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Recently it was shown that certain fluid-mechanical 'pilot-wave' systems canstrikingly mimic a range of quantum properties, including single particlediffraction and interference, quantization of angular momentum etc. How fardoes this analogy go? The ultimate test of (apparent) quantumness of suchsystems is a Bell-test. Here the premises of the Bell inequality arere-investigated for particles accompanied by a pilot-wave, or more generally bya resonant 'background' field. We find that two of these premises, namelyoutcome independence and measurement independence, may not be generally validwhen such a background is present. Under this assumption the Bell inequality ispossibly (but not necessarily) violated. A class of hydrodynamic Bellexperiments is proposed that could test this claim. Such a Bell test on fluidsystems could provide a wealth of new insights on the different loopholes forBell's theorem. Finally, it is shown that certain properties ofbackground-based theories can be illustrated in Ising spin-lattices.

Are Hidden-Variable Theories for Pilot-Wave Systems Possible ?