunate that so much of the literature, and our understanding, has been clouded by claims to the contrary.

It gets complicated insofar as theories do develop according to certain visions of the underlying reality, but those visions should always be based on empirical evidence, not lack of it. We infer from what's known, not from what isn't. It gets even more complicated when theories are developed primarily via abstract mathematics as opposed to primarily via reasonable inference from empirical evidence and sensory experience -- giving rise to paradoxes, pseudo problems and exotic interpretations. Which is not to say that this could be entirely avoided.

Regarding entanglement, it seems that we can reasonably infer from the experimental designs, preparations and observed correlations, that the relationships between the entangled entities are being produced locally via the various experimental protocols.

So, the interesting question has to do with why certain formalisms correctly model entanglement while others don't. What's the important difference between them? The current focus seems to be on separability vs nonseparability. LR formalisms are separable, while qm and Christian's are nonseparable. It's observed that qm and Christian's Clifford algebraic formalisms allow 'communication' between particles in imaginary spaces. But what does that mean? It's speculated that the real reason these formalisms work is because they don't skew the relationships between entangled entities via formal separation which is at odds with experimental design and preparation. This remains to be sorted out, and may never be fully because the exact characteristics of the underlying relationships (in real 3D space and time) are and will remain a matter of speculation.

I think we can say that Christian's current offering isn't an LR model of entanglement. It remains to sort out why it works -- what the formalism does, and maybe more importantly, what it doesn't do in light of reasonable inference from empirical evidence and sensory experience regarding the nature of entanglement.

I've benefitted from your analyses regarding this stuff, that is, your point regarding Bell and DrC is taken, and while your point helps to clean up the language surrounding Bell stuff, it doesn't diminish the correctness of their (Bell, DrC) math or the usefulness of their analyses, so anything you might want to say specifically about Christian's formalism in the current paper is welcomed.

[harrylin]

[..] Incompatibility between LR and qm/experiment doesn't imply that some form of nonlocality exists or that an underlying reality with specific properties doesn't -- in fact there's absolutely no empirical evidence that even suggests those notions. It's unfortunate that so much of the literature, and our understanding, has been clouded by claims to the contrary. [..]

Please clarify what you mean with "Incompatibility between local realism and [..] experiment doesn't imply that some form of nonlocality exists". Why do you say that the one doesn't imply the other? I don't even know the difference!

Thanks,
Harald

[ThomasT]

Please clarify what you mean with "Incompatibility between local realism and [..] experiment doesn't imply that some form of nonlocality exists". Why do you say that the one doesn't imply the other? I don't even know the difference!

Thanks,
HaraldNonlocality for LR and qm refers to different things. For Einstein and local realists it refers to instantaneous action at a distance in real space and time. For qm it refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (ie., not scientifically ascertainable).

[Gordon Watson]

Nonlocality for LR and qm refers to different things. For Einstein and local realists it refers to instantaneous action at a distance in real space and time. For qm it refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (ie., not scientifically ascertainable).


1. This looks to me like an excellent summary of the two positions: mainstream LR versus more mainstream QM. (Or the beginning of one.)

2. It certainly looks like my view of LR, which I associate with Einstein and EPR.

3. So I'd like to be sure that the summary is OK from the QM point of view.

4. In other words: I'd like to see this summary endorsed by those who believe a LR view of the world to be untenable; or by those who might modify the QM view (expressed above) to a more mainstream (and accurate) expression.

5. In other words: Can we sharpen the current dichotomy between LR and QM, in the way ThomasT has begun here, ENSURING that the views he has captured/initiated are "corrected if necessary" so as to be widely accepted by both camps ... and are similarly compressed?

6. In a nutshell: I personally see no objection to the LR view, as expressed above (at this early hour, for me). Is the QM view equally OK?

[DrChinese]

Please clarify what you mean with "Incompatibility between local realism and [..] experiment doesn't imply that some form of nonlocality exists". Why do you say that the one doesn't imply the other? I don't even know the difference!

Thanks,
Harald

You have the option of accepting non-realism and retaining locality.

[ThomasT]

You have the option of accepting non-realism and retaining locality.You mean like QFT? Is that really local in the sense that LR means local, ie., in real space and time? I've not studied it yet.

[DrChinese]

1. This looks to me like an excellent summary of the two positions: mainstream LR versus more mainstream QM. (Or the beginning of one.)


I sometimes call it "quantum non-locality" to make it clear that it complies with the QM formalism.

Since you are also a fan of EPR: I would say that EPR would never have contemplated the kind of correlations that today are commonplace in Bell tests. You have to believe that Bell would have altered Einstein's view of things substantially.

[DrChinese]

You mean like QFT? Is that really local in the sense that LR means local, ie., in real space and time? I've not studied it yet.

I mean as in MWI, which is considered local non-realistic.

[ThomasT]

I mean as in MWI, which is considered local non-realistic.Ah, thanks. I forgot about that one.

[Gordon Watson]

I sometimes call it "quantum non-locality" to make it clear that it complies with the QM formalism.

Since you are also a fan of EPR: I would say that EPR would never have contemplated the kind of correlations that today are commonplace in Bell tests. You have to believe that Bell would have altered Einstein's view of things substantially.

Thanks for added clause, with its emphasis.

Re EPR: MHO is the opposite to yours, entanglement being a commonplace in QM, even in their day. They (in fact) choosing entanglement to emphasize their commitment to local realism.

The final EPR sentence being: "We believe, however, that such a theory is possible."

You and I differing as to whether Bell settles the issue; http://www.physicsforums.com/showpost.php?p=3219776&postcount=153 notwithstanding.



So Nonlocality for LR and qm refers to different things. For Einstein and local realists it refers to instantaneous action at a distance in real space and time. For qm it refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (ie., not scientifically ascertainable). leads to this; Yes, thus far?

...

Nonlocality (NL) in LR and QM refers to different things:

1. In LR, for Einstein, EPR, and local realists, NL refers to instantaneous action at a distance in real space and time. So NL is rejected; it is an unphysical mechanism; an impossibility.

2. In QM, NL refers to an abstract and acausal math formalism whose connection to the reality underlying instrumental behavior is unknowable (i.e., not scientifically ascertainable). Called "quantum non-locality" (QNL) to emphasize its compliance with the QM formalism, there is no connection to any physical mechanism.

...

[DrChinese]

Re EPR: MHO is the opposite to yours, entanglement being a commonplace in QM, even in their day. They (in fact) choosing entanglement to emphasize their commitment to local realism.
...

Ah, not so fast! This was my point, entanglement was only coined as a word around that time (1935). And the theoretical elements of entanglement were not at all well understood then. As far as I know, the first physical entanglement was not demonstrated before 1970. So basically Alf and Bet were in their infancy.

[Gordon Watson]

Ah, not so fast! This was my point, entanglement was only coined as a word around that time (1935). And the theoretical elements of entanglement were not at all well understood then. As far as I know, the first physical entanglement was not demonstrated before 1970. So basically Alf and Bet were in their infancy.

...

Sorry Doc, I thought twas me that was slowing down.*

Please see Schroedinger (1935), where the term "entanglement" was first introduced: To describe the then-well-known connection between quantum systems (Schroedinger, 1935; p. 555):

"When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled." original emphasis by Schroedinger, emphasis added by GW.

PS: We theorists, when theorizing correctly, tend not to wait upon confirmatory experiments.

..........
* a possible impossibility that I need more time to think about.

[DrChinese]

...

Sorry Doc, I thought twas me that was slowing down.*

Please see Schroedinger (1935), where the term "entanglement" was first introduced: To describe the then-well-known connection between quantum systems (Schroedinger, 1935; p. 555):

"When two systems, of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own. I would not call that one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives [the quantum states] have become entangled." original emphasis by Schroedinger, emphasis added by GW.

PS: We theorists, when theorizing correctly, tend not to wait upon confirmatory experiments.

..........
* a possible impossibility that I need more time to think about.

That was actually the exact quote I had in mind, 1935, same year as EPR. :smile: So thanks for sharing this.

Obviously, if a system of 2 particles becomes separated spatially, he is saying there is a non-local connection between them. That's the theory, anyway. And yet many theorists rejected this particular element of QM, including Einstein. Having an experiment in hand does matter to many!

And I have absolutely no doubt Einstein would have been very swayed by Bell's reasoning, and completely convinced after Aspect's experiment. In fact, I cannot think of a single influential physicist who does not accept Bell/Aspect as convincing. Of course, the many successes of QM through the years has been quite important to getting folks to this point.

[ThomasT]

And I have absolutely no doubt Einstein would have been very swayed by Bell's reasoning, and completely convinced after Aspect's experiment.Me too. Einstein was, after all, a great physicist. It's just that he was motivated by a desire for a fundamental theory based more on (and developed in accordance with) natural philosophical insights than on abstract mathematical insights. But the evidence following Bell would have convinced him that such an approach meets insurmountable obstacles wrt the formalisms necessary for correspondence with experimental results. At some point(s), there's only the math (which might or might not lead to insights regarding the underlying reality).

In fact, I cannot think of a single influential physicist who does not accept Bell/Aspect as convincing. Of course, the many successes of QM through the years has been quite important to getting folks to this point.Yes. And to tie this to the Christian offering that's being considered in this thread, my interest is in ascertaining whether it might offer any insights, regardless whether it can be properly called an LR model or not. I think all agree that it isn't an LR model.

So, once again, a call for any observers who can offer some insight into Christian's formalism.

[Q-reeus]

...So, once again, a call for any observers who can offer some insight into Christian's formalism.
Have you tried contacting him directly? Email address is listed on most if not all his arXiv papers.

[ThomasT]

Obviously, if a system of 2 particles becomes separated spatially, he is saying there is a non-local connection between them.That's not exactly what Schrodinger said, and since the term nonlocality has different meanings, it might do to clarify.

What Schrodinger said was:
... after a time of mutual influence the systems separate again, then they can no longer be described in the same way as before, viz. by endowing each of them with a representative of its own.The only connection he refers to is a local one. And that, after that local interaction, neither of the subsystems can be described "by endowing each of them with a representative of its own". In other words, following the interaction, and wrt the system, neither of the subsystems can be described as an entity or function that's separable from the other. Which is in accordance with Bell's theorem and the qm formalism. The standard qm formalism doesn't explicate a nonlocal connection in real space and time. It's acausal.

