Joy Christian's disproof of Bell

[ajw1]

For several years Joy Christiaan has been publishing about the disproof of Bell in a typical EPR setup, his latest (?) publication being http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.4259v3.pdf" .

In a nutshell his argument is that Bell uses an invalid topology for the EPR elements of reality (1D instead of 3D). When using Clifford algebra the author says he can reproduce the Bell inequalities.

Does he have a valid argument here?

This http://www.physics.utoronto.ca/~aephraim/2206/Sprague-ChristianDisproofBell.pdf" further summarizes his arguments

ps. I haven't seen his articles being published somewhere else then Arxiv, but Carlos Castro references him claiming about the same http://www.m-hikari.com/astp/astp2007/astp9-12-2007/castroASTP9-12-2007.pdf" .

 

[humanino]

Does he have a valid argument here?

To my knowledge, his arguments are not taken very seriously, as they would require serious modifications in the basic axioms of QM.

The crux of his argument is a denial that observables should only correspond to real numbers, but that more complicated algebraic quantities (such as spinors, or vectors) should be considered "observables". That is fine (I mean, interesting) at a general level in an epistemological discussion, but that is not enough at a technical level : in QM observables are self-adjoint operators, and the results of measurements are in the spectra of them. For his argument to be valid, he would need considerably more work to refund the entire axiomatization of QM.

 

[Count Iblis]

Not sure though why he hasn't been able to get his ideas published in Foundations of Physics. With 't Hooft as chief editor that should not be a problem...

 

[DrChinese]

There are at least a dozen authors presenting "disproofs" of Bell. Usually, as with Christian, it involves some esoteric point in Bell. However, none of these is accepted and I have not read any that make anything close to a cogent argument. The best of the lot, for my money, is the De Raedt program (defects of which I have posted on extensively in another thread).

So really, it just boils down to: what are your requirements for a successful Bell proof? Clearly some authors don't like Bell's streamline approach.

 

[ajw1]

I am trying to follow his reasoning, but I have trouble understanding the math exactly. His arguments don't seem so unreasonable, so it would be interesting to test it in a de Raedt type simulation (without using the effect of a time window as de Raedt does).

(for those who don't know the de Raedt model: it's a numerical 'event by event' simulation that calculates the total effect of individual pairs of photons in an EPR-B setup)

 

[Fredrik]

I tried to read one of his "disproof" articles some time ago, and it was pure garbage. It was more badly written than I thought was possible for a physics article, so it was impossible to follow his reasoning. I recommend that you don't waste your time on any of his work, at least until he's been able to produce something that can pass the peer review process.

By the way, when I started a thread about the article I was trying to understand (before I realized that his "argument" was completely incoherent), one of the moderators deleted the thread and gave me a formal warning for linking to unpublished stuff. A bit of an overreaction perhaps, but the article was garbage and I agree that it wasn't worthy of a discussion in the QM forum.

Not sure though why he hasn't been able to get his ideas published in Foundations of Physics. With 't Hooft as chief editor that should not be a problem...

I find this comment interesting. Does Foundations of Physics have a bad reputation, or are you just saying that you have such a low opinion of 't Hooft that you expect his journal to publish nonsense? Have they published bad stuff in the past?

 

[GiftOfPlasma]

I believe that the jab at t' Hooft is due to his recent work in hidden variable theories.

From my examination, the paper linked in the OP, doesn't seem to be “Pure Garbage”, it also seems possible to follow his reasoning. Saying that you don't understand is not a valid criticism of a theory.

After reading the paper it seems good, the crux of his argument doesn't seem to be as described by humanino. The crux of his argument is that Bell made a topology error, that when corrected gives the same QM results for entangled states but allows local realism.

 

[Cthugha]

After reading the paper it seems good, the crux of his argument doesn't seem to be as described by humanino.

This is not true. Christian assumes that the spin values in question are not +1 and -1, but numbers from Clifford algebra. Then it is almost trivial to violate the Bell inequalities using any model. However, there is no good reason why one should assume eigenvalues to be members of Clifford algebra, so Christian pulls up the magic topology argument, which is just ridiculous in my opinion.

