Today we’ve published a paper showing that Bell’s inequality is violated in fluid mechanics. What has this to do with computing or security? Well, when we posted a paper back in February pointing out that hydrodynamic models of quantum physics raise questions about the scalability of quantum computing, a number of people asked for a better explanation of how this squares with the Bell tests. John Bell proved an inequality in 1964 that applies to classical particles but that is broken by quantum mechanical ones. In today’s paper we show that Bell’s inequality does not hold in classical fluid dynamics, as angular momentum and energy are delocalised in the fluid.

This may have implications for engineering, science and philosophy. On the engineering front, nine-figure sums have been poured into developing quantum computers, but even advocates of quantum computing admit they don’t really work. As our February paper argued, a hydrodynamic interpretation of quantum mechanics may suggest reasons why.

On the scientific front, the Bell tests are commonly seen as excluding not just local hidden-variable models of quantum mechanics, but local realism too. Our paper shows that the two are distinct, and thus leaves more room for research on quantum foundations. It also shows that we should be more careful in our use of terms such as ‘local’ – which might be of interest to the philosophers; the Bell tests do not draw quite as clear a dividing line between the quantum and classical worlds as many have believed.

Very funny.

You’re saying a classical fluid is ‘non-local’.

Do you understand what non-local means?

Have you an experimental proposal demonstrating this ability of classical fluids to violate Bell inequalities (a la Clauser, Aspect, Zeilinger et al)?

@James: my understanding was that you need both local realism *and* relativistic causality for Bell’s Inequality to hold. In a classical fluid, there’s no relativistic causality, so a violation of Bell’s Inequality should be possible.

e.g., http://www.nature.com/nphys/journal/v8/n12/full/nphys2460.html

(I haven’t read either paper yet, mind you!)

@Harry

That paper http://arxiv.org/abs/1110.3795 shows that quantum correlations can’t be explained by any type of finite speed influence operating faster than the speed-of-light (non-local) – unlessyou also allow superluminal signalling.

I don’t thnk classical fluids are capable of infinite speed influences – so the paper only helps to demolish such ideas.

@James: well, it depends what you mean, I suppose; I interpreted “classical” in this context to mean both non-quantum and non-relativistic. In a non-relativistic fluid, a change at any one point should (I think) immediately cause a small but non-zero effect at any arbitrary distance.

@Harry

No, I don’t see how that’s possible unless you have a non-classical model of the fluid dynamics.

But to save arguing over terminology, just suggest an experiment that would give Bell violations in a classical fluid.

I’m afraid I have neither the expertise or the time necessary for that. But as the simplest possible case, consider a non-compressible fluid in a rigid pipe, with pistons at each end. Push one piston and the other one will move instantly.

I should have mentioned, of course, that if the fluid in Ross’s paper is indeed non-relativistic, that may compromise drawing any conclusions about quantum mechanics, which is of course relativistic.

Thanks for all the comments. The experimental results from Couder, Fort and colleagues show double slit diffraction, tunneling and quantised orbits in a classical fluid system. The measurements show the motion is approximately Lorentz covariant with the speed of sound in place of light. Fluid mechanics are intrinsically “relativistic”.

As for whether the Bell tests demonstrate non-locality, they actually demonstrate non-separability: quantum systems do not obey Einstein’s Trennungsprinzip, but then neither do fluid dynamical systems either (see Don Howard on this). As for how the mechanisms we describe apply to photons, there are two papers by David Ferry which raise some interesting questions.

You might care to note, in addition to this, that our paper explains how spin-half behaviour can come about in a fully classical system. That’s another nail in the coffin of quantum exceptionalism! For almost ninety years now, the priests of the quantum church have held this out as one phenomenon that simply cannot have any classical basis. Well, they were wrong.

Spin was shown to be a non-relativistic property over 40 years ago by Levy-Leblond, you just need to assume a multi-component wave-function.

But really, to be taken seriously you need to propose an experiment where Bell Inequality violations can be demonstrated by a classical fluid – as per the title of your paper.

Our results have been extended from the Bell theorem to the Kochen-Specker theorem in some interesting recent work by Louis Vervoort