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arxiv: 2512.19051 · v5 · submitted 2025-12-22 · 🪐 quant-ph · physics.optics

Critical re-examination of a recent challenge to Bohmian mechanics

S. Di Matteo , C. Mazzoli This is my paper

Pith reviewed 2026-05-16 20:58 UTC · model grok-4.3

classification 🪐 quant-ph physics.optics
keywords Bohmian mechanicsNelson's stochastic mechanicsquantum potentialevanescent statesstationary regimehidden variablesorthodox quantum mechanicsquantum trajectories
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The pith

The data from a recent experiment can be explained within Bohmian mechanics in the stationary regime.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper re-examines an experiment previously presented as a challenge to Bohmian mechanics. It shows that once the analysis focuses on the evanescent states reached in the stationary regime, the measured results match the trajectories and speeds predicted by Bohmian mechanics. The same data can be recast by treating Bohm's quantum potential as a kinetic-energy contribution inside Nelson's stochastic mechanics, where a non-classical hidden speed also reproduces the observations. Because the results remain compatible with standard quantum mechanics, the experiment fails to rule out any of the three frameworks.

Core claim

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 re-interpreted as a kinetic-energy term in the framework of Nelson's stochastic quantum mechanics, with a hidden-variable, non-classical, 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.

What carries the argument

Re-interpretation of the measured trajectories and speeds in the evanescent stationary regime, which permits both Bohmian guidance and a stochastic kinetic-energy term to match the same data.

If this is right

  • The experimental results remain consistent with Bohmian mechanics once transients are excluded.
  • Bohm's quantum potential functions as a kinetic-energy term in a stochastic hidden-variable model that fits the observed speeds.
  • The same dataset is compatible with orthodox quantum mechanics, so no interpretation is singled out.
  • Claims that the experiment challenges any particular quantum framework require explicit separation of transient and stationary contributions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future tests of hidden-variable models will need direct verification that the stationary regime has been reached before claiming decisive evidence.
  • The shown equivalence between deterministic and stochastic reinterpretations indicates that speed or trajectory data alone may not separate these classes of alternatives.
  • Similar re-analyses of other claimed refutations could reveal that transient effects have been under-accounted for across several quantum-interpretation experiments.

Load-bearing premise

The assumption that the experiment has reached a true stationary regime in which evanescent states dominate the signal, allowing the data to be reinterpreted without additional transient effects or unaccounted systematics.

What would settle it

A measurement isolating the stationary regime that shows trajectories or speeds inconsistent with both the Bohmian guidance equation and the non-classical speed required by the stochastic reinterpretation.

Figures

Figures reproduced from arXiv: 2512.19051 by C. Mazzoli, S. Di Matteo.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic view of the experimental setup of [1]. The [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: The two waveguides are centered at y = a (w1) and at y = −a (w2). In correspondance to the doubling of the waveguide, for x ≥ 0, a potential step V0 is also added to both w1 and w2. This experimen￾tal setup can be modeled by the Schr¨odinger equation iℏ∂tψ(x, y, t) = Hˆ (x, y)ψ(x, y, t) with the following time￾independent Hamiltonian in the x and y directions: Hˆ (x, y) = − ℏ 2 2m  ∂ 2 ∂ 2 x + ∂ 2 ∂ 2 y … view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. [Left] Comparison of the energy levels in our notation [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The stationary experimental data (red circles) of [1] [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We re-analyze a recent experiment by Sharoglazova et al. 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 re-interpreted as a kinetic-energy term in the framework of Nelson's stochastic quantum mechanics, with a hidden-variable, non-classical, 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 1 minor

Summary. The manuscript re-analyzes the experiment by Sharoglazova et al. that was presented as challenging Bohmian mechanics. It claims to prove that the data in the evanescent state of the stationary regime admits an interpretation in terms of Bohmian trajectories. The authors further re-interpret Bohm's quantum potential as a kinetic-energy term in Nelson's stochastic quantum mechanics, where a non-classical hidden-variable speed is adjusted to fit the reported signal. They conclude that the same data remains consistent with orthodox quantum mechanics, rendering the experiment inconclusive for selecting among these frameworks.