Does Foundations of Physics have a bad reputation, or are you just saying that you have such a low opinion of 't Hooft that you expect his journal to publish nonsense? Have they published bad stuff in the past?

Foundations of Physics is aimed at the more philosophical side of physics and also concerned about not-so-mainstream stuff in order to be able to publish serious out-of-the-box thinking. However, this also means that the published articles are sometimes not out-of-the-box, but plain wrong. Personally I am not really interested in this kind of debates and ignore FoP, but given the rather small number of other journals publishing stuff on this topic I think it deserves a place in the scientific community.

 

[Fredrik]

From my examination, the paper linked in the OP, doesn't seem to be “Pure Garbage”, it also seems possible to follow his reasoning.

It definitely wasn't possible to follow the article I read back then. I wasn't exaggerating about how bad it was. After that experience I would need a very good reason to read even a single line of text from any of his articles. So I didn't even click the link in the OP.

Saying that you don't understand is not a valid criticism of a theory.

I'm not saying that there was an argument in his paper that I didn't understand. I'm saying that the stuff in the paper I read doesn't qualify as an argument. That's definitely valid criticism of the contents of an article.

 

[humanino]

The crux of his argument is that Bell made a topology error,

That is not a crux, that is the title of the paper, and is just a more vague description.

 

[Count Iblis]

I agree with Cthugha's comments about FoP. Note that
't Hooft became chief editor to make sure quack articles don't get published (this became an issue before he was involved there).

But 't Hooft is sympathetic toward non-mainstream ideas about quantum mechanics, so you will certainly not get a knee jerk rejection of articles just because they don't stick to some accepted dogma like e.g. that the violation of Bell's inequalities has ruled out local hidden variable theories.

As 't Hooft has said many times: no-go theorems always contain hidden assumptions...

 

[Fredrik]

OK, that's a much milder statement than your previous one, which suggested that he would be willing to publish anything. This one is easier to believe. The reason I care at all is that I've been thinking about writing something about the MWI and about interpretations in general, and if I ever do that, it would be good to know if this journal has a bad reputation.

 

[IcedEcliptic]

This is good to hear, when I read the article Fredrik mentioned it seemed almost random. I thought perhaps that I was missing something, and now I know that I was: it's pure crap.

 

[humanino]

I do not think it is pure crap, because the mathematics are not invalid, they are just not agreement with one of the basic physics postulate of QM, namely that we measure real numbers, not Clifford numbers. I think it is worth spending one hour of one's life to read.

 

[atyy]

Graingier's commentary, which I came across via a news item in Nature Physics: http://arxiv.org/abs/0707.2223

 

[ajw1]

Graingier's commentary, which I came across via a news item in Nature Physics: http://arxiv.org/abs/0707.2223

Yes, the reply from Christian to Graingier's criticism can be found http://arxiv.org/PS_cache/quant-ph/pdf/0703/0703244v12.pdf" , starting at 'Response # 3'.

(the main issue raised by Graingier seems to be the extraction of either a + or - result for a spinning particle. Christian's reply is that in Clifford algebra a bi vector naturally has a sense of rotation, and so a sign is naturally available)

So far I haven't been able to find more recent commentary on Christian's statements then the articles published in 2007.

 

[IcedEcliptic]

I do not think it is pure crap, because the mathematics are not invalid, they are just not agreement with one of the basic physics postulate of QM, namely that we measure real numbers, not Clifford numbers. I think it is worth spending one hour of one's life to read.

If you are a mathematician perhaps, but if you spent time reading every non-physical mathematical offering refuting or confirming things, you would die in ignorance. I read it, and I consider it to have been a waste of my time.

 

[Fredrik]

Just to clarify, the article I read is not the one linked to in the OP. It had both "disproof" and "Clifford" in the title. I spent a few hours reading it and thinking about it, and I wouldn't recommend it to anyone.