But, and here's the key point, what Schrodinger said is also in accordance with the understanding that the relationship between the particles can't be represented as a combination of separable and variable λ functions (whether λ is allowed to be continuous or not) , if the underlying parameter determining coincidental detection is constant from pair to pair. It was, apparently, recognized long before Bell, in the development of standard qm, that λ, the determiner of individual detection, was not the determiner of coincidental detection. This understanding is incorporated into the qm formalism in the only way that it could be (via nonseparability) so as to not skew the statistical predictions of the qm formalism.

The qm projection along either of the unit vectors associated with paired detection attributes seems to me to be conceptually based on this understanding, which is compatible with the classical view.

[ThomasT]

Have you tried contacting him directly? Email address is listed on most if not all his arXiv papers.I found this discussion which Christian took part in some time ago:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4174/Bell-s-Theorem

Christian has probably gotten lots of communications on his Bell stuff. I doubt that he'd take the time to respond to anything I wrote -- especially since I'm not fluent with the geometric algebra he uses.

Any insights/clarifications from the linked discussion that you (or anyone else) might offer are welcome.

[DrChinese]

I found this discussion which Christian took part in some time ago:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4174/Bell-s-Theorem

Christian has probably gotten lots of communications on his Bell stuff. I doubt that he'd take the time to respond to anything I wrote -- especially since I'm not fluent with the geometric algebra he uses.

Any insights/clarifications from the linked discussion that you (or anyone else) might offer are welcome.

Nice reference, ThomasT! There is plenty there for anyone who wishes to learn more.

As I always say: where is the dataset which gives the QM expection value as an average? All Joy need do is provide that, and it should answer all questions. He instead describes topological issues that do not seem to relate to the EPR paradox in any sense I understand. In fact, sorta reminds me of Caroline Thompson's Chaotic Ball example. But you can read all that in the thread. An excerpt of Joy's comments, quote:

In my view Bell’s theorem is based on a serious topological error. The error lies in the very first equation of Bell’s famous paper. He associates numbers +1 and -1 with the end results of an EPR-type experiment, and writes them as A ( a, L ) = +1 or -1. What could be wrong with such an innocent assumption? Well, the problem is that A and B are supposed to represent values of the EPR elements of reality (or spin components). But EPR-Bohm elements of reality have a very specific topological structure---they live on a unit 2-sphere (i.e., on the surface of a unit ball). This topological structure differs from the topological structure presumed by Bell in the functions A ( a, L ) = +1 or -1, which live on a unit 0-sphere, not 2-sphere. Thus Bell’s theorem simply does not apply to the EPR argument, unless one modifies his main assumption by writing his function as A ( a, L ) = +1 or -1 about a. After all, no one has ever observed a “click” in an experiment other than about some experimental direction a. With this simple change the function A now takes on values in a topological 2-sphere, not the real line, thereby correctly representing the EPR elements of reality. The values of the spin components are still +1 or -1, but they now reside on the surface of a unit ball. This, in essence, is the only change I have made in any of my papers. But once this change is made, no contradiction with quantum mechanics arises. In fact I have been able to reproduced many complicated quantum mechanical results by implementing this corrected assumption. And I have done this in a manifestly local and realistic manner. Hence the title “disproof of Bell’s theorem.”

[yoda jedi]

I found this discussion which Christian took part in some time ago:

http://www.natscience.com/Uwe/Forum.aspx/physics-research/4174/Bell-s-Theorem

Christian has probably gotten lots of communications on his Bell stuff. I doubt that he'd take the time to respond to anything I wrote -- especially since I'm not fluent with the geometric algebra he uses.

Any insights/clarifications from the linked discussion that you (or anyone else) might offer are welcome.

it seem that this the essence of one of your objections (interesting).
can be traced it in your posts, but it will take time.

..."But for this claim to be true, Bell must first adapt the EPR premises correctly within his own demonstration. So my first observation is that the very first equation of Bell's famous paper is incompatible with the EPR premises---i.e., with their criteria of locality, reality, and completeness. This becomes evident when one looks at these criteria collectively---not individually as is usually done---within the coherence of the EPR argument. Now an inequality derived using a faulty assumption cannot possibly have relevance for the question of local realism. Therefore, just as von Neumann's theorem could not rule out all hidden variable theories because of its faulty assumption, Bell's theorem cannot---and does not---rule out a local-realistic theory of physics. End of the story!"...


.

[ThomasT]

As I always say: where is the dataset which gives the QM expection value as an average? All Joy need do is provide that, and it should answer all questions.It answers the important question of whether it's an LR model (which it isn't), and it tells us that Christian is not understanding fully that the LR program is about producing a viable "LR" model (which is impossible). But it doesn't explore the deeper reasons for why LR models of entanglement are impossible even if the universe and all its subsystems are evolving exclusively in accordance with the principle of local causality and the SR limit.

He instead describes topological issues that do not seem to relate to the EPR paradox in any sense I understand.I don't understand it either. Yet. It will be interesting to reread his stuff and attempt to translate it into some sort of understanding in classical terms.

In fact, sorta reminds me of Caroline Thompson's Chaotic Ball example.I never bothered reading that one. Even in my earlier confusions it seemed clear to me that she had the wrong slant on things.

[ThomasT]

it seem that this the essence of one of your objections (interesting).
can be traced it in your posts, but it will take time.

..."But for this claim to be true, Bell must first adapt the EPR premises correctly within his own demonstration. So my first observation is that the very first equation of Bell's famous paper is incompatible with the EPR premises---i.e., with their criteria of locality, reality, and completeness. This becomes evident when one looks at these criteria collectively---not individually as is usually done---within the coherence of the EPR argument. Now an inequality derived using a faulty assumption cannot possibly have relevance for the question of local realism. Therefore, just as von Neumann's theorem could not rule out all hidden variable theories because of its faulty assumption, Bell's theorem cannot---and does not---rule out a local-realistic theory of physics. End of the story!"...


.Anything that clarifies the discussion is welcomed.

[Gordon Watson]

<SNIP>

As I always say: where is the dataset which gives the QM expection value as an average? All Joy need do is provide that, and it should answer all questions.<SNIP>

Just a reminder: The question of data-sets is being addressed on that other thread. http://www.physicsforums.com/showthread.php?p=3219803#post3219803

PS: Clarification of your "Why" question would ease continuation there. http://www.physicsforums.com/showpost.php?p=3221967&postcount=156

Thanks, as always.

[DrChinese]

Just a reminder: The question of data-sets is being addressed on that other thread. http://www.physicsforums.com/showthread.php?p=3219803#post3219803


Joy clearly thinks that a dataset is unnecessary when his reasoning is so sound. Yet no one really follows the logic of the "disproof" while Bell's own reasoning is easy to follow. So a dataset would be a simple way to demonstrate success to those of us unwilling to accept Joy's characterization of the relevant issues.

As a reminder, here are the dataset rules (which should be demanded of any purported LR model):

a) Perfect correlations
b) QM expectation value
c) Simultaneous hidden variable (HV) values for 3 angle settings: 0, 120, 240 degrees
d) A way to map those HV values to a {+1, -1} observation value without reference to a remote setting

[Gerhard78]

This (http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_ph ysicist_joy_christian_collect_nobel_prize-79614) may help.:smile:

[harrylin]

This (http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_ph ysicist_joy_christian_collect_nobel_prize-79614) may help.:smile:

OMG! ... If those email conversations are true, then I'm afraid that this "alpha male" Sascha is right ("scaling problem"? Why, what scaling?? To me this doesn't make any sense).

PS on second reflection, one should not confuse two very different issues. Take for example if I lived in the middle ages and came with the theorem that it is impossible to make a flying machine because any building material is heavier than air. Comes a guy who says that he derived that it should be possible to fly, thanks to some not-yet understood properties of air. OK then I say, just show us! The guy accepts that challenge but he has a mistaken idea of how to do that and crashes in a cloud of bamboo sticks and feathers. Thus he was wrong and it is impossible to make a flying machine.:wink:

[DrChinese]

Comments on "Disproof of Bell's theorem", Florin Moldoveanu

http://arxiv.org/abs/1107.1007

"In a series of very interesting papers [1-7], Joy Christian constructed a counterexample to Bell's theorem. This counterexample does not have the same assumptions as the original Bell's theorem, and therefore it does not represent a genuine disproof in a strict mathematical sense. However, assuming the physical relevance of the new assumptions, the counterexample is shown to be a contextual hidden variable theory..."

A contextual hidden variable theory is not realistic. (This class of theory flies in the face of the EPR dictate that it is unreasonable for one observer to be able to determine the reality of another who is spacelike separated.) For a number of different reasons, the author is able to demonstrate why the Christian paper does little to Bell.

[Delta Kilo]

Wow, just wow. 5 pages of metaphysical discussion and no-one actually bothered to look at the half-a-page of math to see the elephants lurking therein.

Well, let's look at eq (5). I'll copy it down for your convenience:

E(a,b)=\frac{\lim_{n \to \infty} \{ \frac 1 n \sum_{i=1}^n A(a,\lambda^i) B (b, \lambda^i)\} }{\{-a_j \beta_j\}\{ b_k \beta_k\} }

I assume the intention was to compute correlation as in

corr(X,Y)=\frac{E[(X-E[X])(Y-E[Y])]}{\sigma_X\sigma_Y}

But but look at the denominator:surprised! Note that \beta_j are not real numbers but members of Clifford algebra, and for many a,b they do not cancel each other out! The author says and I quote where the denominators in (5) are standard deviations.Err, WHAT:surprised? Does it look like a standard deviation to you? Last time I checked standard deviation was computed as

\sigma_X=\sqrt{E[(X-E[X])^2]}.

and it was a non-negative number and most certainly not an element of some fancy Clifford algebra.

