Bell's theorem and fluid-mechanical experiments using droplets: are local hidden-variable theories possible after all?

Question

Recent fluid-mechanical experiments by the groups of Couder in Paris and Bush at MIT, mimic a surprisingly wide range of quantum effects. The essential ingredient of these fluid-mechanical systems is a background or pilot-wave that guides the droplets.

Now, surprisingly, a simple analysis of a Bell-type experiment shows that, in the presence of a background field, one of the premises of the Bell inequality, namely measurement independence (MI), is violated. See the paper "No-Go Theorems Face Background-Based Theories for Quantum Mechanics" (available on arxiv). Therefore such classical droplet experiments could violate a Bell inequality. More importantly, if this analysis is correct, background-based hidden-variable theories are admissible, even if they are local (in the sense of ‘involving only (sub)luminal interactions’) and even if they are compatible with free will.

My question: to me the analysis seems fully sound, but maybe there is still an unphysical hypothesis that slipped in ?

Answer 1

For the sake of argument, I will assume that all of the calculations of the authors are correct- I don't see any obvious reason that they cannot be.

A few notes:

1. As the authors note, the measurements independence criterion of the Bell Inequality is a well-known assumption. So pointing it out, by itself, is not an interesting contribution. What one could hope is that analysis of these droplet experiments leads to a plausible model for how this assumption could be violated.

2. The authors show that suitable background correllations could in principle lead to a Bell violation in a droplet experiment, but they do not specify what observable would actually exhibit these correllations. It is presumably the case that such an observable would have to be 'fine-tuned,' in the sense that you would have to work to figure out how to make a measurement that is suitably affected by the background. There is a good reason they do not propose a specific way of doing this- they do not know one, and it may well be that any suitable observable would be too complex a measurement to be practical.

3. In general, their model predicts significant deviations from quantum mechanics. As they note, they predict a Bell violation that depends on how fast one chooses the measurements, and as I mentioned it should depend on the observable chosen as well. Of course, one could imagine that we have picked just the wrong frequency range and observables in all of our Bell experiments to see this disagreement.

4. In a recent claim of a loophole free Bell test, the random choice of measurement comes from both physical processes that are believed to be random, and also from streams of bits that are derived from things like files of various movies and television shows. So a model of Bell's inequality that violated background independence in this case would have to plausibly explain how all these things could be correlated, or how there could be some exploitable glitch in how these random bits are actually implemented as measurement settings. Needless to say, I have not seen such a model yet.

Answer 2

In 2022 they (K Papatryfonos, L Vervoort, A Nachbin, M Labousse, JWM Bush) made experiment claiming CHSH violation: https://arxiv.org/pdf/2208.08940 - using pair of droplets, each being able to choose one of two cavities:

Answer 3

This paper is wrong at the most basic level, without needing to go into the details that Rococo's answer does.

Bell's assumptions were very general: his argument only needs the measurement outcomes to be $A(\mathbf a, λ)$ and $B(\mathbf b, λ)$ where $\mathbf a$ and $\mathbf b$ are the chosen measurement angles, $λ$ is an arbitrary collection of hidden variables, and $A$ and $B$ are arbitrary functions. You may in particular take $λ$ to be a pilot wave or background field or something of that sort. The idea that quantum behavior might be explained by a pilot wave was as old as quantum mechanics, and ruling out models of that sort was the main aim of Bell's paper, as far as I know.

Vervoort suggests in his abstract that Bell (and apparently everyone else since 1964) overlooked the possibility of what he calls "local background-based" theories. I have no idea what he thinks Bell's paper is about.

His argument that measurement independence is violated in background-based theories (section 3) is simply that there is bidirectional interaction between $\mathbf a$ and the background which causes them to become correlated. This argument would demolish Bell's argument in complete generality if it worked. It makes no assumptions related to fluid droplets or the experiments of Couder et al, so I'm not sure why he mentioned those. The problem with the argument is that Bell's $\mathbf a$ is the measurement that the experimenter chooses and writes down in their log book, not the measurement that actually happens. If the background messes with the measurement device and changes the angle before the actual measurement takes place, you can encode that interaction into the definition of $A$, and nothing about Bell's argument changes.