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:
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.