The oil bath experiments of Couder and Fort have been able to reproduce various "pilot wave like" quantum behavior on a macroscopic scale. Particularly striking is the fact that the double-slit interference behavior could be reproduced. Immediately one wonders about the possibility of realizing entanglement phenomena using these oil bath experiments. The article linked to above contains a quote that it is impossible to realize entanglement phenomena in this sort of experiment because a higher dimensional system would be needed to exhibit these phenomena.
Question: Is it theoretically impossible to realize entanglement-like phenomena (e.g. non-local behavior or violation of some sort of Bell inequality) using a Couder-Fort experiment? What are the details of this impossibility claim?
Note that a recent paper further reinforces the claim that the oil bath experiments are closely analogous to quantum mechanics. Violation of Bell inequalities does not appear in this paper, though.
EDIT: To clear up any misunderstanding, I am trying hard here not to make the ridiculous claim that a classical system should violate the Bell inequalities. I am aware that looking at the phase space of a classical system as an underlying space we can only get classical correlations and these must obey the Bell inequalities. I suppose the sharper question I should ask is the following:
Refined Question: Where does the mathematical analogy between the DeBroglie-Bohm pilot wave theory and the mathematical model of the oil bath experiment break down?
If the analogy is perfect, then we should be able to interpret the oil bath experiment mathematically as a non-local hidden variable theory. Such a theory should violate some sort of analogue of Bell's theorem, shouldn't it? The original Bell inequality was perfectly equivalent to an inequality in classical probability, and so I don't see how this is exclusively tied to the dimension of the phase space.
Best Answer
I think that 't Hooft's ideas about superdeterminism and Bell's theorem are relevant to this topic. If the universe is superdeterministic so that all experiments are determined by initial conditions, then the contra-factual arguments that lead to the Bell non-locality conclusions are ruled out. The universe only plays once - is how some have put this. In the early days, this was called "conspiracy against the experimenter", and it was categorically excluded from the discussions. It still remains the biggest loophole, and I don't think it can ever be eliminated. But it means that strict free will doesn't exist. The fact is that both Alice and Bob consist of a finite number of atoms each, and are certainly quantum mechanical systems themselves. Consider the bouncing drop experiments. It's surely a deterministic classical system to a high degree of accuracy. To mimic quantum mechanics, we must not only have bouncing drops that are entangled, we must also have measuring apparatus and observers which consist only of bouncing drops. We are super-observers of the drop motions, but we are not built up of bouncing drops. We are allowed to measure the drops without disturbing them, but "embedded observers" made up entirely of bouncing drops may not be able to measure things as finely as we can. To those embedded observers, the universe of the bouncing drops might appear as undeniably entangled. So there is hope for the bouncing drops as an example of 't Hooft's superdeterministic realization of quantum mechanics as an emergent phenomena. I have no idea whether the classical lagranians for the bouncing drops will allow this behavior, but I see it as the only hope for a description of entanglement in this classical framework.