Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2512.19051 · Physical Review A

The energy-speed relationship of quantum particles challenges Bohmian mechanics?

S. Di Matteo, C. Mazzoli

quant-phphysics.opticsSubmitted Dec 22, 2025• Announced Dec 23, 2025• 0 citations
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
arXivHTMLPDF

Abstract

Recently, Sharoglazova et al. claimed to have proven a violation of the basic tenet of Bohmian mechanics, namely the phase-speed relation $\vec{v}(\vec{r},t)=\frac{\hbar}{m}\vec{\nabla}S(\vec{r},t)$. Here, $S(\vec{r},t)$ is the (real) phase of the wave function $ψ(\vec{r},t)=ρ^{\frac{1}{2}}(\vec{r},t)e^{iS(\vec{r},t)}$. In a nutshell, they have measured the speed of a claimed evanescent wave, which is real and therefore must have $\vec{\nabla}S=\vec{0}$. However, Fig. 2 clearly shows a density motion from one waveguide to the other, implying a nonzero density current, $\vec{j}(\vec{r},t)=\frac{\hbar}{2mi}\Im(ψ^*\vec{\nabla}ψ)$. If we combine this evidence with the mathematical identity $\vec{\nabla}S=\frac{m}ρ\vec{j}$, we should instead conclude that $\vec{\nabla}S\neq\vec{0}$. So, where does this apparent inconsistency come from?

DOI
10.1103/7swm-z666

Related papers

Is Bohmian mechanics missing some motion? Why a recent experiment is inconclusive

Mordecai Waegell

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 $ψ= Re^{iS/\hbar}$, the velocity of interest, $\vec{v}_s = -\frac{\hbar}{m}\frac{\vec{\nabla}R}{R}$, is different from the Bohm velocity $\vec{v}_B=\frac{1}{m}\vec{\nabla}S$, 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 $\vec{v}_s$ 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.

quant-pharXiv:2511.17215•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Nov 24, 2025•2 citations

Apparent energy-speed relationship poses no challenge to Bohmian mechanics

Matthew Dickau

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.

arXiv:2507.18826•Jul 24, 2025•0 citations

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

Mikołaj Sienicki, Krzysztof Sienicki

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.

arXiv:2507.10989•Jul 15, 2025•0 citations

The measured speed in the evanescent regime reflects the spatial decay of the wavefunction, not particle motion

Weixiang Ye

The recent paper by Sharoglazova et al. reports an energy-dependent parameter $ν$ extracted from the spatial distribution of photons in a coupled-waveguide experiment. The authors interpret $ν$ 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.

quant-pharXiv:2512.16580•Dec 19, 2025•0 citations

On the Supposed Surrealism of Bohmian Mechanics

Lon Becker

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.

Zeitschrift für Naturforschung A•Jul 1, 1997•3 citations

Reaffirming a Challenge to Bohmian Mechanics

Jan Klaers, Violetta Sharoglazova, Marius Puplauskis

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.

quant-pharXiv:2509.06584•Sep 9, 2025•0 citations
Recently, Sharoglazova et al. claimed to have proven a violation of the basic tenet of Bohmian mechanics, namely the phase-speed 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, S(r⃗,t)S(\vec{r},t)S(r,t) is the (real) phase of the wave function ψ(r⃗,t)=ρ12(r⃗,t)eiS(r⃗,t)ψ(\vec{r},t)=ρ^{\frac{1}{2}}(\vec{r},t)e^{iS(\vec{r},t)}ψ(r,t)=ρ21​(r,t)eiS(r,t). In a nutshell, they have measured the speed of a claimed evanescent wave, which is real and therefore must have ∇⃗S=0⃗\vec{\nabla}S=\vec{0}∇S=0. However, Fig. 2 clearly shows a density motion from one waveguide to the other, implying a nonzero density current, j⃗(r⃗,t)=ℏ2miℑ(ψ∗∇⃗ψ)\vec{j}(\vec{r},t)=\frac{\hbar}{2mi}\Im(ψ^*\vec{\nabla}ψ)j​(r,t)=2miℏ​ℑ(ψ∗∇ψ). If we combine this evidence with the mathematical identity ∇⃗S=mρj⃗\vec{\nabla}S=\frac{m}ρ\vec{j}∇S=ρm​j​, we should instead conclude that ∇⃗S≠0⃗\vec{\nabla}S\neq\vec{0}∇S=0. So, where does this apparent inconsistency come from?
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.