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arXiv:2512.19051 · Physical Review A

Critical re-examination of a claimed challenge of Bohmian mechanics

S. Di Matteo, C. Mazzoli

quant-phphysics.opticsSubmitted Dec 22, 2025• Announced Dec 23, 2025• 0 citations• Revised Feb 3, 2026 (v3)
v1 · Dec 22, 2025v2 · Dec 28, 2025v3 · Feb 3, 2026v4 · Mar 7, 2026v5 · Apr 6, 2026v6 · Jul 23, 2026v7 · Aug 17, 2026v8 · Oct 5, 2026
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Abstract

A recent experiment by Sharoglazova {\it et al.} was interpreted by the authors as a challenge to the basic idea of Bohmian mechanics, the phase-velocity relation $\vec{v}(\vec{r},t)=\frac{\hbar}{m}\vec{\nabla}S(\vec{r},t)$. Here, we reinterpret their experiment, highlighting the role of the transient regime before the onset of the stationary state. In this way, we show that the experimental data can naturally fit the Bohmian framework when the energy in the evanescent regime is identified with the quantum potential. It is, however, also possible to interpret the same energy as a kinetic energy, in the framework of Nelson's stochastic quantum mechanics. In conclusion, far from challenging the Bohmian mechanics, we find that the experimental results of Sharoglazova {\it et al.} can be interpreted in either ontologies and are therefore not conclusive in selecting one or the other.

DOI
10.1103/7swm-z666

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A recent experiment by Sharoglazova {\it et al.} was interpreted by the authors as a challenge to the basic idea of Bohmian mechanics, the phase-velocity relation v⃗(r⃗,t)=ℏm∇⃗S(r⃗,t)\vec{v}(\vec{r},t)=\frac{\hbar}{m}\vec{\nabla}S(\vec{r},t)v(r,t)=mℏ​∇S(r,t). Here, we reinterpret their experiment, highlighting the role of the transient regime before the onset of the stationary state. In this way, we show that the experimental data can naturally fit the Bohmian framework when the energy in the evanescent regime is identified with the quantum potential. It is, however, also possible to interpret the same energy as a kinetic energy, in the framework of Nelson's stochastic quantum mechanics. In conclusion, far from challenging the Bohmian mechanics, we find that the experimental results of Sharoglazova {\it et al.} can be interpreted in either ontologies and are therefore not conclusive in selecting one or the other.
A recent experiment raises a supposed challenge to Bohmian mechanics, claiming to observe stationary states, which should have zero Bohm velocity, while indirectly measuring a nonzero speed based on how an evanescent wavefunction spreads from one waveguide to another coupled waveguide. There were numerous problems with this experiment and how it was interpreted. First, the experiment is not observing stationary states as claimed, but rather the time-averaged density of wave pulses which reflect off the potential step. Second, the proposed method for measuring a propagation speed is shown to be invalid for true stationary states. Third, the invalid method was misapplied to the time-averaged density, and this is shown to have created the false impression that it yields correct speed values for stationary states. These issues notwithstanding, for a wavefunction ψ=ReiS/ℏψ= Re^{iS/\hbar}ψ=ReiS/ℏ, the velocity of interest, v⃗s=−ℏm∇⃗RR\vec{v}_s = -\frac{\hbar}{m}\frac{\vec{\nabla}R}{R}vs​=−mℏ​R∇R​, is different from the Bohm velocity v⃗B=1m∇⃗S\vec{v}_B=\frac{1}{m}\vec{\nabla}SvB​=m1​∇S, and may be nonzero for stationary states. This quantity has been called the \textit{symmetric} or \textit{osmotic} velocity, and while it emerges naturally as an imaginary component of the velocity in the derivation of the Madelung/Bohm description, it is usually disregarded. So, even though we do not think this experiment makes a compelling case for it, if v⃗s\vec{v}_svs​ is somehow associated with real physical motion, then this motion is indeed absent from Bohmian mechanics, as the authors contend. We discuss a generalized Madelung fluid model where this velocity is given physical meaning, and show how it roughly agrees with the authors' concept of an evanescent De Broglie speed.
A recent article claims to measure the speed of quantum particles in the classically forbidden regime where the energy of the particles is lower than the local potential, and further claims that the results of this experiment challenge Bohmian mechanics. But this interpretation of the experiment is incorrect (and dubious even in the context of ordinary quantum mechanics). A proper analysis of the system from a pilot-wave perspective shows that it predicts the same distribution of particle positions (and so the same experimental results) as ordinary quantum theory. The speed measured by the experiment in this regime is fictitious.
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.
Abstract In a recent paper, Englert et al. reject Bohm's reinterpretation of quantum mechanics as "surrealistic." Responses to this by Dewdney et al. and Durr et al. have generally missed the point of this somewhat strange characterization of the interpretation. In this paper I explain the experiment which is supposed to illustrate the surrealism. I argue that what is really being objected to is the non-locality of the interpretation. While this is an undesirable feature of Bohm's interpretation, it is not a feature of which the standard interpretation gives a more satisfactory account.
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.