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arXiv:2507.10989

Critical Reflections on Overcoming a Challenge for Bohmian Mechanics by H. Nikolic and the Experimental Findings of Sharoglazova et al

Mikołaj Sienicki, Krzysztof Sienicki

Published Jul 15, 2025• 0 citations
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Abstract

This paper offers a brief reflection on H. Nikolic's response to the experimental findings of Sharoglazova et al., which challenge Bohmian mechanics. While Nikolic's revision satisfies the continuity equation, it reintroduces assumptions he seeks to avoid and overlooks key empirical and nonlocal aspects of the system. These issues underscore unresolved tensions in applying Bohmian mechanics to complex, interacting regimes.

DOI
10.48550/arxiv.2507.10989

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This paper offers a brief reflection on H. Nikolic's response to the experimental findings of Sharoglazova et al., which challenge Bohmian mechanics. While Nikolic's revision satisfies the continuity equation, it reintroduces assumptions he seeks to avoid and overlooks key empirical and nonlocal aspects of the system. These issues underscore unresolved tensions in applying Bohmian mechanics to complex, interacting regimes.
We reanalyze a recent experiment by Sharoglazova et al. [Nature (London) 643, 67 (2025)] highlighting the role of the transient regime. We prove that in the evanescent state of the stationary regime their experimental data can be interpreted in terms of Bohmian quantum mechanics. At the same time, Bohm's quantum potential can be reinterpreted as a kinetic-energy term in the framework of Nelson's stochastic quantum mechanics, with a hidden-variable, nonclassical speed fitting the experimental data as well. The experiment can be interpreted as well within orthodox quantum mechanics and is therefore not conclusive in selecting or challenging any framework.
Recently, Sharoglazova et al. [Nature 643, 67 (2025)] proposed a procedure for determining the speed of a quantum particle in the classically forbidden region of a potential step, and implemented it in a beautiful experiment. The inferred speeds disagree significantly with the Bohmian velocities, which the authors presented as an experimental challenge to Bohmian mechanics. This is puzzling because the speeds are inferred from particle populations in coupled waveguides for which Bohmian mechanics and standard quantum mechanics make identical predictions. We resolve the puzzle by a detailed theoretical analysis of the experimental setup. We show that the speed inference rests on an assumption that fails in the relevant (evanescent) regime according to both Bohmian mechanics and standard quantum mechanics -- namely that the inter-waveguide tunneling time is set by the transverse coupling and is not affected by entanglement with the longitudinal degree of freedom. We also consider a second speed estimate suggested by Sharoglazova et al., which is based on the Büttiker dwell time formula for particles in the forbidden region. We show that the authors applied the formula incorrectly, and that a correct application yields exact agreement with the predictions of Bohmian mechanics. Our analysis includes explicit calculations of Bohmian trajectories, dwell times, and longitudinal speeds in the two-dimensional waveguide model of the experiment.
The recent paper by Sharoglazova et al. reports an energy-dependent parameter ννν extracted from the spatial distribution of photons in a coupled-waveguide experiment. The authors interpret ννν as the speed of quantum particles, even in the classically forbidden regime, and claim that its finite value contradicts the Bohmian mechanics prediction of zero particle velocity. This challenge arises from a fundamental misunderstanding of the operational meaning of v within the Bohmian ontological framework. We demonstrate that v quantifies the spatial gradient of the wavefunctions amplitude, a geometric property of the guiding field, not the kinematical velocity of point-like particles. The experiment therefore does not challenge but rather illustrates the clean ontological separation between the wave and particle aspects inherent to Bohmian mechanics.
In our work [Sharoglazova et al., Nature 643, 67-72 (2025)], we reported the first measurement of the speed of tunnelling particles by comparing two orthogonal motions in a coupled-waveguide system. Here we respond to objections raised in comments, referee reports, preprints, and articles. In particular, we distinguish two questions that are often conflated: whether Bohmian mechanics reproduces the measured density, and whether the standard guiding equation assigns the correct state of motion to the particles. The first point follows under the usual quantum equilibrium assumptions. By contrast, identifying the guiding velocity with particle motion is an additional physical postulate, since the standard guiding equation does not follow from the Schrödinger equation alone. We argue that, in the evanescent regime, the state of motion assigned by the standard guiding equation is in disagreement with the speed following from our experiments. To make the distinction explicit, we also present a bidirectional Bohmian model that reproduces the same stationary density while assigning finite speeds compatible with the speed inferred in the evanescent regime.