Joy Christian's theory - a simple explanation for the Bell test paradox?

[DirkMan]

[Note: split out from https://www.physicsforums.com/threads/first-loophole-free-bell-test.829586/]

- noncommutative hidden variables - objective reality exists and is local, but is not represented by commutative numbers (Joy Christian)

Pity about the math errors and the new definition of correlation and general lack of any connection to physics in this so-called theory.

I, as a layman, can only think that Joy Christian's explanation must be the simplest one, at least from what I understood in the last 2 months since I've been trying to understand what his theory is. You mentioned Occam's Razor...well if someone says the math used in applying the quantum correlations to Bell's inequality is wrong, and somebody else says Bell's right and therefore either: the logic we use is wrong, or the universe is weird and the universe splits and the universe does this retrocausal thing and the universe does this and that, shouldn't the simplest explanation be that the math is wrong ?

 

[Ilja]

You mentioned Occam's Razor...well if someone says the math used in applying the quantum correlations to Bell's inequality is wrong, and somebody else says Bell's right and therefore either: the logic we use is wrong, or the universe is weird and the universe splits and the universe does this retrocausal thing and the universe does this and that, shouldn't the simplest explanation be that the math is wrong ?

Joy Christian is interesting only in a sociological sense. In discussions in http://www.sciphysicsforums.com/spfbb1/viewforum.php?f=6 he has made a reference to The true believer: Thoughts on the nature of mass movements by Eric Hoffer. It was, of course, polemical, presenting his opponents as "true believers" of Bell. But considering what he is really doing in this forum, where he has a few guys which support him, and comparing this with the fact that he obviously knows and likes this book, I could not resist to think that he simply tries out the various techniques described in this book to transform his supporters into such "true believers".

The errors in his various preprints and programs are different, but, in fact, quite trivial, and people with sufficient mathematical background are able to identify them without problems.

The consequences of Bell's theorem are much more harmless in comparison with your presentation. No need at all to doubt about logic or classical causality without closed causal loops, no need to accept any many worlds or similar weirdness like retrocausality. Because there is a quite simple possibility - go back to the Lorentz ether, that means, a hidden preferred frame or a hidden absolute time. This absolute time would be the time which rules causality, forbidding causal influences into the past (as defined by this time).

The result is, from point of view of locality, no more weird than Newtonian gravity, which was also acting globally without any speed limit. As in this case, one can reasonably hope that in some future one will observe some speed limit - a limit which would, then, require some modification of the theories, similar to that from NT to GR, but not more weird, so that such a "nonlocal theory" could be, without problem, a limit of some local theory with the relevant limiting speed going infinite.

 

[gill1109]

Sorry it turns out that I am not allowed on this forum to give a link to a paper which I posted on viXra analysing the Christian model and explaining in tutorial fashion the geometric algebra behind it. The title is "Does Geometric Algebra Provide a Loophole to Bell's Theorem?". Google can find it, if anyone is interested.

Here is a link to another paper by me on arXiv about the Christian theory, published in IJTP earlier this year. http://arxiv.org/abs/1412.2677. I also recommend J.O. Weatherall (2013). The Scope and Generality of Bell’s Theorem. Found. Phys. 43, 1153–1169. http://arxiv.org/abs/1212.4854

 

[gill1109]

Sorry it turns out that I am not allowed on this forum to give a link to a paper which I posted on viXra analysing the Christian model and explaining in tutorial fashion the geometric algebra behind it. The title is "Does Geometric Algebra Provide a Loophole to Bell's Theorem?". Google can find it, if anyone is interested.

Here is a link to another paper by me on arXiv about the Christian theory, published in IJTP earlier this year. http://arxiv.org/abs/1412.2677. I also recommend J.O. Weatherall (2013). The Scope and Generality of Bell’s Theorem. Found. Phys. 43, 1153–1169. http://arxiv.org/abs/1212.4854

Here's the link to my IJTP paper: "Macroscopic Unobservability of Spinorial Sign Changes"
http://link.springer.com/article/10.1007/s10773-015-2657-4 It's open access. And it's a response to Christian's "Macroscopic Observability of Spinorial Sign Changes under 2pi Rotations" http://arxiv.org/abs/1211.0784 Int. J. Theor. Phys. 54 (2015) 2042-2067

 

[Jazzdude]

Because there is a quite simple possibility - go back to the Lorentz ether, that means, a hidden preferred frame or a hidden absolute time. This absolute time would be the time which rules causality, forbidding causal influences into the past (as defined by this time).

