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REVIEW 2 major objections 4 minor 113 references

Six models for where a quantum particle hits a waiting screen make different, testable predictions even far away.

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2026-07-12 01:45 UTC pith:3OGUKC6Z

load-bearing objection Clean, usable conversion of the screen problem's position marginal into concrete, currently doable atom-trap experiments that already distinguish six models, including far-field deviations. the 2 major comments →

arxiv 2607.03538 v1 pith:3OGUKC6Z submitted 2026-07-03 quant-ph physics.atom-ph

The arrival position problem in quantum mechanics

Ali Ayatollah Rafsanjani , Will Cavendish This is my paper
classification quant-ph physics.atom-ph
keywords arrival positionscreen problemquantum arrival timequantum fluxabsorbing boundarycomplex absorbing potentialfar-field scatteringatom traps
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Standard quantum mechanics tells us how to predict the result of a position measurement done at a chosen instant, but it has no unambiguous rule for the places where particles are found by a detector that is simply left on until something clicks. This paper isolates that gap as the arrival-position problem and shows that six well-known proposals for solving it already disagree about the angular distribution of hits on a planar screen. The disagreements appear for ordinary single- and double-well atom traps, survive into the far-field regime where semiclassical scattering is usually trusted, and can be read off without recording precise arrival times. Because the contrasts are large enough for existing single-atom detection methods, the work turns a long-standing theoretical blind spot into a concrete experimental question.

Core claim

The six surveyed proposals (semiclassical, quantum flux, standard/Kijowski, complex absorbing potential, absorbing boundary condition, and Marchewka–Schuss path-integral absorption) produce mutually distinguishable angular arrival-position distributions for the same Gaussian single- and double-well initial states. Several of the differences remain even as the screen is moved to infinity, so they cannot be dismissed as near-field corrections.

What carries the argument

The angular arrival-position density A_L(θ), obtained by integrating each joint screen distribution over time and the vertical coordinate and changing variables to the viewing angle θ from the origin; its far-field and oblique-angle limits, together with its response to spatial rescaling of the initial wave packet, serve as the diagnostic that separates the models.

Load-bearing premise

The far-field formulas that separate the models are treated as numerically supported conjectures whose rigorous L1 convergence is left for later work.

What would settle it

Prepare a ground-state single- or double-well atom, release it toward a light-sheet or microchannel-plate screen at known L/σ, accumulate hits without conditioning on detection, and check whether the measured A_L(θ) vanishes at large |θ|, diverges, or stays finite and flat—any of which immediately eliminates whole classes of proposals.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Table-top atom-trap experiments can already decide among leading screen-problem proposals by looking only at hit positions, not times.
  • Agreement with standard scattering theory at all angles forces a precise 1/τ² tail on the arrival-time distribution; any other tail exponent is ruled out.
  • Detector models that remain non-semiclassical in the far field must retain a detectable dependence on screen composition even at large L.
  • Rescaling the trap width while holding detector parameters fixed changes total detection probability for absorbing models but leaves the semiclassical, flux, and standard predictions invariant.

Where Pith is reading between the lines

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

  • If CAP, ABC or MS is correct, two identically placed screens of different physical makeup must produce measurably different far-field angular patterns—an immediate, detector-level test the paper only hints at.
  • The same angular diagnostics can be applied to any future screen-problem proposal simply by computing its γ_tail; the paper thereby supplies a quick filter that later models must pass.
  • Because most of the distributions are mass-independent, the same spatial experiment can be repeated with different atomic species to isolate the one mass-dependent model (CAP) without new apparatus.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper formulates the arrival-position problem (the spatial marginal of the screen problem for always-on detectors) as complementary to the better-known arrival-time problem. It derives explicit angular distributions A_L(θ) for six standard proposals (semiclassical SC, quantum flux QF, Kijowski/standard SD, complex absorbing potential CAP, absorbing-boundary condition ABC, and Marchewka–Schuss MS) applied to single- and double-well Gaussian packets, supplies finite-L numerics for realistic atom-trap parameters, and obtains far-field formulas showing that CAP/ABC/MS remain distinguishable from the semiclassical limit even as L→∞. Feasible cold-atom experiments are outlined that can discriminate the models via total detection probability, oblique-angle tails, and scaling under wave-function dilation.

