I’ve just seen that Open Science, a new journal by the prestigious Royal Society, published the article Quantum correlations are weaved by the spinors of the Euclidean primitives, by Joy Christian. The article, as numerous others by the same author, claims that Bell’s theorem is wrong, and that one can violate Bell inequalities using a local hidden-variables model.

This is of course nonsense. Bell’s theorem is not only a rather simple piece of mathematics, with a few-lines proof that can be understood by high-school students, but also the foundation of an entire field of research — quantum information theory. It has been studied, verified, and improved upon by thousands of scientists around the world.

The form of Bell’s theorem that is relevant for the article at hand is that for all probability distributions $\rho(\lambda)$ and response functions $A(a,\lambda)$ and $B(b,\lambda)$ with range $\{-1,+1\}$ we have that

\begin{multline*}

-2 \le \sum_\lambda \rho(\lambda) \Big[A(a_1,\lambda)B(b_1,\lambda)+A(a_1,\lambda)B(b_2,\lambda) \\ +A(a_2,\lambda)B(b_1,\lambda)-A(a_2,\lambda)B(b_2,\lambda)\Big] \le 2

\end{multline*}

The author’s proposed counterexample? It’s described in equations (3.48) and (3.49): A binary random variable $\lambda$ that can take values $-1$ or $+1$, with $\rho(-1)=\rho(+1)=1/2$, and response functions $A(a,\pm1)=\pm1$ and $B(b,\pm1)=\mp1$. That’s it. Just perfectly anti-correlated results, that do not even depend on the local settings $a$ and $b$. The value of the Bell expression above is simply $-2$.

Now how could Open Science let such trivial nonsense pass? They do provide the “Review History” of the article, so we can see what happened: there were two referees that pointed out that the manuscript was wrong, one that was unsure, and two that issued a blanket approval without engaging with the contents. And the editor decided to accept it anyway.

What now? Open Science can recover a bit of its reputation by withdrawing this article, as Annals of Physics did with a previous version, but I’m never submitting an article to them.

How could Open Science let such trivial nonsense pass? The author’s response to the referees, which the referees never got to see, is illuminating. Apparently his revision of the paper was accepted without showing the revision and the author’s responses to the referees.

The response hides between a number of what I would call *lies*. Firstly, that the author’s model is new and hence critique of earlier models is irrelevant. Secondly that the critique of earlier models was (a) answered by the author in his numerous arXiv preprints (at last count, there are 15 of them in total) and (b) none of the critique succesfully passed peer-review and got published.

Apparently the editors fell for Christian’s bluff and jumped at the opportunity to publish a highly controversial paper.

Indeed the model is “new”. Let’s call it Christian 3.0. It is also vastly more complex. It contains many of the errors of earlier models, both conceptual and technical. Some of the errors of earlier models have been avoided but also new errors have been introduced – the increased complexity gives plenty of scope for this. It’s amusing to see how the programmers of his model have actually diverged from Christian’s recipes in order to get the “right answer”, introducing new errors of their own.

Actually two peer-reviewed papers did discuss Christian’s earlier models, Christian 1.0 and Christian 2.0.

Gill (2016) DOI: 10.1007/s10773-015-2657-4

Weatherall (2013) DOI: 10.1007/s10701-013-9737-1

I also wrote a tutorial on Christian 2.0, and posted it to arXiv. The moderators rejected it … on the grounds that it was a tutorial, not a research paper. It was fun learning about geometric algebra Cl(3, 0), but I don’t presently feel like getting to grips with conformal geometric algebra Cl(4, 1).

This is really funny: apparently arXiv banned the preprint of Joy’s present paper but now that it has appeared in a Real Journal they have been forced to accept it!

http://www.sciphysicsforums.com/spfbb1/viewtopic.php?f=6&t=342#p8054

https://arxiv.org/abs/1806.02392