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arXiv:2506.02637

Proposed experiments for detecting contextual hidden variables

Konstantinos Papatryfonos, Louis Vervoort

Published Jun 3, 2025• 0 citations
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Abstract

We propose two quantum experiments - modified Bell tests - that could detect contextual hidden variables underlying quantum mechanics. The experiments are inspired by hydrodynamic pilot-wave systems that mimic a wide range of quantum effects and exhibit a classical analog of contextuality. To justify the experiments, we show that contextual hidden variables are 'physics as usual' if a unification between quantum mechanics and general relativity is possible. Accordingly, contextual theories can bypass Bell's theorem in a way that is both local and non-conspiratorial. We end with a note on the relevance of exploratory experiments in the foundations of quantum physics.

DOI
10.48550/arxiv.2506.02637

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We propose two quantum experiments - modified Bell tests - that could detect contextual hidden variables underlying quantum mechanics. The experiments are inspired by hydrodynamic pilot-wave systems that mimic a wide range of quantum effects and exhibit a classical analog of contextuality. To justify the experiments, we show that contextual hidden variables are 'physics as usual' if a unification between quantum mechanics and general relativity is possible. Accordingly, contextual theories can bypass Bell's theorem in a way that is both local and non-conspiratorial. We end with a note on the relevance of exploratory experiments in the foundations of quantum physics.
Abstract We propose two quantum experiments – modified Bell tests – that could detect contextual hidden variables underlying quantum mechanics. The experiments are inspired by hydrodynamic pilot-wave systems that mimic a wide range of quantum effects and exhibit a classical analog of contextuality. To justify the experiments, we show that contextual hidden variables are inevitable and ‘physics as usual’ if a unification between quantum mechanics and general relativity is possible. Accordingly, contextual theories can bypass Bell’s theorem in a way that is both local and non-conspiratorial. We end with a note on the relevance of exploratory experiments in the foundations of quantum physics.
Abstract Quantum theory has accounted for a wide range of physical effects in systems ranging from microscopic to macroscopic. However, it is associated with various paradoxes—such as the well-known EPR example. Einstein’s suggestion that the theory was incomplete has led to numerous attempts to underpin quantum theory by a hidden variable theory, including the Bell approach. This approach was originally based on certain assumptions: (i) realism (ii) locality and (iii) non-contextuality. In its developed form, the theory involved only probabilities for outcome values of system observables. For systems involving two sub-systems, the hidden variable theory predicted that correlations between measurement outcomes of observable pairs of from different sub-systems would satisfy certain—such as the CHSH Bell inequality. The inequality was inconsistent with quantum theory predictions and with experiment. Hence, the question arose: Which of the three assumptions was invalid? A widely held view is that a non-local theory is needed—another is that hidden variable theory should be contextual. In this article, derivations of the CHSH Bell inequality based on various combinations of locality/non-locality and non-contextuality/contextuality assumptions are outlined, leading to the conclusion that for a hidden variable theory to underpin quantum theory, it must be both non-local and contextual. Non-locality or contextuality alone is insufficient. However, it is also concluded that the realism assumption is questionable. At present an alternative approach of augmenting quantum theory by adding additional features—such as the deterministic trajectories of Bohmian mechanics (also a non-local theory) may be a better route for completeness.
The experimental violation of Bell's Theorem in quantum systems is generally taken as proof of the impossibility of local hidden variable theories, as would provide a rational dynamical underpinning for quantum mechanics. We here present a platform for executing Bell tests in pilot-wave hydrodynamics, a system known to capture many features of the quantum realm. We execute a static test in a bipartite tunneling system, and rationalize the emergent violations in terms of the wave-mediated coupling between the two subsystems.
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful theorems against the hidden-variable theories showing that certain quantum features cannot be reproduced based on two rationale premises of locality, Bell's theorem, and noncontextuality, due to Bell, Kochen and Specker (BKS). Noncontextuality is independent of nonlocality, and the contextuality manifests itself even in a single object. Here we report an experimental verification of quantum contextuality by a single spin-1 electron system at room temperature. Such a three-level system is indivisible and then we close the compatibility loophole which exists in the experiments performed on bipartite systems. Our results confirm the quantum contextuality to be the intrinsic property of single particles.
Bell’s inequality is an empirical constraint on theories with hidden variables, which Einstein, Podolsky and Rosen argued are needed to explain observed perfect correlations if keeping locality. One way to deal with the empirical violation of Bell’s inequality is by openly embracing nonlocality, in a theory like the pilot-wave theory. Nonetheless, recent proposals have revived the possibility that one can avoid nonlocality by resorting to superdeterministic theories. These are local hidden variables theories which violate statistical independence which is one assumption of Bell’s inequality. In this paper I compare and contrast these two hidden variable strategies: the pilot-wave theory and superdeterminism. I show that even if the former is nonlocal and the other is not, both are contextual. Nonetheless, in contrast with the pilot-wave theory, superdeterminist contextuality makes it impossible to test the theory (which therefore becomes unfalsifiable and unconfirmable) and renders the theory uninformative (measurement results tell us nothing about the system). It is questionable therefore whether a theory with these features is worth its costs.
We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and then analyse it's weakness in terms of Bell's explicit hidden variable model of spin one-half particles. We next discuss Gleason's theorem and Kochen-Specker theorem and bring out the troublems with non contextual hidden variable theories. An important role is played by Einstein locality in the discussion of hidden variable theories as was first brought out by Einstein, Podolsky and Rosen. We elaborate it's various implications such as Bell's theorem in terms of Bell's inequalities as well as later work in which Bell's theorem follows without using inequalities.