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

To Rococo: Your notes do not address the question and the model that is referred to in the article. To be sure we are talking about the same thing, the question is whether the article http://arxiv.org/abs/1406.0901 (published in Found. Phys. 2016) is correct in its main claim, namely that local hidden-variable models that include a background field are possible (and plausible) after all. This is important, since it goes against Bell’s theorem (as it is usually understood). Concerning your notes: 1. You say “What one could hope is that analysis of these droplet experiments leads to a plausible model for how this assumption [measurement independence] could be violated.” My answer: this is precisely what is what is proposed in the article, in a detailed way. If a background is present (e.g. one that has similar properties as the fluid’s pilot wave in the droplet experiments), the article shows that measurement independence and the Bell inequality can be violated. The arguments are pretty straightforward, so if you find a math error or an unphysical assumption, I would be much interested ! 2. You say: “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”. The topic of the article is not to argue that a Bell inequality can be violated in droplet experiments. The article concerns the admissibility of background-based hidden-variable theories for quantum mechanics. Only as a corollary, in a few lines, the article suggests that a Bell inequality can possibly be violated in a Bell-type experiment on droplets, because such systems contain a background (the surface or pilot wave on the fluid film). 3. You say: “one could in principle imagine some weird electrical surge that is just right to trick us. My personal feeling is that until I see a plausible physical model for such 'conspiracies,' I do not find them very interesting.” The goal of the article is to show that there is nothing weird to be assumed: just a background field (the physical vacuum, a zero-point field, a dark field,…). Note that that is all what quantum field theory is about. There is no conspiracy at all going on ! Really, your “personal feeling” is the standard opinion; but it is precisely what the article tries to counter, by a straightforward physical model. If you wish to help to assess the validity of the model, you would have to dig into it, and assess the validity of the physical assumptions and of the math.