At the beginning of this month, New Scientist’s cover story detailed the work of Oxford physicist Joy Christian. He recently released a paper on quant-ph (apparently its a cheap copy of of astro-ph) with the provocative title:
Disproof of Bell’s Theorem by Clifford Algebra Valued Local Variables.
Here’s the idea. Quantum mechanics doesn’t predict deterministic quantities – it only gives the probability of measuring various outcomes. If quantum mechanics is the final word in microscopic physics, then it suggests that, at its most fundamental, the universe is really quite weird – it has a ghostly, fuzzy existence, only making up its mind when observed.
But what if quantum mechanics is just an approximation to a better theory? What if the reason that quantum mechanics only gives us probabilities is that it is ignoring hidden variables?
Enter Bell’s theorem, which states that “no physical theory which is realistic as well as local in a specified sense can reproduce all of the statistical predictions of quantum mechanics.” Roughly, realistic means that reality exists independently of being observed; local means that no physical influence can travel faster than the speed of light. In other words, we either get spooky particles that pop into existence when they are observed, or we mess with causality via ‘spooky action at a distance’, as Einstein said.
Enter Christian. He claims that Bell’s reasoning is correct, but relies on an unjustified assumption. Bell assumed that the hidden variables would commute under multiplication: like ordinary numbers, a x b = b x a. Christian claims that if we instead consider non-commutative variables then Bell’s theorem fails. Such variables are provided by Clifford algebras. (Consult Wikipedia and references therein. I know practically nothing about Clifford algebras, other than that they are particularly useful for dealing with rotations).
There have been critics, replies and further work so the debate is not over. This is either the first step in a major revision and extension of quantum mechanics, or the mathematical equivalent of cold fusion. The whole thing thing almost makes me want to go learn Clifford algebras.
Almost.
Letters to Nature 
I don’t know what a Clifford Algebra is, but it’s one of those topics that seems to have a small but very enthusiastic following.
As for quantum mechanics, it’s been known to all sane people that the spookiness will one day be resolved as soon as QM is superseded or explained by some more fundamental theory. I think it may happen when we understand the meaning of the probabilities in the theory. I find Chris Fuchs’ writings on these topics promising.
Joy Christian is perhaps as correct as ambitious. However, do we really need non-commutative variables as to understand Buridan’s ass? I rather prefer Salviati’s (Galileo Galilei’s) reasoning concerning infinite quantities and the admission that continuous and discrete models complement each other.
I vote for |sign(0)|=1 at least in physics.
Schroedinger’s cat gave rise to quantum entanglement and computing. How does Joy Christian judge the chance to ultimately succeed with them?
I’m not sure what the quantum community has decided over Joy Christian …
As to be expected, most of the audience of recent Azores conference stood by Bell. However, they could neither refute Joy’s reasoning nor did they manage providing a quantum computer that works as promised.
Incidentally, read some essays and discussions at fqxi in order to get aware of substantiated fresh ideas, for instance by Alan Schwartz.