Significance. If the stationary-regime assumption is independently validated and the trajectory derivations are supplied, the paper would usefully illustrate that the experiment does not discriminate between Bohmian, Nelsonian, and standard interpretations. It correctly stresses the distinction between transient and stationary contributions. The work is constructive in showing interpretive flexibility, but the current gaps in explicit calculations and regime diagnostics limit its immediate value to the foundations literature.

major comments (3)
  1. Abstract: the assertion that the data 'can be interpreted in terms of Bohmian quantum mechanics' in the evanescent state of the stationary regime is presented as a proof, yet no trajectory equations, boundary conditions, or quantitative comparison to the measured signal are supplied; this derivation gap is load-bearing for the central claim that the original challenge is neutralized.
  2. Nelson's stochastic mechanics re-interpretation: the hidden-variable non-classical speed is explicitly fitted to the experimental data, which reduces the claimed reinterpretation to a post-hoc parameter adjustment rather than an independent consistency check; this directly undermines the assertion of a parameter-free or predictive re-derivation.
  3. Stationary-regime analysis: the manuscript assumes that evanescent states dominate the signal once transients are set aside, but provides no independent diagnostic (time-resolved decay, comparison to a transient-inclusive model, or exclusion criteria) to confirm that residual non-stationary contributions are negligible in the measurement window; if even modest transients remain, both the Bohmian trajectories and the fitted speed become artifacts.
minor comments (1)
  1. The introduction should include a concise, self-contained description of the Sharoglazova et al. experimental setup (physical system, measurement technique, and reported observable) so that readers need not consult the original work to follow the re-analysis.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments correctly identify areas where the manuscript would benefit from greater explicitness. We address each major point below and will incorporate revisions to strengthen the presentation of our re-analysis.

read point-by-point responses

  1. Referee: Abstract: the assertion that the data 'can be interpreted in terms of Bohmian quantum mechanics' in the evanescent state of the stationary regime is presented as a proof, yet no trajectory equations, boundary conditions, or quantitative comparison to the measured signal are supplied; this derivation gap is load-bearing for the central claim that the original challenge is neutralized.

    Authors: We accept that the abstract's phrasing ('we prove') is stronger than the level of explicit derivation supplied in the current text. The re-interpretation rests on applying the standard Bohmian guidance equation to the stationary evanescent wave function obtained from the Schrödinger equation with the appropriate boundary conditions at the barrier. To address the gap, the revised manuscript will include the explicit trajectory equations, the initial conditions used for integration, and a quantitative comparison (e.g., a plot of predicted versus measured signal features) between the resulting Bohmian arrival-time distribution and the experimental data reported by Sharoglazova et al. revision: yes

  2. Referee: Nelson's stochastic mechanics re-interpretation: the hidden-variable non-classical speed is explicitly fitted to the experimental data, which reduces the claimed reinterpretation to a post-hoc parameter adjustment rather than an independent consistency check; this directly undermines the assertion of a parameter-free or predictive re-derivation.

    Authors: The referee is correct that the non-classical speed in the Nelsonian formulation is chosen to reproduce the observed signal. Our purpose was to demonstrate consistency rather than to offer a parameter-free prediction: once the quantum potential is re-expressed as a kinetic-energy term, a hidden-variable velocity field exists that matches the data within Nelson's framework, just as Bohmian mechanics reproduces the same quantum predictions. We will revise the relevant section to state this explicitly as a consistency check, remove any implication of independent predictive power, and note the fitting procedure as a limitation of the present demonstration. revision: partial

  3. Referee: Stationary-regime analysis: the manuscript assumes that evanescent states dominate the signal once transients are set aside, but provides no independent diagnostic (time-resolved decay, comparison to a transient-inclusive model, or exclusion criteria) to confirm that residual non-stationary contributions are negligible in the measurement window; if even modest transients remain, both the Bohmian trajectories and the fitted speed become artifacts.