Now, just for fun, let's take a closer look at A(a,\lambda):

A(a,\lambda) = \{ -a_j \beta_j \} \{ a_k \beta_k(\lambda) \}

written with explicit summation:

A(a,\lambda) = \underset{\small j}{\Sigma} [ - a_j \beta_j ] \underset{\small k}{\Sigma} [a_k \beta_k (\lambda) ]

substitute \beta_j(\lambda)=\lambda\beta_j:

A(a,\lambda) = \underset{\small j}{\Sigma} [ - a_j \beta_j ] \underset{\small k}{\Sigma} [a_k (\lambda \beta_k) ]

move -\lambda outside the sum:

A(a,\lambda)=-\lambda\underset{\small j}{\Sigma} [a_j \beta_j ] \underset{\small k}{\Sigma} [a_k \beta_k ]

open the brackets:

A(a,\lambda) = -\lambda \underset{\small j,k}{\Sigma} (a_j a_k \beta_j \beta_k)

re-group:

A(a,\lambda)= -\lambda [\underset{\small j}{\Sigma} (a_j^2 \beta_j \beta_j) + \underset{\small j \ne k}{\Sigma} a_j a_k (\beta_j \beta_k + \beta_k \beta_j)]

use \beta_j \beta_j = -1 and \beta_j \beta_k = - \beta_k \beta_j, j \ne k:

A(a,\lambda)= \lambda \underset{\small j}{\Sigma} a_j^2

and since |a|=1:

A(a,\lambda) = \lambda, and similarly B(b,\lambda) = -\lambda

Err, WTF?!:bugeye: Hello-o-o?!:eek:

From here we have E_A(a)=E_B(b)=0, \sigma_A(a)=\sigma_B(b)=1, E(a,b)=-1 and therefore

|E(a,b)+E(a,b')+E(a'b)-E(a'b')|=2 \forall a,b,a',b'

Dum dum dum dum another one bites the dust dum-dum :smile:

DK

[FlorinM]

Dear Delta Kilo,

the multiplication in:
A(a,λ)={−ajβj}{akβk(λ)}

is not the usual multiplication, but the "geometric algebra" multiplication as the elements beying multiplied are bivectors. Consequently your following math is wrong.

[FlorinM]

A quick note:

On FQXi's web site Joy Christian and I are arguing for and against his "disproof"

http://www.fqxi.org/community/blogs

Please join in the discussion there. Let the best argument win.

[Delta Kilo]

the multiplication in:
A(a,λ)={−ajβj}{akβk(λ)}

is not the usual multiplication, but the "geometric algebra" multiplication as the elements beying multiplied are bivectors. Consequently your following math is wrong.
Please tell me which line is wrong. I am aware that these are elements of Clifford algebra, they follow their fancy rules for multiplication. But they can still be multiplied by ordinary (complex) numbers and follow associativity and distributivity laws (but not commutativity of course). I believe I handled them correctly. If there is an error, please point it to me.

PS: Had a quick look at the paper again and just noticed that it actually says at the very beginning in eq (1):
A(a,\lambda)= \cdots = \begin{cases} +1, & \text{if } \lambda=+1 \\ -1, & \text{if } \lambda=-1 \end{cases}
Which means (a) my math is correct, (b) I shouldn't have bothered and (c) WTF all these \beta_j are there for in the first place?

Regards,
DK

[FlorinM]

DK,

The multiplication between the sigmas
A(a,λ)=−λΣj[ajβj]Σk[akβk]
is not the regular multiplication.

And indeed, Eq.1 looks like is agreeing with your calculation, but it is not. The variables A and B Alice and Bob are equipped are not scalars (as resulting from your math), but bivectors representing the handedness of a shared sense of rotation.

Your kind of approach for proving Joy Christian wrong was tried 2 years ago, but his math still stands. However, I am not agreeing with him and I think I have a solid argument against his position in my achive preprint. I am challenging him on FQXi's website and I will attempt to make my position easier to understand. Please join the discussion there. I am preparing a massive rebuttal of his arguments.

[Delta Kilo]

The multiplication between the sigmas
A(a,λ)=−λΣj[ajβj]Σk[akβk]
is not the regular multiplication.
Indeed it is not. But it is nevertheless associative and distributive is it not? As in a \beta_i(b \beta_j+c \beta_k) = a b \beta_i \beta_j + ac \beta_i \beta_k
And I believe I have been careful about that. I'm sorry for not numbering my equations. I've copied them here with numbers. Please specify exactly which steps (from-to) you believe to be in error:
(1) A(a,λ)={−ajβj}{akβk(λ)}
(2) A(a,λ)=Σj[−ajβj]Σk[akβk(λ)]
(3) βj(λ)=λβj:
(4) A(a,λ)=Σj[−ajβj]Σk[ak(λβk)]
(5) A(a,λ)=−λΣj[ajβj]Σk[akβk]
(6) A(a,λ)=−λΣj,k(ajakβjβk)
(7) A(a,λ)=−λ[Σj(a2jβjβj)+Σj≠kajak(βjβk+βkβj)]
(8) βjβj=−1 and βjβk=−βkβj,j≠k:
(9) A(a,λ)=λΣja2j
(10) |a|=1:
(11) A(a,λ)=λ, and similarly B(b,λ)=−λ

And indeed, Eq.1 looks like is agreeing with your calculation, but it is not.How is it so? It agrees for every possible value of \lambda, that is for -1 and 1 and for every possible a, that is for every possible real a_j provided that \sum{a_j^2}=1
The variables A and B Alice and Bob are equipped are not scalars (as resulting from your math), but bivectors representing the handedness of a shared sense of rotation.There are no variables A and B. There are functions A(a,λ) and B(b,λ). These functions were introduced by Bell in his paper as possible outcomes of the experiment. Their range was explicitly given as a set {-1, 1}. This agrees with my previous post and with eq (1) of the paper in question.

[DrChinese]

Your kind of approach for proving Joy Christian wrong was tried 2 years ago, but his math still stands. However, I am not agreeing with him and I think I have a solid argument against his position in my achive preprint. I am challenging him on FQXi's website and I will attempt to make my position easier to understand. Please join the discussion there. I am preparing a massive rebuttal of his arguments.

Welcome to PhysicsForums, Florin!

I am very interested in learning more about this. Any comments you can share, including background on the subject, is very welcome.

-DrC

[Delta Kilo]

A quick note:

On FQXi's web site Joy Christian and I are arguing for and against his "disproof"

http://www.fqxi.org/community/blogs

Please join in the discussion there. Let the best argument win.
Thanks for the invitation but no thanks. I went there, pointed out some issues and received a sermon back.

All right, I'll try one last time.

This time I draw your attention to http://arxiv.org/abs/1106.0748 by the same author.

Equation (16) says \mathcal{A} (\alpha,\boldsymbol{ \mu})=(-I \cdot \tilde{a})(+\boldsymbol{ \mu} \cdot \tilde{a})= \begin{cases} +1 & \text{if } \mu = +I \\ -1 & \text{if } \mu = -I \end{cases}Here I is a unit trivector, \boldsymbol{ \mu}= \pm I is two-valued random parameter with equal probability of outcomes, \tilde{a} is a vector derived from scalar parameter \alpha. Incidentally the values in brackets are bivectors and the multiplication between the brackets is geometric product, all that in grassman algebra. The result is \pm 1 as it should be. So far so good.

Now the author wants to calculate correlation. And for that he needs standard deviation which appears in the denominator.

Well, since the only values of \mathcal{A} are -1 and +1 and they are equally probable, it is immediately obvious that the expectation E[\mathcal{A}] =0 and the standard deviation \sigma(\mathcal{A})=1.
I'll do it again real slow just in case. We have 2 equiprobable outcomes, n=2, p_1=p_2=\frac{1}{2}, \mathcal{A}_1 = \mathcal{A}(\alpha,\mu_1) = -1, \mathcal{A}_2 = \mathcal{A}(\alpha,\mu_2) = +1,
E[\mathcal{A}] =\displaystyle \sum_{i=1}^n p_i \mathcal{A}(\alpha,\mu_i) = \frac{1}{2}(-1) + \frac{1}{2}(+1) = 0,
\sigma(\mathcal{A})=\sqrt{\displaystyle \sum_{i=1}^n p_i [\mathcal{A}(\alpha,\mu_i) - E[\mathcal{A}]]^2 } = \sqrt{\frac{1}{2}(-1)^2 + \frac{1}{2}(+1)^2} = 1

But apparently it's not good enough for the author for he knows better. Allow me to quote:
These deviations can be calculated easily. Since errors in linear relations such as (16) and (17) propagate linearly, the standard deviation of \mathcal{A} (\alpha,\boldsymbol{ \mu}) is equal to (−I \cdot \tilde{a}) times the standard deviation of (+\boldsymbol{ \mu} \cdot \tilde{a}) (which we write as \sigma(A)):surprised Basically, the author just claimed that standard deviation is linear with respect to geometric product of grassman bivectors. And the words are quickly followed by deeds, eq (23):\sigma(\mathcal{A})=(−I \cdot \tilde{a})\sigma(A)Note that while \mathcal{A} as defined by eq (16) has a value range \pm 1 and \sigma(\mathcal{A}) is quite ok , A=(+\boldsymbol{ \mu} \cdot \tilde{a}) is a grassman bivector and \sigma(A) simply does not compute. So what, the author just quietly replaces the bivector with its norm in eq (24):
\sigma(A)=\sqrt{\frac{1}{n} \displaystyle \sum_{i=1}^n \left| \left|A(\alpha, \boldsymbol{ \mu}^i) - \overline{A(\alpha, \boldsymbol{ \mu}^i) } \right|\right| ^2 }As a result, \sigma(A) comes out as 1 (a scalar). What was geometric product in eq (16) now becomes multiplication by a scalar 1 in (23) so now \sigma(\mathcal{A}) comes out as a bivector!
The author now uses this strange quantity \sigma(\mathcal{A}) to "normalize" \mathcal{A} (\alpha,\boldsymbol{ \mu}), eq (25):
A(\alpha,\boldsymbol{ \mu}) = \frac{\mathcal{A}(\alpha, \boldsymbol{ \mu}) - \overline{\mathcal{A}(\alpha, \boldsymbol{ \mu}) }}{\sigma(\mathcal{A})} = (+\boldsymbol{ \mu} \cdot \tilde{a})
Note that A(\alpha,\boldsymbol{ \mu}) again comes out as a bivector. And as a final touch the author plugs these grassman whatsises instead of outcomes into the formula for covariance eq (30):
E(\alpha,\beta)=\displaystyle \lim_{n \gg 1}[\frac{1}{n}\displaystyle \sum_{i=1}^n A(\alpha,\boldsymbol{\mu}^i)B(\beta, \boldsymbol{\mu}^i)]
Now the trick finally pays off, things get cancelled out and the value comes out which was supposed to violate Bell's inequality. And it does not matter that a direct application of a standard textbook formula gives different answer (which happen to agree with Bell).

I pointed all these issues to the author and received the following reply:
Neither Bell’s, nor your calculations agree with what is observed in the experiments. This is because neither Bell, nor you are calculating the correlations correctly. Your calculation, as I pointed out to you more than once, produces statistical nonsense, because it is based on elementary errors. My calculation, on the other hand, agrees with the experiment, event-by-event, number-by-number, because it is based on a conceptually superior framework, and is entirely free of error. It is based on the correct model of the physical space introduced by Grassmann some 160 years ago, and further developed by many people, including Clifford and Hestenes. It is a pity that you do not have the proper background to see this.