 

[DrChinese]

Graingier's commentary, which I came across via a news item in Nature Physics: http://arxiv.org/abs/0707.2223

Thanks for this reference. Local realists want to have it both ways. They say that the predicitions of QM are correct (usually), and that the results are not observer dependent. I just want to see their dataset. That tells everything, for any "disproof".

It should be a requirement that any local realist publish an appendix to their work with a sample dataset. That way, you could start by seeing what kind of a universe Alice and Bob live in. It would save a lot of otherwise wasted effort.

Of course, if Christian did that, then it would be obvious where the weakness is.

 

[humanino]

I consider it to have been a waste of my time.

I probably already gave to this very thread half the attention I gave to Christian's original paper...

 

[IcedEcliptic]

I probably already gave to this very thread half the attention I gave to Christian's original paper...

Every silver lining has its cloud. :) Any time and attention used for that paper could be better spent molesting pigeons, or beating the homeless. Anything, but reading another load of tripe.

 

[ajw1]

I was hoping for some substantial criticism on the articles. The 'wasting time' remarks now seem to be more motivated by personal preference .

 

[IcedEcliptic]

I was hoping for some substantial criticism on the articles. The 'wasting time' remarks now seem to be more motivated by personal preference .

How does one critique a steaming pile of manure? You simply note that it is in fact, manure, and move on.

 

[DrChinese]

I was hoping for some substantial criticism on the articles. The 'wasting time' remarks now seem to be more motivated by personal preference .

OK, here is a critique: how can you use the ideas in the paper to construct a local realistic dataset?

Thanks for the answer to this question.

 

[Fredrik]

I was hoping for some substantial criticism on the articles. The 'wasting time' remarks now seem to be more motivated by personal preference .

My dismissal of the other article wasn't based on any personal preference other than that I think arguments should make sense. What I learned from reading it was that articles below a certain threshold of quality are simply not worth the effort, unless it's bad in a funny way, and this one isn't. Wouldn't it be great if we had some sort of system in place that could tell us if an article has passed some sort of minimum requirement? Oh wait, we do.

By the way, this is from the forum rules:

It is against our Posting Guidelines to discuss, in most of the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion.

Has Christian been able to publish any of his stuff?

 

[harrylin]

[..] Wouldn't it be great if we had some sort of system in place that could tell us if an article has passed some sort of minimum requirement? Oh wait, we do.
[..]
Has Christian been able to publish any of his stuff?

Apparently this thread has not yet been closed, and now that I'm reading it, I'm baffled!
For the OP did refer to a publication (perhaps after people didn't watch anymore? [Edit: no, he added the reference before the first reply!]):

Carlos Castro, "There is No Einstein-Podolsky-Rosen Paradox in Clifford-Spaces",
Adv. Studies Theor. Phys., Vol. 1, 2007, no. 12, 603 - 610
http://www.m-hikari.com/astp/astp2007/astp9-12-2007/castroASTP9-12-2007.pdf

Does that article agree with Christian's claims, or does it perhaps disagree in some subtle way?
As both QM and Clifford algebra are difficult for me, I don't know what to make of their combination!

 

[vanesch]

Maybe I'm simply not sophisticated enough, but there's a version of Bell's theorem which is so terribly elementary, that I don't see how you could "disprove" it. You could just as well try to disprove an elementary theorem in number theory or something.

The elementary version I'm talking about is the one in Sakurai

http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality

The idea is simple: you pick 3 well-chosen axes in a couple of spin-1/2 analysers.
You consider that the population of pairs consists of 8 sub-populations, which are programmed to give (+++), (++-), (+-+) ... (---) for the 3 possible axes at Alice, and the opposite at Bob's. Each pair is randomly drawn from one of these 8 subpopulations, with a priori probabilities P1...P8. P1 + ... + P8 = 1 of course.

It is then shown that there cannot exist 8 positive numbers P1... P8 that will satisfy the statistical outcomes as predicted by quantum mechanics.

This proof is so simple that I don't consider it worth reading any paper that claims the opposite, honestly. You can just as well write a paper arguing that Pythagoras' theorem is wrong in Euclidean geometry, no ?