    Authors: We agree that an explicit diagnostic would strengthen the claim. The original experiment identifies the reported data as belonging to the stationary regime after transients have decayed, and our analysis focuses on the evanescent component within that window. The revised manuscript will add a dedicated paragraph that (i) recalls the decay time scales given by Sharoglazova et al., (ii) provides a simple estimate showing that residual transient amplitudes fall below the reported noise level within the measurement interval, and (iii) briefly sketches how a transient-inclusive model would modify the trajectory ensemble. This addition will make the regime assumption more transparent without altering the central conclusion. revision: yes

Circularity Check

1 steps flagged

Hidden-variable speed fitted to data presented as independent Bohmian/Nelsonian reinterpretation

specific steps
  1. fitted input called prediction [Abstract]
    "Bohm's quantum potential can be re-interpreted as a kinetic-energy term in the framework of Nelson's stochastic quantum mechanics, with a hidden-variable, non-classical, speed fitting the experimental data as well."

    The reinterpretation is achieved by introducing a non-classical speed whose value is chosen to match the reported signal. This makes the claimed compatibility with Bohmian and Nelsonian mechanics a direct consequence of the fitting step rather than an independent prediction or derivation from the underlying equations.

full rationale

The paper's central claim reinterprets the Sharoglazova et al. data via Bohmian trajectories and a Nelsonian hidden-variable speed. However, the speed is explicitly introduced as fitting the experimental data, making the match a post-hoc adjustment rather than a first-principles derivation. The stationary-regime assumption is invoked to isolate the evanescent component but is not shown to be independently verified; the fitting step itself reduces the 'proof of interpretability' to a parameter choice that reproduces the input signal by construction. No load-bearing self-citation chain or ansatz smuggling is present; the circularity is limited to the fitted-input pattern.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the experiment has entered a stationary regime dominated by evanescent states and on a free parameter (non-classical hidden speed) that is fitted to the data.

free parameters (1)
  • non-classical hidden-variable speed
    Introduced and adjusted to match the experimental data inside Nelson's stochastic framework.
axioms (1)
  • domain assumption The experiment reaches a stationary regime in which evanescent states dominate the observed signal
    Invoked to allow reinterpretation of the data within Bohmian mechanics.

pith-pipeline@v0.9.0 · 5391 in / 1275 out tokens · 33509 ms · 2026-05-16T20:58:03.602389+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

17 extracted references · 17 canonical work pages

  1. [1]

    Such a transverse motion show up in the transient state, wherej y ̸= 0, as shown below

    is simpler for the calculations, it may hide that the in- tercoupling of the two waveguides corresponds to a trans- verse (y) motion and not to an abstract degree of free- dom. Such a transverse motion show up in the transient state, wherej y ̸= 0, as shown below. We have three different behaviours according to whether: a)E k0 > V 0 + ℏωs 2 (Region 1); b)...

    work page

  2. [2]

    Violetta Sharoglazova, Marius Puplauskis, Charlie Mattschas, Chris Toebes and Jan Klaers, ’Energy-speed relationship of quantum particles challenges Bohmian mechanics.’ Nature643, 67-72 (2025)

    work page 2025

  3. [3]

    Bohm, ’A suggested interpretation of the quantum the- ory in terms of hidden variables

    D. Bohm, ’A suggested interpretation of the quantum the- ory in terms of hidden variables. I’, Phys. Rev.85, 166- 179 (1952)

    work page 1952

  4. [4]

    So, ’velocity’ is the vector and ’speed’ is the magnitude of the velocity

    We remind the following distinction, in the English lan- guage, between ’speed’ (the time rate at which an object is moving along a path) and ’velocity’ (the rate and direc- tion of an object’s movement). So, ’velocity’ is the vector and ’speed’ is the magnitude of the velocity

    work page

  5. [5]

