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.
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