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arxiv: 2604.21543 · v1 · submitted 2026-04-23 · ⚛️ physics.flu-dyn · cond-mat.soft

Unified Hydrodynamic Analogue of Aharonov-Bohm and Lense-Thirring Effects

Aditya Singh , Joseph Samuel , Chien-chia Liu , Luiza Angheluta , Andr\'es Concha , Mahesh Bandi This is my paper

Pith reviewed 2026-05-09 20:58 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn cond-mat.soft
keywords hydrodynamic analogueAharonov-Bohm effectLense-Thirring effectdraining bathtub vortexsurface wavesframe draggingphase holonomyshallow water equation
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The pith

Surface waves in a draining-bathtub vortex realize both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging in one hydrodynamic system.

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

The paper shows that a draining vortex in shallow water produces an effective vector potential for surface waves through a mapping of the wave equation, so that the flow circulation sets a global phase holonomy. Traveling waves then develop wavefront dislocations matching the Aharonov-Bohm scattering pattern, while standing-wave combinations form nodal lines that rotate at an angular speed fixed by the same circulation, reproducing the Lense-Thirring drag effect. Experiments on a controlled vortex confirm both signatures. A reader would care because the setup turns two distinct physical phenomena—one from quantum gauge theory and one from general relativity—into measurable fluid behaviors controlled by a single, accessible velocity field.

Core claim

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analog

What carries the argument

The static time transformation that converts the flat-space wave equation into the convected shallow-water equation, thereby inserting the vortex flow as an effective vector potential whose circulation produces the phase holonomy.

If this is right

  • Traveling waves acquire wavefront dislocations whose spacing is set by the circulation, reproducing Aharonov-Bohm scattering.
  • Standing-wave patterns rotate rigidly at an angular velocity determined solely by the background circulation.
  • For non-integer values of the circulation the wave problem is formulated on the universal cover to keep partial-wave solutions single-valued.
  • The same velocity field simultaneously encodes both the topological phase and the inertial dragging effect.

Where Pith is reading between the lines

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

  • The platform could let researchers vary circulation continuously while tracking both phase and rotation effects in the same run.
  • The universal-cover construction suggests the setup may also host analogues of other multi-valued phase phenomena in fluids.
  • If the mapping remains accurate at higher flow speeds, the vortex could serve as a test bed for combined gauge-gravity analogues beyond the linear regime.

Load-bearing premise

The static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation without introducing significant discrepancies or requiring additional corrections for the vortex geometry and flow.

What would settle it

Measurement showing that nodal lines in standing-wave superpositions on the vortex either fail to rotate or rotate at a speed unrelated to the measured circulation.

Figures

Figures reproduced from arXiv: 2604.21543 by Aditya Singh, Andr\'es Concha, Chien-chia Liu, Joseph Samuel, Luiza Angheluta, Mahesh Bandi.

Figure 1
Figure 1. Figure 1: FIG. 1: Traveling waves with wavefront dislocations showing map of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Topological representation of the universal cover of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Phase evolution [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.

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

1 major / 1 minor

Summary. The paper claims that surface waves in a draining-bathtub vortex realize both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging in one hydrodynamic system. A static time transformation is used to map the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, producing an effective vector potential from the background flow. Circulation induces global phase holonomy, leading to wavefront dislocations in traveling waves and rotating nodal patterns in standing-wave superpositions; noninteger circulations are treated on the universal cover. Experiments on a controlled vortex are stated to confirm the predictions.

Significance. If the central mapping holds without unaccounted discrepancies, the work supplies a single controllable fluid platform that unifies topological phase effects from gauge theory with inertial frame-dragging analogues from general relativity. The reliance on a measurable velocity field rather than fitted parameters, together with the experimental confirmation, strengthens its value as a laboratory testbed for comparative studies of these phenomena.

major comments (1)
  1. [static time transformation derivation] The static time transformation (described immediately after the abstract and in the derivation of the effective wave operator) is asserted to convert the flat wave equation directly into the convected shallow-water equation. However, with nonzero radial inflow v_r(r) present in the draining-bathtub profile, the convective derivative contains cross terms that a purely temporal shift does not automatically eliminate; an explicit cancellation check for the chosen vortex is required to confirm that no residual scalar potential or dispersion modification appears, as any mismatch would undermine the claimed Aharonov-Bohm plus Lense-Thirring mapping.
minor comments (1)
  1. [experimental confirmation paragraph] The abstract states that experiments confirm the predictions, but the manuscript would benefit from a brief statement on how the universal-cover treatment for noninteger circulations is implemented in the data analysis.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We are grateful to the referee for the positive summary and recommendation. We provide a point-by-point response to the major comment and will update the manuscript to incorporate the requested clarification.

read point-by-point responses

  1. Referee: The static time transformation (described immediately after the abstract and in the derivation of the effective wave operator) is asserted to convert the flat wave equation directly into the convected shallow-water equation. However, with nonzero radial inflow v_r(r) present in the draining-bathtub profile, the convective derivative contains cross terms that a purely temporal shift does not automatically eliminate; an explicit cancellation check for the chosen vortex is required to confirm that no residual scalar potential or dispersion modification appears, as any mismatch would undermine the claimed Aharonov-Bohm plus Lense-Thirring mapping.

    Authors: We thank the referee for this insightful comment. The derivation in the manuscript uses a static time transformation specifically tailored to the background flow to map the operators. We agree that providing an explicit verification of how the cross terms cancel for the draining bathtub vortex (including the radial inflow) would clarify the mapping and rule out any residual effects. We will revise the manuscript to include this detailed cancellation check in the section describing the effective wave operator. revision: yes

Circularity Check

0 steps flagged

No significant circularity: explicit mapping derives effective potential from flow without reduction to inputs or self-citations

full rationale

The central derivation applies a static time transformation to the flat (2+1)D wave equation, producing the convected shallow-water equation and an effective vector potential directly from the background velocity field. This step is a coordinate redefinition whose output (phase holonomy and nodal rotation) follows mathematically from the circulation parameter without fitting to the target Aharonov-Bohm or Lense-Thirring observables. No load-bearing self-citation, ansatz smuggling, or renaming of known results appears; experimental confirmation on a physical vortex supplies independent verification. The chain remains self-contained and does not reduce by construction to its starting assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim depends on the validity of the time transformation and the shallow-water approximation; no free parameters or new entities are introduced in the abstract description.

axioms (1)
  • domain assumption A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow.
    This mapping is the central step that produces the effective vector potential and the two analogue effects.

pith-pipeline@v0.9.0 · 5485 in / 1164 out tokens · 31152 ms · 2026-05-09T20:58:01.297601+00:00 · methodology

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Reference graph

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