pith. sign in

arxiv: 2507.20101 · v3 · submitted 2025-07-27 · 🪐 quant-ph

Tunneling photons pose no challenge to Bohmian mechanics

Yun-Fei Wang , Xiao-Yu Wang , Hui Wang This is my paper

Pith reviewed 2026-05-19 03:01 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Bohmian mechanicsphoton tunnelingcoupled waveguidesquantum interpretationstunneling dynamicssemi-classical speedBohmian velocity
0
0 comments X

The pith

A photon tunneling experiment in coupled waveguides does not challenge Bohmian mechanics.

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

The paper sets out to refute the idea that recent measurements of photon speeds in coupled waveguides contradict Bohmian mechanics. It does so by showing that the semi-classical speed formula used in the original work measures a different physical quantity from the Bohmian velocity, so the reported discrepancy has no bearing on which interpretation is correct. The authors further calculate that the actual time evolution of the photon wave function and the resulting intensity patterns are identical under both the standard quantum account and the Bohmian account. A sympathetic reader would care because the result removes one proposed experimental test that had appeared to separate the two pictures of quantum reality.

Core claim

The semi-classical speed v equals the square root of 2 times the absolute value of the energy difference divided by mass, while the Bohmian velocity v_S is obtained from the probability current. These two quantities are not the same, so equating them cannot decide between interpretations. Explicit solution of the coupled-mode equations for the waveguide system shows that the probability density and the phase evolution are the same whether one uses the Copenhagen or the Bohmian description, even in the regime where the energy difference is less than minus h-bar times the coupling strength.

What carries the argument

The demonstration that both interpretations produce identical photon dynamics in the coupled-waveguide Hamiltonian, together with the argument that semi-classical speed and Bohmian velocity are distinct quantities whose comparison is physically unjustified.

If this is right

  • The reported experimental data cannot be used to prefer one quantum interpretation over the other.
  • Photon tunneling times and output intensities in this geometry are predicted identically by both pictures.
  • Any future velocity comparison intended to test Bohmian mechanics must first establish that the measured quantity corresponds to the Bohmian velocity field.
  • The waveguide model supplies an exact arena in which the two interpretations agree on all observable dynamics.

Where Pith is reading between the lines

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

  • Careful separation of velocity definitions may be needed in other tunneling or scattering experiments that aim to test alternative quantum interpretations.
  • The agreement on dynamics suggests that trajectory-based pictures can be consistent with wave-function evolution in linear optical systems without altering measurable outcomes.
  • Similar re-examination could be applied to claims of superluminal effects or negative dwell times in quantum tunneling.

Load-bearing premise

That the semi-classical speed formula correctly captures a measurable quantity that Bohmian mechanics must reproduce in this waveguide geometry.

What would settle it

A direct calculation or measurement that yields different photon intensity distributions or arrival statistics in the same coupled waveguides under Bohmian mechanics versus standard quantum mechanics would falsify the claim of identical predictions.

Figures

Figures reproduced from arXiv: 2507.20101 by Hui Wang, Xiao-Yu Wang, Yun-Fei Wang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
read the original abstract

Very recently, Sharoglazova et al. performed an experiment measuring the energy-velocity relationship and Bohmian velocity in coupled waveguides. Their data show a discrepancy between the semi-classical `speed' $v=\sqrt{2|\Delta|/m}$ and Bohmian velocity $v_s$ for $\Delta<-\hbar J_0$, leading them to claim a challenge to Bohmian mechanics. Here, we definitively demonstrate this experiment poses no challenge to Bohmian mechanics. First, $v$ and $v_S$ represent fundamentally distinct physical quantities -- comparing them is physically unjustified and cannot adjudicate between Copenhagen and Bohmian interpretations. Second, we rigorously show that both interpretations predict identical photon tunneling dynamics in coupled waveguides.

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

2 major / 2 minor

Summary. The manuscript claims that the experiment by Sharoglazova et al. on energy-velocity relations in coupled waveguides poses no challenge to Bohmian mechanics. It advances two arguments: (1) the semi-classical speed v = sqrt(2|Δ|/m) and the Bohmian velocity v_S are fundamentally distinct physical quantities whose direct comparison is physically unjustified and cannot distinguish interpretations; (2) both Copenhagen and Bohmian interpretations rigorously predict identical photon tunneling dynamics in the coupled-waveguide system.

Significance. If the two central arguments are fully substantiated, the work would usefully clarify that reported discrepancies in tunneling experiments do not falsify Bohmian mechanics, reinforcing the standard result that ensemble predictions coincide while underscoring the need to compare like quantities. It contributes to ongoing discussions of quantum interpretations in optical analogs of tunneling.

major comments (2)
  1. [Section presenting the rigorous demonstration of identical predictions] The second main claim (identical tunneling dynamics) is load-bearing for the 'no challenge' conclusion yet lacks an explicit derivation mapping the two-mode waveguide Hamiltonian, the experimental intensity/phase extraction protocol, and the Bohmian guidance equation to the same observable statistics as the Copenhagen probability current, particularly in the discrepant regime Δ < -ħ J0 where the original data show mismatch with the semi-classical formula.
  2. [Discussion distinguishing v and v_S] The first argument requires a concrete demonstration that the semi-classical v is not the appropriate comparator for v_S; without showing how the guidance equation or probability current in the waveguide model yields a different functional dependence on Δ, the claim that comparison is 'physically unjustified' remains conceptual rather than tied to the specific Hamiltonian and measurement.
minor comments (2)
  1. Define all symbols (including J0, Δ, v_S) at first use and ensure the waveguide Hamiltonian is written explicitly before discussing dynamics.
  2. Add a brief comparison table or plot of the predicted v_S(Δ) under both interpretations versus the original experimental points to make the equivalence claim visually verifiable.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments help clarify how to strengthen the presentation of our two central arguments. We address each major comment below and will expand the derivations in the revised manuscript to make the mappings and distinctions fully explicit.