I'll be blunt but I'm going to call it a bluff. I do not believe the author has any answers at all.

DK
PS: Can I too get a mini-grant please?:biggrin:

[DrChinese]

All right, I'll try one last time.

This time I draw your attention to http://arxiv.org/abs/1106.0748 by the same author.
...

DK
PS: Can I too get a mini-grant please?:biggrin:

Delta Kilo,

Riddle me this: if someone (i.e. Christian) has a model which is local non-contextual, why won't they simply supply a set of values for 3 simultaneous angle settings (you know the kind I mean) for a set of data points and be done with it? I can't get past this simple requirement. It seems as if the focus is on presenting a complex model which will emulate the predictions of QM (for Alice and Bob, 2 values) but FAILS the EPR test (i.e. multiple simultaneous elements of reality independent of the act of observation). By presenting a complicated mathematical derivation, it just pulls things away for what I think are the real issues.

I guess I am just dumb on this point. Maybe you can enlighten me... The de Raedt team is the only one who has even attempted to address this with their simulations (which present values for any simultaneously desired angles).

-DrC

[FlorinM]

DK,

Thanks for participating on FQXi's web site. Indeed, Joy is not the easiest guy to challenge and he even got criticised for it on the achive for the lack of a collegial tone. I had some doubts about challenging him myself for the same very reason, but his results were too interesting and his interpretation too wrong to pass the opportunity.

I answered one of your questions on FQXi's blog, and I read your comments above. I did not find any mathematical mistakes in his approach and after I'll be done rebutting his reply I may come back here and show in detail why he is correct. In the meantime, I recommend you to read the geometric algebra book by David Hestenes.

[Delta Kilo]

Floring,

Please try answering the following quiz:

* Do you agree that standard deviation of a random variable A is computed according to \sigma(A)=\sqrt{E[(A-E[A])^2]}? (if not, please post alternative definition)

* Do you agree that if random variable A takes the value of either -1 or +1, each with probability of 1/2, then its standard deviation \sigma(A)=1?

* Do you agree that functions A(\alpha,\lambda) and B(\beta,\lambda) representing individual outcomes in Bell's experiment satisfy the above criteria ant therefore have standard variation of 1?

* Do you agree that standard deviation is not a linear function, that \sigma(aA)=a\sigma(A) is incorrect in general, and in particular it is violated for a=-1, not to mention complex numbers, vectors, bivectors, quaternions etc.?

* Do you agree that standard deviation is a non-negative real number (fer crying out loud)?

* In the view of the above, do you agree that eq (23) from the paper which I cited in my previous post is incorrect?

* Finally, do you agree that if two mathematical derivations starting from the same premise, arrive at different results, then at least one of them must be in error?

* Did you point out the error in my (or better yet, Bell's) derivation, indicating which particular equation is not correct? (Please quote)

* Did I point out the error in the paper in question? (I can answer that: yes I did. See above)

DK
I'm sick of people on high horses telling me to go read some books. All right, it's a deal: I'll go read to refresh my memory on Grassman algebra, and you guys go read up some basics on statistics 101, starting with the definition of standard deviation. Wake me up when you are ready to point which one of my equations is incorrect.

[FlorinM]

DK,

Against my better judgement not to get sidetracked, here are the answers:

* Do you agree that standard deviation of a random variable A is computed according to σ(A)=E[(A−E[A])2]−−−−−−−−−−−−√? (if not, please post alternative definition)
Yes, it's valid

* Do you agree that if random variable A takes the value of either -1 or +1, each with probability of 1/2, then its standard deviation σ(A)=1?
Yes

* Do you agree that functions A(α,λ) and B(β,λ) representing individual outcomes in Bell's experiment satisfy the above criteria ant therefore have standard variation of 1?
Yes

* Do you agree that standard deviation is not a linear function, that σ(aA)=aσ(A) is incorrect in general, and in particular it is violated for a=-1, not to mention complex numbers, vectors, bivectors, quaternions etc.?
yes, the correct formula is σ(aA)=norm(a)σ(A) when a is a constant (because the expectation value can be redefined with norms). Alternatively σ(aA)=aσ(A) when σ(A) is (re)defined correctly.

* Do you agree that standard deviation is a non-negative real number (fer crying out loud)?
Not necessarily. In geometric algebra it is not. It is a "number" in that formalism. Joy makes this distiction between "raw" and "standard" scores. For the standard score you are correct, but not for the raw ones.

* In the view of the above, do you agree that eq (23) from the paper which I cited in my previous post is incorrect?
Eq. 23 is correct. This may sound paradoxical especially since I agreed that σ(aA)=aσ(A) is not correct in general, but there is no contradiction. σ(aA)=aσ(A) is right in geometric algebra only for raw intermediate calculations, but not in the end for standard results where we deal only with pure scalars as outcomes of experiments. Eq. 23 is an intermediate "raw" geometric algebra step.

* Finally, do you agree that if two mathematical derivations starting from the same premise, arrive at different results, then at least one of them must be in error?
yes (but Joy's computation is not the one in error - I wish it were, and in that case it would make my challenge of his results that much easier)

* Did you point out the error in my (or better yet, Bell's) derivation, indicating which particular equation is not correct? (Please quote)
In your case you make geometric algebra mistakes when analysing Joy's computations. Bell does not make any mistakes, and Joy is incorrect in asserting that. Joy states that Bell makes a "topological error" and I am after Joy proving him wrong on that.

* Did I point out the error in the paper in question? (I can answer that: yes I did. See above)
See my answers

Florin

[SpectraCat]

* In the view of the above, do you agree that eq (23) from the paper which I cited in my previous post is incorrect?
Eq. 23 is correct. This may sound paradoxical especially since I agreed that σ(aA)=aσ(A) is not correct in general, but there is no contradiction. σ(aA)=aσ(A) is right in geometric algebra only for raw intermediate calculations, but not in the end for standard results where we deal only with pure scalars as outcomes of experiments. Eq. 23 is an intermediate "raw" geometric algebra step.



Sorry, but that claim is utterly opaque to a non-expert. Can you please provide a deeper explanation, or at least an example where what you say is true? Specifically, which properties of a and A cause the simple linear relationship that you claim holds true? Is this general or coincidental (and thus true for this specific "raw geometric algebra step")? What is the distinction you are using to define a "raw" geometric algebra step?

[FlorinM]

SpectraCat

You say: "Sorry, but that claim is utterly opaque to a non-expert. Can you please provide a deeper explanation, or at least an example where what you say is true? Specifically, which properties of a and A cause the simple linear relationship that you claim holds true? Is this general or coincidental (and thus true for this specific "raw geometric algebra step")? What is the distinction you are using to define a "raw" geometric algebra step? "

Let me try to explain it by an analogy. The results of experiments are numbers. To an experimentalist standard statistical methods do apply. However, in standard QM formalism, a theoretician uses complex numbers. There are stranger "raw" rules which work there and you have this Born rule which acts as a translation layer between raw "complex probabilities" or the complex wavefunction and standard probabilities. In a similar way, Joy Christian is using a different formalism (the geometric algebra formalism) and in the end he converts the "raw" calculations into "standard" ones. When checking his computation you need to watch 2 things: 1. is the raw (or internal, or geometric algebra) computation correct? and 2. does he apply the correct translation mechanism at the end to recover standard probabilities?

DK's mistake in geometric algebra was to impose the rules of standard statistics in the middle of computation. The corresponding mistake in standard QM formalism would be to add probabilities and not amplitudes in the middle of computation.

[DrChinese]

Let me try to explain it by an analogy. The results of experiments are numbers. To an experimentalist standard statistical methods do apply. However, in standard QM formalism, a theoretician uses complex numbers. There are stranger "raw" rules which work there and you have this Born rule which acts as a translation layer between raw "complex probabilities" or the complex wavefunction and standard probabilities. In a similar way, Joy Christian is using a different formalism (the geometric algebra formalism) and in the end he converts the "raw" calculations into "standard" ones. When checking his computation you need to watch 2 things: 1. is the raw (or internal, or geometric algebra) computation correct? and 2. does he apply the correct translation mechanism at the end to recover standard probabilities?


If Christian's technique were correct, he could provide answers for any group of angle settings I choose REGARDLESS of whether they could be tested experimentally or not. What else does it mean to be realistic if you cannot do that? In other words: For Alice and Bob, I want to see a dataset in which the "answer" for polarization for 0, 120 and 240 degrees is presented for every photon. Then for each of the 6 theta=120 pairing permutations, I want them to average to the QM value of .25 [.75]. For each of the 3 theta=0 pairing permutations, I want them to average to the QM value of 1.00 [0.00]. Hopefully, you understand the intent of the challenge - a data point by data point result set from the candidate formula.

Unless he can provide that, I fail to see the significance of anything being done here other than an exercise in hyperbole. On the other hand, there is a local realistic simulation from the group of de Raedt et al which provides answers to the above challenge (and exploits the so-called fair sampling assumption to operate). Of course, it suffers from other issues but at least addresses what I consider to be the acid test.

If the formula works, where is the example data? Why not generate 30 or 40 data points and be done with it? I realize you do not speak for Christian, I am simply asking why you do not demand the same of any candidate model.

[FlorinM]

Dr Chinese,

I don't quite get your challenge, but let me make a critical point for spin 1/2. Joy's method is completely equivalent with the standard QM formalism in this case. The state space in this case is SU(2) which is isomorphic with SO(3) where geometric algebra can be naturally used. It can be actually proven mathematically that what he is doing in those cases are a 100% faithful translation to the standard complex QM formalism into a geometric algebra formalism. (If he does not recover all QM predictions completely it means that he a mathematical mistake in his computation.) QM can be done in many formalisms: complex numbers, real numbers, quaternions, Bohm. Joy simply found another equivalent formalism (for spin 1/2 only).

For SU(2)~SO(3) Joy is using the double cover property to introduce his "hidden variables" which are basically the disambiguation on which one-to-two map you are located (similar with Riemann's sheets in complex analasys).

My challenge to his method is using spin 1 where there is no such kind of isomorphism and this clearly illuminates his interpretation mistakes.