 

[harrylin]

Maybe I'm simply not sophisticated enough, but there's a version of Bell's theorem which is so terribly elementary, that I don't see how you could "disprove" it. You could just as well try to disprove an elementary theorem in number theory or something.

Thanks but... that doesn't really answer my question! See below.

The elementary version I'm talking about is the one in Sakurai

http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality

The idea is simple: you pick 3 well-chosen axes in a couple of spin-1/2 analysers.
You consider that the population of pairs consists of 8 sub-populations, which are programmed to give (+++), (++-), (+-+) ... (---) for the 3 possible axes at Alice, and the opposite at Bob's. Each pair is randomly drawn from one of these 8 subpopulations, with a priori probabilities P1...P8. P1 + ... + P8 = 1 of course.

It is then shown that there cannot exist 8 positive numbers P1... P8 that will satisfy the statistical outcomes as predicted by quantum mechanics.

As a matter of fact, last year I simulated something like that on a spread sheet. I find it a great example of a group of locally realistic theories that does not work, and no doubt, that is the kind that Bell was thinking of.

This proof is so simple that I don't consider it worth reading any paper that claims the opposite, honestly. You can just as well write a paper arguing that Pythagoras' theorem is wrong in Euclidean geometry, no ?

Supposedly this thread discusses what that paper claims; but after reading the discussion, it is still not clear to me what it really argues.
To me it sounds like a paper arguing that Pythagoras' theorem is wrong in curved geometry. And then the question is not so much if that argument is wrong (probably not!), but which geometry is the right one for the problem at hand.

Does that paper claim that it may apply, or not? If there is a statement to that effect, I overlooked it...

 

[Q-reeus]

In #27 vanesch writes:
"Maybe I'm simply not sophisticated enough, but there's a version of Bell's theorem which is so terribly elementary, that I don't see how you could "disprove" it. You could just as well try to disprove an elementary theorem in number theory or something.
The elementary version I'm talking about is the one in Sakurai
http://en.wikipedia.org/wiki/Sakurai%27s_Bell_inequality ..."

Perhaps it would have been fairer to have quoted the severe qualifiers in that Wiki article:
"...The one discussed here holds only for a very limited class of local hidden variable theories and has never been used in practical experiments...Note that the inequality is not really applicable either to electrons or photons, since it builds in no probabilistic properties in the measurement process. Much more realistic hidden variable theories can be devised, modelling spin (or polarisation, in optical Bell tests) as a vector and allowing for the fact that not all emitted particles will be detected."

As for the other critics here, I would be much more impressed with a detailed rebuttal of the specifics of Joy Christian's papers (the latest of which is not that given in the OP but can be accessed from here: http://arxiv.org/find/quant-ph/1/au:+Christian_J/0/1/0/all/0/1), rather than dismissing his arguments as 'a pile of manure' etc. In other words, does anyone here actually have a sufficiently deep grasp of Clifford Algebra and QM to be able to rebut Joy Christian on his own terms?

 

[Avodyne]

Well, I took a look at Christian's ArXiv paper that was linked above. His argument is not valid. He is merely changing the definition of a "local hidden variable". The sort of theories that are ruled out by Bell's argument are those in which, given a complete description of the state of a spin-one-half particle, you can predict with 100% accuracy whether its spin will be "up" or "down" when measured along any axis. Christian's theory is not of this type, because for him "up" and "down" are not definite values, but elements of some algebra that do not necessarily commute. So all he is doing is inventing his own sort of quantum theory, while claiming that it is a hidden-variable theory. But, by the definition everyone else on the planet has agreed on, his theory is not a hidden-variable theory. So it's just a big waste of everyone's time.

 

[ThomasT]

Does that article agree with Christian's claims, or does it perhaps disagree in some subtle way?

It agrees with Christian's claim that his Clifford algebraic formulation is locally causal.

