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 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

Understanding quantum mechanics: a review and synthesis in precise language

“…Bell experiment results are often claimed to constrain how quantum mechanics can be understood. Many such claims appear, however, to be inappropriate, given the lack of consensus (outlined above) on the theoretical aspects of the inequalities [132,166,338,[367][368][369].…”

Probability Theory as a Physical Theory Points to Superdeterminism

“…Still, it may make sense to perform experiments on well-chosen macroscopic systems to verify this claim. In [ 36 ] it is argued that fluid-mechanical pilot-wave systems are interesting candidates to answer Q2 or Q3 experimentally; they consist of oil droplets resonantly interacting with a surface wave. These fluid systems, with a “wave-particle” nature, have an intriguing capacity to mimic quantum properties [ 37 , 38 , 39 , 40 ].…”

Simulation of Bell Correlations in Walker Systems

“…We use as starting point a scheme recently suggested by Vervoort [3]. Conceptually, we have a source in the center (the black box of figure 1) emitting anti-correlated walkers, one propagating to the left and the other to the right.…”

“…We speak about the force imparted by the wake on the walker, a force proportional to the gradient at the point of impact. The wake results from waves emitted by the walkers as well as the measurement apparatus as modeled by Vervoort [3] with static and dynamical pins. The walkers also feel a viscous force, following a hydrodynamic treatment [1].…”

“…Vervoort [3]. It states that the measure in one arm cannot influence the walker in other arm, we have separability of the walker in one arm to the pin in the other.…”