Florin

[Delta Kilo]

here are the answers:
Thank you very much. I appreciate that we are back from wooly vague words and into the realm of verifiable math. Please bear with me, this might take a while.

We are still talking about http://arxiv.org/abs/1106.0748 as it appears to be far more detailed than the original paper that started this topic.

Start with eq(1). Here the author gives the results predicted by QM and observed in experiments:
\mathcal{A}(\alpha)=\pm 1, \mathcal{B}(\beta)=\pm 1
E(\alpha)=0, E(\beta)=0
E(\alpha,\beta)=-\cos^2(\alpha-\beta)
(eq 1)

Here E(\alpha,\beta) represents the expected value of simultaneously observing remote measurement results \mathcal{A}(\alpha) and \mathcal{B}(\beta) along the polarization angles \alpha and \beta, respectively.
First a small clarification, the text should read: "E(\alpha,\beta) represents the expected value of the product \mathcal{A}(\alpha)\mathcal{B}(\beta) of simultaneously observing...". I added the words in bold because it is important exactly what kind of product we are dealing with here.

Now, the range of \mathcal{A}(\alpha) and \mathcal{B}(\beta) is a set of {-1, +1}. I stress that these are normal ordinary everyday integer +1 and -1, not some fancy Grassman +1 and -1 and the multiplication between \mathcal{A}(\alpha) and \mathcal{B}(\beta) for the purposes of computing E(\alpha,\beta) is normal everyday multiplication, not an inner product, not an outer product, not an wedge product, not a geometric product, not any other fancy kind of product.

Why is that so? Because Bell chose it to be so. The experiment itself can produce any kind of indication of the outcome, it could be 0 or 1, 'X' or 'O', up or down, red LED or green LED. Bell chose to associate these outcomes with numbers +1 and -1 for the purposes of deriving his inequality. And this is how the data is presented in real Bell-type experiments.

Obviously these numbers, be it theoretical results or real experimental data, are computed using normal everyday arithmetic, normal everyday definitions of expectation value, standard deviation, correlation etc, taken from the statistics 101.

Therefore if the author claims to disprove Bell and to demonstrate \cos^2 rule arising from locally realistic \mathcal{A}(\alpha) and \mathcal{B}(\beta), then he has to play by the rules. This means, internally \mathcal{A}(\alpha) and \mathcal{B}(\beta) can use whatever fancy math you want, but their outcomes should be counted the same way the outcomes of real experiments are counted.

To summarize: for the results to be relevant to Bell's theorem and to real-life experiments, functions \mathcal{A}(\alpha) and \mathcal{B}(\beta) should return either -1 or +1 which are to be treated as normal integer numbers using normal arithmetic and statistics. Do you agree with this statement?

Why do I have to explain is so painstakingly? Because I'm sick of people saying "this is not an ordinary multiplication/You won't understand/Go read a book" when in fact it is (should have been) ordinary multiplication.

Now, fast-forward to eq (16).
To this end, we have assumed that the complete state of the photons is given by \mu = \pm I, where I is the fundamental trivector defined in Eq. (2). The detections of photon polarizations observed by Alice and Bob along their respective axes \alpha and \beta, with the bivector basis fixed by the trivector \mu, can then be represented intrinsically as points of the physical space S^3, by the following two local variables:
S^3 \ni \mathcal{A} (\alpha,\mu)=(-I \cdot \tilde{a})(+\mu \cdot \tilde{a})= \begin{cases} +1 & \text{if } \mu = +I \\ -1 & \text{if } \mu = -I \end{cases}
(eq 16)
and
S^3 \ni \mathcal{B} (\beta,\mu)=(+I \cdot \tilde{b})(+\mu \cdot \tilde{b})= \begin{cases} -1 & \text{if } \mu = +I \\ +1 & \text{if } \mu = -I \end{cases}
(eq 17)
with equal probabilities for \mu being either +I or -I, and the rotating vectors \tilde{a} and \tilde{b} defined as

\tilde{a} = e_x \cos 2\alpha + e_y \sin 2\alpha, \tilde{b} = e_x \cos 2\beta + e_y \sin 2\beta
(eq 18)
[not sure it is meant to be \cos 2\alpha or \cos^2\alpha it won't matter much though]
and further down:
Putting these two results together, we arrive at the following standard scores corresponding to the raw scores (16) and (17):
A(\alpha,\mu) = \frac {\mathcal{A} (\alpha,\mu) - \overline{\mathcal{A} (\alpha,\mu)}} {\sigma(\mathcal{A})} = \frac {\mathcal{A} (\alpha,\mu) - 0} {(-I \cdot \tilde{a})} = (+\mu \cdot \tilde{a})
(eq 25)
B(\beta,\mu) = \frac {\mathcal{B} (\beta,\mu) - \overline{\mathcal{B} (\beta,\mu)}} {\sigma(\mathcal{B})} = \frac {\mathcal{B} (\beta,\mu) - 0} {(+I \cdot \tilde{b})} = (+\mu \cdot \tilde{b})
(eq 26)

The question is: which one of these should be identified with A(a,\lambda) and B(b,\lambda) from Bell's paper and with the outcomes collected in the actual experiments to compute E(a,b)? Should it be \mathcal{A} (\alpha,\mu) and \mathcal{B} (\beta,\mu) from eq 16-17, or "normalized" A(\alpha,\mu) and B(\beta,\mu) from eq 25-26? Please answer.

Case 1: the answer is the former (\mathcal{A} (\alpha,\mu) and \mathcal{B} (\beta,\mu)):

We agreed (I hope) that individual outcomes of measurements are represented by (mapped onto) normal integer numbers -1 and 1. So the first order of business is to drop the notion of \mathcal{A} \in S^3 and replace it with simple \mathcal{A} \in \{-1, +1\} (by establishing 1:1 map if you wish).
The next thing we do is define \mu_+ = +I, \mu_- = -I. Once this is done we can rewrite eq 16-17, removing all traces of Grassman algebra from them:

\mathcal{A} (\alpha,\mu)=\begin{cases} +1 & \text{if } \mu = \mu_+ \\ -1 & \text{if } \mu = \mu_- \end{cases}, \mathcal{B} (\beta,\mu)=\begin{cases} -1 & \text{if } \mu = \mu_+ \\ +1 & \text{if } \mu = \mu_- \end{cases}

where \mu \in \{ \mu_+, \mu_- \} is some opaque random parameter taking up one of the two opaque values with equal probability.

From here we can immediately obtain:

\mathcal{A} (\alpha,\mu)\mathcal{B} (\beta,\mu)=-1, \forall \mu \in \{ \mu_+, \mu_- \}

and therefore

E(a,b)=-1, \forall a,b

and therefore

|E(a,b) + E(a',b) + E(a,b') -E(a',b')|= 2, \forall a,b,a',b'

So far the results agree with Bell and do not exhibit \cos^2 rule, which is exactly the opposite of what the author claimed.

Case 2: The answer is A(\alpha,\mu) and B(\beta,\mu) from eq 25-26. That appears to be author's intention because that's what he uses in eq 30 to calculate E(a,b). But what is the value of A(\alpha,\mu)? It is a whatsis bivector in whatever space.

Since the goal is to provide a working model explaining experimental results of \cos^2 rule (and thus disproves Bell) , we need to identify A(\alpha,\mu) unambiguously with the outcome of a measurement, such as either detector D+ or D- clicking in a typical two-channel Bell type experiment by mapping it into { -1, +1 }. The answer is that we cannot because A(\alpha,\mu) is not a two-valued function. It's value, whatever is it, cannot be obtained in the experiment, therefore it cannot be used to calculate E(a,b) (since E(a,b) is calculated from experimental data and we wish to provide a model for it).

As it is, A(\alpha,\mu) might refer to some internal state of the system, but an extra step is required to obtain the actual outcome of a measurement. This extra step ( which can be achieved by some sort of map M: A(\alpha,\mu) \mapsto \{-1, +1\} will encapsulate in itself the process of measurement. And to maintain connection with actual physical experiments, we would have to use the value of this M(\alpha,\mu) and not the unobservable A(\alpha,\mu). Well, guess what, doing this will bring us back to agreement with Bell and disagreement with reality.

So where it all went wrong? Well, when calculating standard deviation.

To begin with, the whole issue of standard deviation and "normalizing" is a red herring. If you bother to read Bell's original paper, you will see that there is no reference to mean or standard deviation. What's more, Bell's derivation works just fine for any A(a,\lambda) as long as A(a,\lambda) \in \{-1, +1 \} and A(a,\lambda)=-B(a,\lambda). The mean does not have to be 0 and sigma does not have to be 1 and there is no need to "normalize" anything.

Having said that, everyone knows that standard deviation of individual measurements in Bell type experiment is 1 (assuming ideal 100% efficient detector) . It is so bleedingly obvious that no-one needs to explain that. Still, there is nothing wrong with actually calculating one, as long as one's math is correct. The sigma would come out as 1, eq 25-26 would be exactly the same as 16-17 and we would be back to where we started.

But the math is not correct. Instead of directly calculating σ from the definition, which would be far easier but would not produce the desired effect, the author averts his eyes and carefully walks along the wall pretending there is no elephant in the room starts mucking around with it with no clear purpose.

As I already pointed out, eq (23) is wrong. I said and you agreed that σ(aA)=aσ(A) is in general incorrect. You said:
yes, the correct formula is σ(aA)=norm(a)σ(A) when a is a constant (because the expectation value can be redefined with norms).
Well, I have news for you: σ(aA)=norm(a)σ(A) does not work either. I gave you the example already:

\sigma( \vec{a} \cdot \vec{b} ) \ne \vec{a} \cdot \sigma( \vec{b} ) \ne ||\vec{a}||\sigma( \vec{b} ) \ne \vec{a}\sigma( ||\vec{b})|| ) \ne ||\vec{a}||\sigma( ||\vec{b}|| )

in fact, 2d ad 3rd terms simply do not compute and 4th term gives a value of a vector where the original was a scalar. This is, by the way, exactly the case with eq. 23-24.
Alternatively σ(aA)=aσ(A) when σ(A) is (re)defined correctly.Please enlighten us, what is the correct redefinition of σ(A) that allows σ(aA)=aσ(A). All I can see in eq (24) is the same old σ with the argument A (which is a vector) quietly replaced with its norm |A|, which bring us back to my previous point.