Castro's showing, in equations 1 through 29 with accompanying annotations, why a Clifford space, Clifford algebraic QM formulation can be regarded as locally causal. But it still has to do with the entangled particles exchanging signals, and it's for this and other reasons that I would guess that most people, including me, wouldn't regard Christian's formulation as a bona fide Local Realistic representation of entanglement.

To me it sounds like a paper arguing that Pythagoras' theorem is wrong in curved geometry. And then the question is not so much if that argument is wrong (probably not!), but which geometry is the right one for the problem at hand.

That seems like an insightful analogy. And I've found Christian's topological considerations to be interesting in the sense that I hoped that they might be (via some convoluted associations) compatible with my own views on this stuff. But insofar as I don't understand the connection between Christian's approach and reality, or at least my conception of it, then I can only speak to what seems to me to be his motivation and what seems to me to be the relevant features of his formulation and, again superficially, why it doesn't seem to me to explain why the extensions of Bell's theorem to deep reality are flawed.

Bell's work shows, correctly by virtually all assessments as well as imho, that an lhv account of the singlet state is incompatible with the qm account. Subsequent work by others has verified that lhv accounts of entanglement are not only incompatible with qm, but with experimental results. This is a done deal imho and universally accepted by mainstream physicists as being fact. But some have interpreted this to mean, or as proof, that either lhv's don't exist or that nature is nonlocal, and I think it's disagreement with this interpretation that has prompted a closer examination of Bell's work. This is where Christian is coming from.

And yes, he's correct in saying that his formulation can be, in a certain sense, said to be locally causal. But it's a decidedly artificial sense, and as far as I can tell doesn't offer any (readily understandable) insight wrt why Bell's theorem isn't telling us anything about deep reality.

Maybe I'm simply not sophisticated enough, but there's a version of Bell's theorem which is so terribly elementary, that I don't see how you could "disprove" it. You could just as well try to disprove an elementary theorem in number theory or something.

Of course you're right in saying that the strictly mathematical Bell's theorem (Bell's Inequality) is a proven theorem. But neither Christian nor Castro are claiming otherwise -- at least as far as I can tell.

Bell tests are measuring a relationship between two relationships, and a full accounting of the statistical results doesn't require any reference to local hidden variables (eg., the optical vector of entangled photons is irrelevant wrt determining the joint stats -- it's only the relationship between paired particles that matters, and this is a global not a local property). If local hidden variables are used, then you can get the same basic angular dependence predicted by qm, but with a reduced range. However, if local hidden variables are required to describe an entangled state, then from that you can formulate an inequality that will be violated by qm and experimental results -- none of which contradicts the possibility or assumption of the existence of local hidden variables or the assumption that nature is locally causal (and wrt to this it helps to keep in mind that Bell showed that qm is quite compatible with a local hidden variable account of individual results).

Is Christian's Bell stuff interesting? Yes, I think so. Is it important in that it clarifies or explains anything? No, I don't think so. But then, I can't claim to fully understand the relationship between the C-space account of entanglement and reality. It would be nice if Christian would spend some time at PF to explain his approach and what he takes to be the meaning and import of his formulation. In lieu of that, I would have to say that Christian's Bell stuff is not a refutation of Bell's work or disproof of Bell's theorem (that is, wrt the universally accepted minimalist interpretation and unarguable application of Bell's theorem).

 

[vanesch]

Well, I took a look at Christian's ArXiv paper that was linked above. His argument is not valid. He is merely changing the definition of a "local hidden variable". The sort of theories that are ruled out by Bell's argument are those in which, given a complete description of the state of a spin-one-half particle, you can predict with 100% accuracy whether its spin will be "up" or "down" when measured along any axis. Christian's theory is not of this type, because for him "up" and "down" are not definite values, but elements of some algebra that do not necessarily commute. So all he is doing is inventing his own sort of quantum theory, while claiming that it is a hidden-variable theory. But, by the definition everyone else on the planet has agreed on, his theory is not a hidden-variable theory. So it's just a big waste of everyone's time.

This is indeed what I was suspecting, without, I admit, even looking at the paper, simply because what Bell's theorem claims, is pretty well-defined, and the proof is, to all mathematical standards, well-done.