read point-by-point responses

  1. Referee: [Section presenting the rigorous demonstration of identical predictions] The second main claim (identical tunneling dynamics) is load-bearing for the 'no challenge' conclusion yet lacks an explicit derivation mapping the two-mode waveguide Hamiltonian, the experimental intensity/phase extraction protocol, and the Bohmian guidance equation to the same observable statistics as the Copenhagen probability current, particularly in the discrepant regime Δ < -ħ J0 where the original data show mismatch with the semi-classical formula.

    Authors: We agree that an explicit step-by-step mapping strengthens the claim. The manuscript already notes that both interpretations start from the same two-mode Hamiltonian and therefore produce identical ensemble statistics for measurable intensities and phases. To address the referee's point directly, the revised version will add a dedicated subsection that (i) writes the two-mode Hamiltonian, (ii) extracts the intensity and phase from the experimental protocol, (iii) applies the Bohmian guidance equation to obtain the velocity field, and (iv) shows that this field reproduces the probability current used in the Copenhagen analysis. Explicit analytic expressions and numerical checks will be provided for the regime Δ < -ħ J0, confirming that the observable statistics coincide exactly and that the reported mismatch is only with the semi-classical formula, not with either quantum interpretation. revision: yes

  2. Referee: [Discussion distinguishing v and v_S] The first argument requires a concrete demonstration that the semi-classical v is not the appropriate comparator for v_S; without showing how the guidance equation or probability current in the waveguide model yields a different functional dependence on Δ, the claim that comparison is 'physically unjustified' remains conceptual rather than tied to the specific Hamiltonian and measurement.

    Authors: We accept that the distinction should be tied explicitly to the waveguide Hamiltonian. In the revised manuscript we will derive the functional form of v_S(Δ) directly from the guidance equation applied to the coupled-mode amplitudes. This yields v_S = (ħ / m) * (phase gradient term involving the coupling J0 and the relative phase between waveguides), which has a different dependence on Δ than the semi-classical sqrt(2|Δ|/m). We will contrast this with the probability current expression and include a short analytic expansion or plot showing the two functional forms diverge for Δ < -ħ J0. This concrete derivation demonstrates why equating the two velocities is physically unjustified within the model and measurement protocol of the experiment. revision: yes

Circularity Check

0 steps flagged

No circularity: claims rest on standard QM equivalence and conceptual distinction of velocities

full rationale

The paper's two main pillars—distinguishing the semi-classical speed v from the Bohmian velocity v_S as physically distinct quantities whose comparison is unjustified, and asserting that Copenhagen and Bohmian mechanics yield identical photon tunneling dynamics in the coupled-waveguide model—are presented as following from established quantum theory rather than any internal fitting, self-definition, or self-citation chain. No equation or result in the provided abstract and structure reduces by construction to a fitted parameter renamed as a prediction, nor does the equivalence rely on a uniqueness theorem imported from the authors' prior work. The argument applies the standard result that ensemble predictions coincide under both interpretations to the two-mode Hamiltonian without introducing new fitted inputs or definitional loops. This is the normal case of a self-contained interpretive clarification.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on standard quantum mechanical frameworks for both interpretations and the assumption that the waveguide system is modeled identically in the theoretical analysis.

axioms (1)
  • domain assumption Bohmian mechanics and Copenhagen interpretation predict identical observable dynamics for photon tunneling in coupled waveguides.
    Invoked as the second main point in the abstract.

pith-pipeline@v0.9.0 · 5651 in / 1162 out tokens · 44440 ms · 2026-05-19T03:01:09.817262+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Trajectories in coupled waveguides: an application to a recent experiment and Hiley's lessons on the falsification of the Bohmian model

    quant-ph 2025-10 unverdicted novelty 4.0

    Bohmian trajectories computed for coupled waveguides reproduce standard quantum predictions and refute a recent experimental claim of falsification.

Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages · cited by 1 Pith paper

  1. [1]

    La m´ecanique ondulatoire et la structure atomique de la mati`ere et du rayonnement

    De Broglie, L. La m´ecanique ondulatoire et la structure atomique de la mati`ere et du rayonnement. J. Phys. Radium 8, 225 (1927)

    work page 1927

  2. [2]

    A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden Variables’ I.Phys

    Bohm, D. A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden Variables’ I.Phys. Rev. 85, 166-179 (1952)

    work page 1952

  3. [3]

    & Klaers, J

    Sharoglazova, V ., Puplauskis, M., Mattschas, C., Toebes C. & Klaers, J. Energy–speed relationship of quantum particles chal- lenges Bohmian mechanics. Nature 643, 67–72 (2025). Methods Deriving the ψm, ψa solution from Schr ¨odinger equation The two coupled Schr ¨odinger equations 1 in the main text satisfy: iℏ∂t(ψm + ψa) = − ℏ2 2m d2(ψm + ψa) dx2 + V0(ψ...

    work page 2025