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

TL;DR

This paper investigates whether hidden-variable theories in pilot-wave systems can violate Bell inequalities, suggesting that background fields may lead to such violations and proposing experiments to test this possibility.

Contribution

It re-examines Bell test premises in pilot-wave systems with background fields and proposes hydrodynamic experiments to explore potential violations.

Findings

Outcome independence and measurement independence may not hold with background fields.

Bell inequalities could be violated in fluid-based pilot-wave systems.

Hydrodynamic Bell experiments can shed light on quantum loopholes.

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.