    Jan Klaers, Violetta Sharoglazova, and Marius Pu- plauskis ’Titolo.’ Phys. Rev. A , (2025)

    work page 2025

  6. [6]

    Del Campo, G

    A. Del Campo, G. Garc´ ıa-Calder´ on, and J.G. Muga, Quantum transients, Phys. Rep.476, 1-50 (2009)

    work page 2009

  7. [7]

    Moshinsky,Diffraction in time and time-energy un- certainty relation, Am

    M. Moshinsky,Diffraction in time and time-energy un- certainty relation, Am. J. Phys.44, 1037-1042 (1976)

    work page 1976

  8. [8]

    Moshinsky, Phys

    M. Moshinsky, Phys. Rev.84, 525 (1951)

    work page 1951

  9. [9]

    Jan Klaers, Violetta Sharoglazova, and Marius Pu- plauskis,Reaffirming a Challenge to Bohmian Mechanics arXiv:2509.06584

    work page arXiv

  10. [10]

    Though the final results are different in the two cases, in both cases we obtain a nonzero current in the transient region, which was our objective

    We remark that there is no apriori reason to prefer the first-order expansion inκ(k) compared to a zeroth-order expansion, as done forT(k). Though the final results are different in the two cases, in both cases we obtain a nonzero current in the transient region, which was our objective. Aposteriori, it turns out that the spatial de- pendence of the first...

    work page

  11. [11]

    Eugene Merzbacher,Quantum Mechanics, 3 rd Edition, Sect 8.5, John Wiley and Sons (1998)

    work page 1998

  12. [12]

    Edward Nelson,Derivation of the Schr¨ odinger equation from Newtonian mechanics,Phys. Rev. 150, 1079–1085 (1966)

    work page 1966

  13. [13]

    Hall and M

    M.J.W. Hall and M. Reginatto, J. Phys. A: Math. Gen. 35(2002) 3289–3303

    work page 2002

  14. [14]

    In the hamiltonian formalism of quantum mechanics ki- netic and potential energies appear in a symmetric way and it is not necessarily evident how to identify each. For example, potential and kinetic energy can be inverted by a canonical transformation in the harmonic oscilla- tor and, in one-dimensional radial problems, the kinetic origin of the centrifu...

    work page

  15. [15]

    We remind the identity: ∇2R R = 1 2 ∇2ρ ρ − 1 4 |∇ρ|2 ρ2 , allowing to move from the usual, space-time dependent, expression of Bohm’s quantum potentialQ(⃗ r, t) =− ℏ2 2m ∇2R R , to its integral expression,Q= R dV Q(⃗ r, t) = ℏ2 8m R dV ρ ( ⃗∇ρ)2 ρ2 (second term of Eq. (14)). The two expressions differ by an exact divergence that is supposed to go to zero...

    work page

  16. [16]

    (15) only af- ter removing the exact divergence term ⃗∇ ·⃗ ufrom the integral, by supposing that at the boundary there is no flux

    Similarly to the description of [14], starting from the definition⃗ u= ℏ 2m ⃗∇lnρ, we obtain: 1 2 u2 + ℏ 2m ⃗∇ ·⃗ u= ℏ2 4m2 ∇2ρ ρ − 1 2 ( ⃗∇ρ)2 ρ2 , we can recover Eq. (15) only af- ter removing the exact divergence term ⃗∇ ·⃗ ufrom the integral, by supposing that at the boundary there is no flux

    work page

  17. [17]

    (14), we get:Q=Q x +Q y, withQ n = ℏ2 8m R dV (∂nρ)2 ρ ,n=x, y

    From the definition of the integrated quantum potential Q= ℏ2 8m R dV ( ⃗∇ρ)2 ρ of Eq. (14), we get:Q=Q x +Q y, withQ n = ℏ2 8m R dV (∂nρ)2 ρ ,n=x, y

    work page