Quantum theory even contains such a preferred frame structure in its mathematical formulation: The frame in which remote correlations evolve instantly. That frame is not detectable, because the order of measurement on distant entangled partners does not influence the outcome statistics, but mathematically its existence seems unavoidable. Still, nobody seems to care about the deeper meaning of a Lorentz-variant structure like that and it's implications for a description of underlying physical reality. I would not be surprised at all if a final conclusion of the Measurement problem revealed a fundamentally non-relativistic structure and left special relativity as a symmetry of interactions only, broken by entanglement and more generally, the quantum state space.

Cheers,

Jazz

 

[gill1109]

Quantum theory even contains such a preferred frame structure in its mathematical formulation: The frame in which remote correlations evolve instantly. That frame is not detectable, because the order of measurement on distant entangled partners does not influence the outcome statistics, but mathematically its existence seems unavoidable. Still, nobody seems to care about the deeper meaning of a Lorentz-variant structure like that and it's implications for a description of underlying physical reality. I would not be surprised at all if a final conclusion of the Measurement problem revealed a fundamentally non-relativistic structure and left special relativity as a symmetry of interactions only, broken by entanglement and more generally, the quantum state space.

Cheers,

Jazz

Some people do care about this. And there is promissing recent work e.g. by Daniel Beddingham http://link.springer.com/article/10.1007/s10701-010-9510-7 "Relativistic state reduction dynamics". Found. Phys. 41 (2011), no. 4, 686–704. You can also find it on arXiv.

 

[Nugatory]

there is promissing recent work e.g. by Daniel Beddingham http://link.springer.com/article/10.1007/s10701-010-9510-7 "Relativistic state reduction dynamics". Found. Phys. 41 (2011), no. 4, 686–704. You can also find it on arXiv.

ArXiv link: http://arxiv.org/abs/1003.2774

 

[DrChinese]

I, as a layman, can only think that Joy Christian's explanation must be the simplest one, at least from what I understood in the last 2 months since I've been trying to understand what his theory is. ... shouldn't the simplest explanation be that the math is wrong ?

You pretty well say it all right there. Joy's explanation has yet to be understood by you, so obviously the fact that it is not yet accepted by the scientific establishment should give you pause. Joy is what is called a local realist (and a Bell denier). Unfortunately for those for those lonely souls, there are many experiments which plainly show that nature is not local realistic. These leave little to the imagination, which is why local realism is so firmly rejected. I have asked Joy in the past to simply skip the math and provide a concrete example of data which can match his conjecture, but there are no examples forthcoming. It is Joy whose math is wrong.

As with anything, you are free to hold whatever opinion you like. Some people deny evolution too, for much the same reason.

 

[stevendaryl]

You pretty well say it all right there. Joy's explanation has yet to be understood by you, so obviously the fact that it is not yet accepted by the scientific establishment should give you pause. Joy is what is called a local realist (and a Bell denier). Unfortunately for those for those lonely souls, there are many experiments which plainly show that nature is not local realistic. These leave little to the imagination, which is why local realism is so firmly rejected. I have asked Joy in the past to simply skip the math and provide a concrete example of data which can match his conjecture, but there are no examples forthcoming. It is Joy whose math is wrong.

As with anything, you are free to hold whatever opinion you like. Some people deny evolution too, for much the same reason.

As I said in a different thread, it seems to me that, regardless of whether he made any mistakes in his mathematics, Joy Christian's model is just a non-sequitur when it comes to disproving Bell's theorem. Bell says: "There is no way, using local hidden variables, to implement a pair of real-valued functions satisfying blah, blah, blah." Joy Christian's response is: "I have found a way, using local hidden variables, to implement a pair of quaternion-valued functions satisfying blah, blah, blah."