This is all so wrong and so crude I'm surprised anyone can fall for this trick. The whole thing reminds me of Bistromatic Drive (http://en.wikipedia.org/wiki/Technology_in_The_Hitchhiker%27s_Guide_to_the_Gala xy#Bistromathic_drive)

DK

[ppnl]

Does everyone agree that anyone who claims to have developed a local realistic model for QM should be able to meet Sascha's Quantum Crackpot Randi Challenge?

http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_ph ysicist_joy_christian_collect_nobel_prize-79614

Bell's theorem seems to me to say nothing more than that such programs cannot exist.

[DrChinese]

Dr Chinese,

I don't quite get your challenge, but let me make a critical point for spin 1/2. Joy's method is completely equivalent with the standard QM formalism in this case. ...

I follow the assertion that Joy's method is completely equivalent with the QM expectation value for electrons. I say (following Bell) that won't ever provide a realistic dataset to be produced for election angle settings A=-22.5, B=0, C=22.5. Here is a very small sample to illustrate:

Alice / Bob
A B C/A B C
+ + +/- - -
+ + +/- - -
+ + +/- - -
+ + -/- - +

The AC expectation value for correlation is .25 (.5*sin(theta)^2) which matches the dataset (AC: 1 of 4). However, the AB and BC expectation values, being equal, should average .073. However, they actually come out as .125 above (AB:0 of 4 and BC:1 of 4). In fact, there is no dataset possible which will be counterfactually realistic AND match QM. (This is basic Bell/Sakurai, right?)

So my point is that Christian's method is actually incapable of making counterfactual predictions even if the math yields the QM expectation for 2 angles. So it seems at best he has a non-realistic local model, in accordance with Bell's Theorem.

[DrChinese]

...

http://www.science20.com/alpha_meme/quantum_crackpot_randi_challenge_help_perimeter_ph ysicist_joy_christian_collect_nobel_prize-79614

Bell's theorem seems to me to say nothing more than that such programs cannot exist.

Why, this is almost exactly the same as the DrChinese challenge! Awesome!!

:smile: :smile: :smile:

I am glad SOMEBODY sees my point. I was starting to feel lonely. :biggrin:

[FlorinM]

Dear Dr. Chinese and DK,

Thank you for your messages, there were really helpful.

Let me start with Dr. Chinese.
I enjoyed the link "http://www.science20.com/alpha_meme/...el_prize-79614" a lot, I was not aware of it. No, the classical computer model is not possible in this case. And this can be established rigurously mathematically by a theorem by Clifton arXiv:quant-ph/9711009v1 which I cite in my preprint: http://arxiv.org/abs/1107.1007 Clifton proved under what conditions Bell's beables must be commutative and Joy's are not. The reason why Joy's theory fails to be modeled on a computer is because his hidden variable theory is contextual. (and contextual hidden variables' ontology is basically junk). Joy's interpretations are all wrong and misleading. What he calls realistic is actually factorizable.

DK,

You are 100% right from the beginning until "So where it all went wrong? Well, when calculating standard deviation." The right approach is your step 2.

Let me quote you: "This extra step ( which can be achieved by some sort of map M:A(α,μ)↦{−1,+1} will encapsulate in itself the process of measurement. And to maintain connection with actual physical experiments, we would have to use the value of this M(α,μ) and not the unobservable A(α,μ). Well, guess what, doing this will bring us back to agreement with Bell and disagreement with reality."

So here is the deal: consider the map M ("which can be achieved by some sort of map M:A(α,μ)↦{−1,+1} will encapsulate in itself the process of measurement"). Such a map is illegal in his formalism and computations should be caried all the way in geometric algebra formalism until you reach the answer. If you say at this point: "but this is not a realistic local model" you are right. The pollitically correct description for his model is "contextual hidden variable theory", and the pollitically incorrect description is "BS".

I was pointing earlir to Dr. Chinese that what Joy uses is the SU(2)~SO(3) isomorphism and his hidden variable is the extra degree of freedom resulting from the double cover property. As such his formalism is actually only a rewrite of QM standard formalism from the spin1/2 SU(2) state space in the fancy geometric algebra on SO(3). What he gets is a factorization between Alice and Bob in the new formalism which he illegally calls "realism". Applying the map M calls his realistic bluff because the ontological meaning of his hidden variables is not fixed. Joy's is protected by appying M by the Hestenes' formalism and he will always argue that appying M at any stage violates geometric algebra (go directly to jail, do not pass go, do not collect 200, and read a geometric algebra book). What is needed is another way of proving him wrong.

Please see my preprint and my FQXi post to see how I prove that his model is only a contextual hidden variable theory with the help of a spin 1 state and a nice decomposition trick into 2 spin 1/2's where I can use Joy's model. This bypasses all geometric algebra defence from Joy. Right now I am preparring a massive rebuttal of his answer to my FQXi post which I hope will clearly show his interpretation mistakes.

Florin

[Delta Kilo]

Florin,

There are 2 main things wrong.

First, is the conceptual BS, his insistence on extending the use of his fancy geometric formalism beyond the boundaries of the model and into the statistical processing of the outcomes of measurements. I spent the first 1/3 of my post debunking that, I'm not going to repeat myself again.

The second is the fact that equation 23 is plain WRONG. It violates basic rules of arithmetic.

DK

[FlorinM]

Dr. Chinese and DK,

I believe I made a wrong statement earlier when I said that Joy Christian's work contained no mathematical mistakes. I unfortunately got blinded by high level arguments and did not see the trees from the forest. However, I am here to set the record straight and point you to my latest preprint: http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.0535v1.pdf which hopefully will close this debate once and for all. (see also my FQXi blog post: http://www.fqxi.org/community/forum/topic/983)

By the way, I am still disagreeing with DK on σ(aA)=aσ(A). Suppose “a” is the unit of measurement (temperature, meters, kilograms, etc). Then the equation is actually correct, and therefore it is not incorrect in general and cannot be used as a decisive argument against Joy's math. Other more blatant mistakes can be used however. It is embarrassing to admit for me I never bothered to check Joy's math up close before, but now that I did I hope this would absolve me for at least part of the blame.

[DrChinese]

Dr. Chinese and DK,

I believe I made a wrong statement earlier when I said that Joy Christian's work contained no mathematical mistakes. I unfortunately got blinded by high level arguments and did not see the trees from the forest. However, I am here to set the record straight and point you to my latest preprint: http://arxiv.org/PS_cache/arxiv/pdf/1109/1109.0535v1.pdf which hopefully will close this debate once and for all. (see also my FQXi blog post: http://www.fqxi.org/community/forum/topic/983)

Nice paper. :smile: I didn't follow all of it, but it is well written. No question that Christian is wrong in my opinion anyway, hardly surprising.

[FlorinM]

Thanks. There are some heated exchanges between Joy and me now on FQXi blog right now. The icing on the cake was when Joy called Hodge duality his own: "It is a Christian duality not Hodge duality, with a very specific Christian meaning attached to it." :) Now this is precious.

[billschnieder]

Florin,
After reading your paper, I doubt that you understand Joy's model at all. It does not appear you have recognized the difference between averaging over a series of events each of which can only be one of two possibilities, and picking a convention for a series of equations.

Your complex number example is humorous. If 3 + 2i and 3 - 2i are equal alternate posibilities for z, <z> is 3. But if you select a convention for your equations where only one is possible, then <z> = 3 is wrong. This is what you are missing.

[FlorinM]

Bill,

I don't quite get your criticism and I don't want to give an answer which may not be what you are looking for. Can you please specify the context a bit more? What do you mean by: "averaging over a series of events"? Let's frame the discussion around http://arxiv.org/PS_cache/quant-ph/pdf/0703/0703179v3.pdf to be specific. Are you talking about Eqs. 18, 19 of that paper, or are you talking about what Bell does in his theorem?

Thanks,

Florin

[billschnieder]

Bill,

I don't quite get your criticism and I don't want to give an answer which may not be what you are looking for. Can you please specify the context a bit more? What do you mean by: "averaging over a series of events"? Let's frame the discussion around http://arxiv.org/PS_cache/quant-ph/pdf/0703/0703179v3.pdf to be specific. Are you talking about Eqs. 18, 19 of that paper, or are you talking about what Bell does in his theorem?

Thanks,

Florin
Not sure what is not clear as I'm responding directly to what you have written in your paper for which you gave the complex number analogy. You are using the orientation of the 3-sphere as a convention in your equations, whereas Joy is using it as a hidden variable.

Remember Alice is making multiple measurements of different particles and averaging over them not repeated measurements of the same particle. But each particle has a different hidden variable or in other words, there is an ambiguity in the orientation for the different particles arriving at Alice. Finally remember that the hidden variables are not the outcomes of the experiments. The *different* hidden variables must interact with Alice's device in Alice's frame and only after that can you average and obtain Alice's result.

Until you understand this simple fact, you will not understand his model. Your rebuttal is flawed because of this.

[FlorinM]

Dear billschnieder,

Or should I say Joy Christian?

First naming equations after yourself, and now sockpuppetry?

I have exchaged way too many messages with you already not to recognize your writing style. I guess it is time for a new pen name, this one was already exposed.

Best,

Florin

[Gordon Watson]

Dear billschnieder,

Or should I say Joy Christian?

First naming equations after yourself, and now sockpuppetry?

I have exchaged way too many messages with you already not to recognize your writing style. I guess it is time for a new pen name, this one was already exposed.

Best,

Florin

Are you sure? The styles are not nearly the same, imho!

[billschnieder]

Dear billschnieder,

Or should I say Joy Christian?

First naming equations after yourself, and now sockpuppetry?

I have exchaged way too many messages with you already not to recognize your writing style. I guess it is time for a new pen name, this one was already exposed.

Best,

Florin

Now this is funny. Your judgement is so obviously clouded for you to think that everyone challenging your rebuttal must somehow be Joy Christian.

In your paper you say on page 1:

"Even without spelling in detail the error, it is easy
to see that the exterior product term should not vanish
on any handedness average because handedness is just
a paper convention on how to consistently make compu-
tations."

All I have done is point out to you that you are missing the point because Joy Christian is not using handedness as a convention but as the hidden variable itself.

My criticism is very clear and instead of addressing it, you decide to accuse Joy Christian of acts for which you have no proof. Very disappointing.

[FlorinM]

Dear billschnieder,

Let me start by saying that on the very remote possibility that you are indeed not Joy Christian, I am apologizing to you.

I replied earlier, but my post did not appear and unfortunaley I did not saved it.