If you enlarge the scope of what you call "local realistic theories", of course you will end up at a point where you WILL find agreement with quantum predictions, but that's not Bell's theorem of course. The reason why you will find such a solution, is that there is one which exists: the MWI version of a "Bell-experiment" in the Heisenberg picture. I can't find the paper directly, I think it was by Rubin (not sure), where it is worked out in all detail.
We already know that a "local" explanation of entanglement is possible in MWI.

In essence, this is possible because the "measurement outcomes" are still "superpositions" which can interfere when we calculate correlations between them. This is the basis of MWI: that the observer is himself/herself in an entangled state, and not in a well-defined projected state.

Maybe I should take the time to read the paper after all, maybe the author simply re-invented a kind of Heisenberg representation of the problem in an MWI setting :-)

 

[yoda jedi]

If you enlarge the scope of what you call "local realistic theories", of course you will end up at a point where you WILL find agreement with quantum predictions, but that's not Bell's theorem of course. The reason why you will find such a solution, is that there is one which exists: the MWI version of a "Bell-experiment" in the Heisenberg picture. I can't find the paper directly, I think it was by Rubin (not sure), where it is worked out in all detail.
We already know that a "local" explanation of entanglement is possible in MWI.

the consistent histories approach too.

griffith
http://arxiv.org/PS_cache/arxiv/pdf/1007/1007.4281v1.pdf








------------
rubin
http://arxiv.org/PS_cache/quant-ph/pdf/0103/0103079v2.pdf

 

[harrylin]

Well, I took a look at Christian's ArXiv paper that was linked above. His argument is not valid. He is merely changing the definition of a "local hidden variable". The sort of theories that are ruled out by Bell's argument are those in which, given a complete description of the state of a spin-one-half particle, you can predict with 100% accuracy whether its spin will be "up" or "down" when measured along any axis. Christian's theory is not of this type, because for him "up" and "down" are not definite values, but elements of some algebra that do not necessarily commute. So all he is doing is inventing his own sort of quantum theory, while claiming that it is a hidden-variable theory. But, by the definition everyone else on the planet has agreed on, his theory is not a hidden-variable theory. So it's just a big waste of everyone's time.

For Christian, the output values of the function A (the measured "spin" components) are only +1 and -1.*
A is function of hidden variable L and detector angle a. His beef is with Bell's statement that A (L , a ) = +1 or -1, it should be A ( L , a ) = +1 or -1 *about* a, as the output is relative to the chosen detector position. It is completely unclear to me if, as he suggests, that makes any difference for the calculation.

So, his analysis (it's not a theory!) may certainly be erroneous and a waste of time; but clearly, it does concern hidden variable theories.

*Personal communication, Sep 2009

 

[harrylin]

(About the paper of Carlos Castro, "There is No Einstein-Podolsky-Rosen Paradox in Clifford-Spaces":)

It agrees with Christian's claim that his Clifford algebraic formulation is locally causal.

Castro's showing, in equations 1 through 29 with accompanying annotations, why a Clifford space, Clifford algebraic QM formulation can be regarded as locally causal. But it still has to do with the entangled particles exchanging signals, and it's for this and other reasons that I would guess that most people, including me, wouldn't regard Christian's formulation as a bona fide Local Realistic representation of entanglement.

Thank you!
About the exchange of signals, does he state that somewhere? I must have overlooked it...

(Next I wrote, following up on vanesch: "it sounds like a paper arguing that Pythagoras' theorem is wrong in curved geometry")

That seems like an insightful analogy. And I've found Christian's topological considerations to be interesting in the sense that I hoped that they might be (via some convoluted associations) compatible with my own views on this stuff. But insofar as I don't understand the connection between Christian's approach and reality, or at least my conception of it, then I can only speak to what seems to me to be his motivation and what seems to me to be the relevant features of his formulation and, again superficially, why it doesn't seem to me to explain why the extensions of Bell's theorem to deep reality are flawed.[..]

Same problem for me!

Thanks,
Harald