 

[gill1109]

As I said in a different thread, it seems to me that, regardless of whether he made any mistakes in his mathematics, Joy Christian's model is just a non-sequitur when it comes to disproving Bell's theorem. Bell says: "There is no way, using local hidden variables, to implement a pair of real-valued functions satisfying blah, blah, blah." Joy Christian's response is: "I have found a way, using local hidden variables, to implement a pair of quaternion-valued functions satisfying blah, blah, blah."

For Bell's proof, it doesn't matter whether we consider +/-1 as real numbers, quaternions, or something more fancy. As long as the usual rules of arithmetic apply to them. The fact is that Christian doesn't just change the "co-domain" (range) of the measurement functions A(a, lambda) etc ... he also changes the definition of correlation! He divides the average of the product by quaternionic theoretical standard deviations. What he proceeds to do has got nothing to do with Bell's theorem and nothing to do with QM experiments: counting +/-1 outcomes and calculating correlations as (# equal - # unequal)/(# trials). If you read Christian's papers you will see that his definition of A(a, lambda) is such that the measurement outcomes are equal and opposite with probability 1, hence all correlations (in the usual sense) are equal to -1. In order to reproduce the singlet correlations - a . b he not only needs a new definition of correlation, he also needs to make an algebraic error; or if you prefer, he needs a new random geometric product: x (*Christian) y = x (* geometric product) y with probability half, x (*Christian) y = y (* geometric product) x with probability half.)
http://www.math.leidenuniv.nl/~gill/#crackpot http://www.math.leidenuniv.nl/~gill/1504.0102v2.pdf

 

[stevendaryl]

For Bell's proof, it doesn't matter whether we consider +/-1 as real numbers, quaternions, or something more fancy. As long as the usual rules of arithmetic apply to them.

Well, for the specific case of EPR, the outcomes that are actually measured are empirically binary: You measure spin along an axis, and you either get spin-up, or spin-down. So if those results are to be explained by a deterministic hidden-variables theory, it seems that at some point, you would have to have a quantity in the theory that is two-valued.

 

[gill1109]

Well, for the specific case of EPR, the outcomes that are actually measured are empirically binary: You measure spin along an axis, and you either get spin-up, or spin-down. So if those results are to be explained by a deterministic hidden-variables theory, it seems that at some point, you would have to have a quantity in the theory that is two-valued.

Christian's first lines of his model usually come down to A(a, lambda) = - B(b, lambda) = +/-1 (independent of the settings a, b) and that +/-1 is the result of a fair coin toss. You can think of it as a real number or as a member of a Clifford algebra or as a quaternion. Doesn't make any difference. The correlation (as defined in the conventional way) is E(a, b) = - 1 independently of a and b. In order to get something different you have to redefine "correlation" and possibly also redefine Clifford algebra multiplication ... does it matter? Is this physics?

 

[stevendaryl]

Is what physics?

I thought that Christian originally defined $A(\vec{n},\vec{\mu}) = \vec{\mu} \cdot \vec{n}$ (Equation 16 of this paper: http://arxiv.org/pdf/quant-ph/0703179v3.pdf

That is a quaternion, not $\pm 1$.

 

[gill1109]

What about formula (8)? What about formulas (1) and (2) of http://arxiv.org/abs/1103.1879 ? (Contained in the first chapter of Christian's book)

(Is what physics? Christian's "model")

 

[stevendaryl]

What about formula (8)?

Formula 8 is not talking about Christian's model, it's talking about Bell's toy model. That section begins:

"Before formally proving the theorem, however, Bell provides an illustration of the tension between quantum mechanics and local causality by means of a local model."
​

This is the local model that leads to the red-line prediction showed here:
https://en.wikipedia.org/wiki/Bell's_theorem#/media/File:Bell.svg

 

[stevendaryl]

What about formula (8)? What about formulas (1) and (2) of http://arxiv.org/abs/1103.1879 ? (Contained in the first chapter of Christian's book)

(Is what physics? Christian's "model")

You're right, that paper does seem to use a two-valued model for $A(a,\lambda)$. I'm not sure what Christian thought was the connection between these two different papers. You're right; in that paper, the problem isn't the fact that $A$ is quaternion-valued, it is the fact that $A(a,\lambda)$ is independent of $a$, and that model predicts that $A(a, \lambda) \cdot B(b, \lambda) = -1$, independent of $a$ or $b$.