Let me list the reasons why Joy's model is wrong:

Physical reasons:

- Never in his model he is using the fact that the original state in in the Bell state. Start with any other Psi and you will still get -a.b if you believe his math.
- The model does not respect the detector swapping symmetry: Swap Alice and Bob's detectors and you get the same results. Joy is using DIFFERENT analyzers for Alice and Bob to recover the minus sign on -a.b. Restoring the symmetry results in + a.b
- Holman's argument: Once MU is set, perform the EPR-B experiment on z axis and do a subsequent measurement on one arm of the experiment on the x axis. You get 2 choices: MU does not change between measurement, or MU changes between measurement. MU does not change: this means the x measurement outcome is always the same as the z outcome. Experiments show you get 50% the same answer and 50% the opposite answer. MU does change: than you have problems explaining 3 1/2 spin particle experimental results.

Mathematical reasons:

-incorrect Hodge duality between pseudo-vectors and bivectors in a left handed basis. In a right handed bases a^b = I (axb) (Joys agrees with it). In a left handed basis Joy claims incorrectly a^b = -I (axb). This is wrong, it is still with +. Easy way of seeing this: changing handedness comes from a mirror reflection. In a mirror reflection I = e1^e2^e3 changes signs because it is a PSEUDO-scalar (Joy does this correctly). However (axb) changes signs as well (Joy forgets that axb is a PSEUDO-vectors and treats it like a vector)
-On FQXi website Joy now claims a different thing: he is using left and right algebras instead of left and right handedness. To debunk this I spelled out all 4 combinations: left algebra-left handedness, left algebra-right handedness, right algebra-left handedness, right algebra-right handedness. In each algebra Hodge duality preserves the sign, and mixing algebras is inconsistent (it is like adding kets with bras, row and column vectors: "go direcly to jail, do not pass go do not collect 200"). All associative algebras have left and right implementations (and the name comes from the matrix formalism). Only in 3D there is handedness-a property of the cross product. Handedness is the sign of the pseudo-scalar I = e1^e2^e3 = e1e2e3 and not of the bivector product: B1B2B3. The sign of the bivector product gives you the left or right algebra.
-Any generalization of Joy's model in the Clifford algebra formalism breaks either -a.b correlation, or the zero average in each arm of the experiment
-Joy takes a 0/0 limit: sin(epsilon)/sin(epsilon) and claims it equals zero because the nominator goes to zero.
-Joy computes incorrectly a rotation with a bad rotor in geometric algebra. (the last 2 errors are used to fight Holman's analysis)

Computer simulation arguments:
-By now there are 2 independent simulations of Joy's model both recovering the classical limit. One of the simulation was validated by obtaining -cos correlation on other models

Sociological factors:
-I have never ever got any mathematical arguments from Joy. Instead he used only lies, insults, fallacious arguments, and obfuscation of simple mathematical facts.
-naming the Hodge duality after himself – a major score on Baez’s crackpot index.
-His archive replies are using a bullying tone which scared away critics. You want proof? Sure. The +1=-1 mistake from the wrong sign of Hodge duality was almost found by the very first critic and the tone of Joy’s reply: “rectify this pedagogical error”-like the first critic was an idiot, scared other people from checking his math.
Frankly, I have no explanation for his behavior and obstinate denial of obvious elementary mistakes except that he is doing a cover-up. But a coverup is worse than the offense, and if he can now say: look, I made a sign mistake and I did not treat axb as a pseudo-vector – I am only human, publishing anything else on the archive denying the obvious mistakes can only be achieved by doing other mistakes. And after that he will lose all his mathematical credibility. I plead with him to see reason and stop this self-destruction madness.

[DrChinese]

Posted today by Richard Gill, of the Mathematical Institute:

http://arxiv.org/abs/1203.1504

Abstract:

"I point out a simple algebraic error in Joy Christian's refutation of Bell's theorem. In substituting the result of multiplying some derived bivectors with one another by consultation of their multiplication table, he confuses the generic vectors which he used to define the table, with other specific vectors having a special role in the paper, which had been introduced earlier. The result should be expressed in terms of the derived bivectors which indeed do follow this multiplication table. When correcting this calculation, the result is not the singlet correlation any more. Moreover, curiously, his normalized correlations are independent of the number of measurements and certainly do not require letting n converge to infinity. On the other hand his unnormalized or raw correlations are identically equal to -1, independently of the number of measurements too. Correctly computed, his standardized correlations are the bivectors - a . b - a x b, and they find their origin entirely in his normalization or standardization factors; the raw product moment correlations are all -1. I conclude that his research program has been set up around an elaborately hidden but trivial mistake. "

--------------------------------------------

It is interesting to add this note, addressed to those who suggest Jaynes is the only person who properly understands how probability applies to Bell's Theorem, entanglement, etc: Gill is also an expert in statistical theory, and has done extensive research in this area (including the application of Bayes). He apparently does not see the issue Jaynes does. Gill frequently collaborates with the top scientists in the study of entanglement, so I think it is safe to say this area has been well considered and has not been overlooked somehow.

[kith]

I conclude that his research program has been set up around an elaborately hidden but trivial mistake.
Puh, this is definitely not something you want to read in a serious paper addressing your work. ;-)

[DrChinese]

Puh, this is definitely not something you want to read in a serious paper addressing your work. ;-)

That would sting. I would say that Gill addressing this shows that top teams take challenges to Bell quite seriously. Gill has previously brought down at least one of the Hess-Philipp stochastic models.

[Delta Kilo]

Told you so! :mad:
... and no-one actually bothered to look at the half-a-page of math to see the elephants lurking therein.

Well, let's look at eq (5). ...

[Zarqon]

Hehe, what's funny is that as I found this paper on the archives yesterday, my first thought was: wow, DrChinese will find that funny.

On another note, I think the strong language at the end of the abastract suggests that some people in the community is starting to get annoyed by joy christians continuing crusade against Bell. I guess he should maybe try to put up a bit more humble attitude in the future (assuming he has one :tongue2: )

[DrChinese]

Told you so! :mad:

Ahead of the pack is a good place to be... :smile:

[DrChinese]

Hehe, what's funny is that as I found this paper on the archives yesterday, my first thought was: wow, DrChinese will find that funny.

On another note, I think the strong language at the end of the abastract suggests that some people in the community is starting to get annoyed by joy christians continuing crusade against Bell. I guess he should maybe try to put up a bit more humble attitude in the future (assuming he has one :tongue2: )

Heh, I'm so predictable...

Yes, I think the issue is: if someone (such as Christian) really has an angle on something, why not collaborate on it rather than this process of trying to upend something which has been thoroughly studied (Bell)? Every entanglement test shows the same pattern of impossibly high correlations, which again should be a tip-off. Some mathematical sleight of hand is not going to do it, there is going to need to be something very convincing - something like a new testable prediction.

[ThomasT]

Posted today by Richard Gill, of the Mathematical Institute:

http://arxiv.org/abs/1203.1504

Abstract:

"I point out a simple algebraic error in Joy Christian's refutation of Bell's theorem. In substituting the result of multiplying some derived bivectors with one another by consultation of their multiplication table, he confuses the generic vectors which he used to define the table, with other specific vectors having a special role in the paper, which had been introduced earlier. The result should be expressed in terms of the derived bivectors which indeed do follow this multiplication table. When correcting this calculation, the result is not the singlet correlation any more. Moreover, curiously, his normalized correlations are independent of the number of measurements and certainly do not require letting n converge to infinity. On the other hand his unnormalized or raw correlations are identically equal to -1, independently of the number of measurements too. Correctly computed, his standardized correlations are the bivectors - a . b - a x b, and they find their origin entirely in his normalization or standardization factors; the raw product moment correlations are all -1. I conclude that his research program has been set up around an elaborately hidden but trivial mistake. "

--------------------------------------------

It is interesting to add this note, addressed to those who suggest Jaynes is the only person who properly understands how probability applies to Bell's Theorem, entanglement, etc: Gill is also an expert in statistical theory, and has done extensive research in this area (including the application of Bayes). He apparently does not see the issue Jaynes does. Gill frequently collaborates with the top scientists in the study of entanglement, so I think it is safe to say this area has been well considered and has not been overlooked somehow.I thought at first that Christian might be on to something, because I intuited a connection between his approach and mine. But, after further consideration, imho, his stuff is just too mathematically circuitous to be considered. I've read his papers and his replies to various discussions, and in none of it is there a clear explanation of why his stuff should be considered a local realistic model of quantum entanglement.

[billschnieder]

Richard Gill's refutation is not a new critique. It is essentially the same as one of the critiques advanced by a certain Florin Moldoveanu in the fall last year to which Joy Christian has already replied (http://arxiv.org/abs/1110.5876). It originates from a misunderstanding of Joy's framework which admittedly is not very easy to understand especially for those who have blinders of one kind or another.

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

I remember Florin came here to boast about his critique and I pointed out his misunderstanding at the time in this thread: http://www.physicsforums.com/newreply.php?do=newreply&noquote=1&p=3806400

... you are missing the point because Joy Christian is not using handedness as a convention but as the hidden variable itself.
This is the same error Gill has made. See section (II) of Joy's response to Moldoveanu.

[bohm2]

More on this from Joy Christian and I don't understand any of it:

Refutation of Richard Gill's Argument Against my Disproof of Bell's Theorem
http://lanl.arxiv.org/pdf/1203.2529.pdf

[Delta Kilo]

More on this from Joy Christian and I don't understand any of it:

Refutation of Richard Gill's Argument Against my Disproof of Bell's Theorem
http://lanl.arxiv.org/pdf/1203.2529.pdf

Oh-ho, here we go again. No, Joy, measurement outcomes are not bivectors from unit sphere, they are numbers { -1; 1 }. That's how they are defined in Bell's paper and that is also the way how they come out of experiments. And their mean is 0 and their standard deviation is 1. Not bivectors, just numbers 0 and 1.

with \sigma(A) = (−I · \textbf{a} ) and \sigma(B) = (+I · \textbf{b} ), respectively, being the standard deviations in the results A and B.I can't be bothered anymore, but if you substitute I and \textbf{a} from definitions elsewhere in his paper, you will get \sigma(\textbf{a})=\sum a_{j}\beta_{j} where a_{j} are coefficients of unit vector \textbf{a} and \beta_{j} are "basis bivectors". Brain ruptures at this point...

[gill1109]

Richard Gill's refutation is not a new critique. It is essentially the same as one of the critiques advanced by a certain Florin Moldoveanu in the fall last year to which Joy Christian has already replied (http://arxiv.org/abs/1110.5876). It originates from a misunderstanding of Joy's framework which admittedly is not very easy to understand especially for those who have blinders of one kind or another.

