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

Abstract

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 spin-lattices.

This version emphasizes the importance of performing the proposed hydrodynamic Bell test. Compared to the first version it phrases things more precisely, notably the assumptions that are made in the model. Also, a few more insights were gained through discussions with experts. The main conclusions remain the same

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Cited by in corpus (8)

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• A Family of Local Deterministic Models for Singlet Quantum State Correlations
• Observations of Bell Inequality Violations with causal isolation between source and detectors
• Violation of Bell Inequalities: Mapping the Conceptual Implications