 

[Strilanc]

Scott Aaronson, a reasonably well-known researcher in algorithmic complexity (including quantum algorithms), has written a few blog posts about Joy Christian. They are not positive.

 

[Avodyne]

Christian's first lines of his model usually come down to A(a, lambda) = - B(b, lambda) = +/-1 (independent of the settings a, b) and that +/-1 is the result of a fair coin toss. You can think of it as a real number or as a member of a Clifford algebra or as a quaternion. Doesn't make any difference. The correlation (as defined in the conventional way) is E(a, b) = - 1 independently of a and b. In order to get something different you have to redefine "correlation"

Yes, this seems to have been Christian's fundamental misunderstanding: the meaning of "correlation". Physicists use the phrase "correlation function" in a way that is different than is used by statisticians: see the first displayed equation in https://en.wikipedia.org/wiki/Correlation_and_dependence for the statisticians' definition. Physicists omit the denominator on the right-hand side in that equation. Of course in the end the terminology doesn't matter: you just have to compare apples to apples. But that is what Christian gets wrong: he compares the physicists' experimentally-defined "correlation function" to one he derived from his model, but he used the statisticians' definition of "correlation function" in his derivation. He is thus comparing apples to oranges, and so comes to a wrong conclusion.

 

[stevendaryl]

Yes, this seems to have been Christian's fundamental misunderstanding: the meaning of "correlation". Physicists use the phrase "correlation function" in a way that is different than is used by statisticians: see the first displayed equation in https://en.wikipedia.org/wiki/Correlation_and_dependence for the statisticians' definition. Physicists omit the denominator on the right-hand side in that equation.

Yes, that is another problem for Christian to compare his result with what is used by Bell. But in any case, the "denominator" that Christian uses is not a real number, but a quaternion. If the point of the denominator is to normalize the distribution, then does it really make any sense to divide by a quaternion?

 

[Avodyne]

I would say no, it doesn't make sense. But I'm sure Christian would disagree.

I was trying to guess how Christian (clearly a smart person) got it wrong at first. But this does not explain why he is apparently incapable of understanding his error, after it has been explained (extremely clearly) by Gill, Weatherall, Aaronson, et al.

 

[gill1109]

I would say no, it doesn't make sense. But I'm sure Christian would disagree.

I was trying to guess how Christian (clearly a smart person) got it wrong at first. But this does not explain why he is apparently incapable of understanding his error, after it has been explained (extremely clearly) by Gill, Weatherall, Aaronson, et al.

Smart in a way. Remember, Christian comes from (a) the philosophical foundations of physics and (b) relativity theory. He appears to know a lot of mathematics but if you look closely at what he is doing, he clearly is quite mixed up. For instance, the relations which define an algebra are not the same as the algebra itself. He makes a quite elementary error through this confusion. It means that he doesn't appreciate the mathematical notion of isomorphism and doesn't actually have a deep grasp of the mathematical definitions of quite simple objects (such as the basic Clifford algebra). He also makes a big deal of the "co-domain" of Bell's measurement functions. Notice, this is not the question whether or not the hidden variables might lie in some fancy spaces. No it is a question of the values of the measurement results. You can think of -1 and +1 as being quaternions if you like, it doesn't change Bell's theorem. So this is a quite spectacular misunderstanding of what Bell's theorem is all about as well as a spectacular misunderstanding of abstract mathematical structures.

Here is his latest arXiv publication, it's a reply to criticism by me. Just take a look at it and see if it makes any sense. http://arxiv.org/abs/1501.03393

 

[Nugatory]

This thread has pretty much run its course - time to close it.