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

I remember Florin came here to boast about his critique and I pointed out his misunderstanding at the time in this thread: http://www.physicsforums.com/newreply.php?do=newreply&noquote=1&p=3806400


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

It's true that Moldoveanu had earlier seen the same error, in a sense ... but Joy's definitions have not remained constant over the years, so it's a moot point whether the error in one of the earlier, long accounts, is the same error as in Joy's beautiful and simple one-page paper. Florin's focus was not the one-page paper, but the whole corpus of work at that point.

Joy and Bill Schnieder may find it legitimate, when one has freedom to make an arbitrary choice of "handedness", to make different and mutually contradictory choices at different locations in the same computation, but to my mind this is just licence to get any result one likes by use of poetry.

Joy's one page paper and my refutation are exercises in simple algebra. I suggest that Bill Schnieder and others work through my algebra and through Joy's algebra, themselves.

The reference to Hess and Phillip is also amusing. Not many people actually read through all the details of Hess and Phillips "counterexample" to Bell's theorem. Somewhere in the midst of that, a variable which had three indices suddenly only had two. This is where a joint probability distribution is being factored into a marginal and the product of two conditionals. Because of the notational slip-up, the normalization factor was wrong. All rather sad.

[gill1109]

DrChinese refered to Jaynes. Jaynes (1989) thought that Bell was incorrectly performing a routine factorization of joint probabilities into marginal and conditional. Apparently Jaynes did not understand that Bell was giving physical reasons (locality, realism) why it was reasonable to argue that two random variables should be conditionally *independent* given a third. When Jaynes presented his resolution of the Bell paradox at a conference, he was stunned when someone else gave a neat little proof using Fourier analysis that the singlet correlations could not be reproduced using a network of classical computers, whose communication possibilities "copy" those of the traditional Bell-CHSH experiments. I have written about this in quant-ph/0301059. Jaynes is reputed to have said "I am going to have to think about this, but I think it is going to take 30 years before we understand Stephen Gull's results, just as it has taken 20 years before we understood Bell's" (the decisive understanding having been contributed by E.T. Jaynes.

[gill1109]

PS, Bill Schnieder thinks that I prefer a different route to get Joy Christian's result because it gives a different answer, but this means he has not read my paper carefully. I discovered a short route, and it appeared to give Joy's answer. I showed this proudly to Joy. He pointed out that I was making a mistake, there was a missing term. I went back and looked more closely at his longer route, and discovered that they both gave the same answer. With the missing term.

[bohm2]

Just curious. Doesn't the new PBR theorem reach the same conclusion as Bell's making Joy Christian's refutation of Bell's theorem (even if it was conceivable) a mute point, at least with respect to arguing for a local realistic model:
Thus, prior to Bell’s theorem, the only open possibility for a local hidden variable theory was a psi-epistemic theory. Of course, Bell’s theorem rules out all local hidden variable theories, regardless of the status of the quantum state within them. Nevertheless, the PBR result now gives an arguably simpler route to the same conclusion by ruling out psi-epistemic theories, allowing us to infer nonlocality directly from EPR.
Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

The quantum state cannot be interpreted statistically
http://lanl.arxiv.org/pdf/1111.3328v1.pdf

[DrChinese]

DrChinese refered to Jaynes. Jaynes (1989) thought that Bell was incorrectly performing a routine factorization of joint probabilities into marginal and conditional. Apparently Jaynes did not understand that Bell was giving physical reasons (locality, realism) why it was reasonable to argue that two random variables should be conditionally *independent* given a third. When Jaynes presented his resolution of the Bell paradox at a conference, he was stunned when someone else gave a neat little proof using Fourier analysis that the singlet correlations could not be reproduced using a network of classical computers, whose communication possibilities "copy" those of the traditional Bell-CHSH experiments. I have written about this in quant-ph/0301059. Jaynes is reputed to have said "I am going to have to think about this, but I think it is going to take 30 years before we understand Stephen Gull's results, just as it has taken 20 years before we understood Bell's" (the decisive understanding having been contributed by E.T. Jaynes.

Thanks so much for taking time to share this story. For those interested, here is the direct link to your paper:

http://arxiv.org/abs/quant-ph/0301059

I like your example of Luigi and the computers. I would recommend this paper to anyone who is interested in understanding the pros AND cons of various local realistic positions - and this is a pretty strong roundup!

[gill1109]

Thanks, Bohm2 and thanks DrChinese.

Regarding PBR: I have to admit to have not got the point of PBR. PBR argue that the quantum state is not statistical, but real. That argument depends on definitions of those two words "statistical", "real". My own opinion about quantum foundations is summarized by statements that (1) the real world is real, and its past is now fixed (2) the future of the real world is random, (3) the quantum state is what you need to know about the past in order to determine the probability distribution of the future (so it's just as real as the real world, if you like, since the past real world is real and the probability distribution of the future is real too). This point of view is argued in http://arxiv.org/abs/0905.2723 which is actually just an attempt to explain the ideas which I got from V.P. Belavkin But you could also say that this is just a rigorous Copenhagen approach in which we don't talk about things which we don't need to, and in which we admit the necessity of defining quantum physics on a platform of naive classical physics.

[harrylin]

DrChinese refered to Jaynes. Jaynes (1989) thought that Bell was incorrectly performing a routine factorization of joint probabilities into marginal and conditional. Apparently Jaynes did not understand that Bell was giving physical reasons (locality, realism) why it was reasonable to argue that two random variables should be conditionally *independent* given a third. When Jaynes presented his resolution of the Bell paradox at a conference, he was stunned when someone else gave a neat little proof using Fourier analysis that the singlet correlations could not be reproduced using a network of classical computers, whose communication possibilities "copy" those of the traditional Bell-CHSH experiments. I have written about this in quant-ph/0301059. Jaynes is reputed to have said "I am going to have to think about this, but I think it is going to take 30 years before we understand Stephen Gull's results, just as it has taken 20 years before we understood Bell's" (the decisive understanding having been contributed by E.T. Jaynes.
Thanks for giving your opinion on this matter which happens to be the discussion topic of a parallel thread:
http://physicsforums.com/showthread.php?t=581193
I can copy your comment there, but it would be nicer if you would do it yourself. :smile:

[DrChinese]

Thanks for giving your opinion on this matter which happens to be the discussion topic of a parallel thread:
http://physicsforums.com/showthread.php?t=581193
I can copy your comment there, but it would be nicer if you would do it yourself. :smile:

I copied my comment + reference over there, which has the effect of including the above.

[harrylin]

I copied my comment + reference over there, which has the effect of including the above.
Looking at the time stamp, we had the same idea at the same time. :tongue:

[StevieTNZ]

Oh-ho, here we go again. No, Joy, measurement outcomes are not bivectors from unit sphere, they are numbers { -1; 1 }. That's how they are defined in Bell's paper and that is also the way how they come out of experiments. And their mean is 0 and their standard deviation is 1. Not bivectors, just numbers 0 and 1.

I can't be bothered anymore, but if you substitute I and \textbf{a} from definitions elsewhere in his paper, you will get \sigma(\textbf{a})=\sum a_{j}\beta_{j} where a_{j} are coefficients of unit vector \textbf{a} and \beta_{j} are "basis bivectors". Brain ruptures at this point...

So that pretty much destroys Joy's response to the argument against his original paper?

[billschnieder]

Joy Christian has now responded to Richard Gill's purported refutation:

http://arxiv.org/abs/1203.2529

I identify a number of errors in Richard Gill’s purported refutation of my disproof of Bell’s theorem.
In particular, I point out that his central argument is based, not only on a rather trivial misreading
of my counterexample to Bell’s theorem, but also on a simple oversight of a freedom of choice in
the orientation of a Clifford algebra. What is innovative and original in my counterexample is thus
mistaken for an error, at the expense of the professed universality and generality of Bell’s theorem.

[gill1109]

Thanks, Bill Schnieder. Joy has changed his postulates to patch the error. The new postulates are mutually contradictory. So first there was a model and a mistake, now there's no mistake but no model either. Vanished in a puff of smoke.

[bohm2]

I posted that paper in this thread above but I gave up trying to understand the debate. A very long one and not too friendly one that can be followed more fully here in this FQXi Blog:

Disproofs of disproofs of disproofs of disproofs...
http://www.fqxi.org/community/forum/topic/1247

[yoda jedi]

Just curious. Doesn't the new PBR theorem reach the same conclusion as Bell's making Joy Christian's refutation of Bell's theorem (even if it was conceivable) a mute point, at least with respect to arguing for a local realistic model:

Thus, prior to Bell’s theorem, the only open possibility for a local hidden variable theory was a psi-epistemic theory. Of course, Bell’s theorem rules out all local hidden variable theories, regardless of the status of the quantum state within them. Nevertheless, the PBR result now gives an arguably simpler route to the same conclusion by ruling out psi-epistemic theories, allowing us to infer nonlocality directly from EPR.

Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/

The quantum state cannot be interpreted statistically
http://lanl.arxiv.org/pdf/1111.3328v1.pdf

PBR place strong constraints on epistemic interpretations rather than rule out.

[bohm2]

PBR place a strong constraints on psi-epistemic interpretations rather than rule out.
My question really wasn't about this point. Joy Christian's preservation of local realism relies on refutation of Bell's. Even if that could be done, my question was whether non-locality can be inferred directly via PBR without Bell's theorem. Matt Leifer in his blog answered in a post:

Question by poster:
Hi Matt, Do you still believe that PBR directly implies non-locality, without Bell’s as I think you argued in a section of Quantum Times article?
“It (PBR) provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell’s theorem. ”
Matt's reply:
Yes, but this requires the factorization assumption used by PBR. At the time of writing, I was hopeful that we could prove the PBR theorem without factorization, but now I know that this is not possible. Therefore, the standard Bell-inequality arguments are still preferable as they involve one less assumption.
Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/comment-page-1/#comment-2877

[yoda jedi]

my question was whether non-locality can be inferred directly via PBR without Bell's theorem. Matt Leifer in his blog answered in a post:


Quantum Times Article on the PBR Theorem
http://mattleifer.info/2012/02/26/quantum-times-article-on-the-pbr-theorem/comment-page-1/#comment-2877

i understand, like your question of "Loophole-free demonstration of nonlocality"




.

[bohm2]

i understand, in the same manner, like your question of "Loophole-free demonstration of nonlocality".

Exactly.