Recently it was shown that certain fluid-mechanical 'pilot-wave' systems can strikingly mimic a range of quantum properties, including single particle diffraction and interference, quantization of angular momentum etc. How far does this analogy go? The ultimate test of (apparent) quantumness of such systems is a Bell-test. Here the premises of the Bell inequality are re-investigated for particles accompanied by a pilot-wave, or more generally by a resonant 'background' field. We find that two of these premises, namely outcome independence and measurement independence, may not be generally valid when such a background is present. Under this assumption the Bell inequality is possibly (but not necessarily) violated. A class of hydrodynamic Bell experiments is proposed that could test this claim. Such a Bell test on fluid systems could provide a wealth of new insights on the different loopholes for Bell's theorem. Finally, it is shown that certain properties of background-based theories can be illustrated in Ising spinlattices.
Introduction.Since the birth of quantum mechanics, physicists have been intrigued by its counterintuitive features, such as the collapse of the wave function, the uncertainty relations, wave-particle duality, the probabilistic nature of the theory, etc. Many attempts have been made to restore a more classic character to quantum mechanics, notably by efforts aiming at deriving the theory from a more fundamental, deeper-lying theorymaybe even a deterministic one. Such a hidden-variable theory (HVT) would contain yet unknown variables which, once integrated-out, yield quantum theory.This would after all be a familiar situation in physics: quantum mechanics would have the status of an 'effective' theory, as other theories. But this quest for sub-quantum theories, initiated by such giants as Einstein, de Broglie, Schrödinger etc., has been restrained, not only by the unprecedented precision and efficiency of quantum theory, but also by certain abstract mathematical results that seem to prove the impossibility of constructing any reasonable HVT. These are the so-called 'nogo' theorems, among which Bell's theorem [1-3] but also the Kochen-Specker theorem [4] are best known. What I call 'Bell's theorem' (as a physical, and not just mathematical, theorem) states, in short, that 'local hidden-variable theories are impossible'. It is essential here to be clear about what