Significance. If the distinctions hold, the work converts a long-standing foundational gap into a set of concrete, table-top falsifiable predictions that do not require time-resolved data. Strengths include fully explicit formulas for every model, open-source code that regenerates the figures, mass-independence of A_L for five of the six proposals, and clear experimental signatures (vanishing oblique density for absorbing models, 50 % detection probability for SC/QF/SD, non-trivial scaling of CAP/ABC/MS). These features make the paper immediately useful both for theorists refining screen models and for experimental groups already performing single-atom release-and-detect protocols.

major comments (2)
  1. §IV.B, Eqs. (13)–(19): the far-field expressions for CAP, ABC and MS are labelled “numerically supported conjectures” whose L^{1} convergence is left unproved. While the L = 10^{3}σ panels of Figs. 2–3 already display the claimed qualitative distinctions, a short appendix quantifying the L^{1} distance to the limiting formulas (or a reference to a rigorous stationary-phase argument under the stated Gaussian regularity) is needed before the persistence-as-L→∞ claim can be regarded as fully established.
  2. §III.A and §IV.A: the quantum-flux proposal is applied only under the current-positivity condition, which the authors verify for the chosen Gaussians and L. A brief statement of the range of L/σ and well separations for which positivity continues to hold (or a note that the truncated-flux prescription of Ref. [12] would be used otherwise) would remove any ambiguity about the domain of the QF curves shown in the figures.
minor comments (4)
  1. Fig. 1 caption: the value λ = 2σ is given without units; since λ has dimensions of length it would be clearer to write “λ = 2σ (with σ = 1 µm)”.
  2. Eq. (7): the angular density A_L is defined with an integral over z and τ; a parenthetical remark that the z-integral is trivial by separability would help readers who skip §III.B.
  3. §IV.D, Fig. 4: the horizontal axis is labelled α while the caption speaks of “rescaling parameter α”; adding the explicit relation α = σ_new/σ_old would avoid momentary confusion.
  4. References [105] and [111] are listed as 2026 arXiv preprints; if they have since been published, the journal citations should be updated.

Circularity Check

0 steps flagged

No circularity: independent literature models are imported and their arrival-position marginals are computed for concrete wave functions; free parameters remain free inputs, not fitted outputs.

full rationale

The paper’s central claim is that six previously published proposals (SC, QF, SD, CAP, ABC, MS) produce mutually distinguishable angular distributions A_L( heta) for single- and double-well Gaussians, including non-recovery of the semiclassical far-field limit by CAP/ABC/MS. Each proposal is introduced by an explicit formula taken from the cited literature (Eqs. 1–6); the subsequent numerical and asymptotic evaluations (Figs. 2–3, Eqs. 10–19) are direct consequences of those formulas applied to the stated initial states. Free parameters (eta, heta, u height/width) are treated as model inputs to be fixed by future experiment, never adjusted to manufacture the reported differences. Far-field expressions are labeled “numerically supported conjectures” whose rigorous L1 convergence is left open, so they are not presented as derived theorems. Occasional self-citations (e.g., [14], [107]) supply background or related discussion but are not load-bearing for the distinguishability claim. No equation reduces a claimed prediction to a tautology, a fit, or a self-cited uniqueness result. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The paper does not invent new dynamical laws; it evaluates six existing proposals. Free parameters belong to those proposals. Domain assumptions are standard non-relativistic QM plus the idealizations needed to map each proposal onto a planar screen. No new entities are postulated.

free parameters (3)
  • CAP height h and width w (or sigmoid µ_h^w)
    Phenomenological absorption strength and spatial profile; chosen by hand for numerics (e.g. h = 1 in units ħ²/(2mσ²), w = σ).
  • ABC complex parameter β
    Boundary-condition strength; set to i/(2σ) in the plots.
  • MS absorption length λ
    Path-integral absorption strength; set to 2σ in the plots; to be fixed experimentally according to the original authors.
axioms (4)
  • domain assumption Non-relativistic Schrödinger evolution (or its non-unitary variants) for a spin-0 particle of mass m under gravity after trap release.
    Standard atomic-physics setting used throughout Sections II–IV.
  • domain assumption Current-positivity condition holds on the screen locus for the chosen initial states and L, so the quantum-flux formula can be used without truncation.
    Explicitly invoked to justify applying QF (Introduction and Section III).
  • domain assumption Each of the six proposals supplies a well-defined joint distribution Π_L(s,τ;Ψ) whose position marginal is the object of study.
    Taken from the cited literature for SC, QF, SD, CAP, ABC, MS.
  • ad hoc to paper Far-field limits of A_L may be obtained by formal stationary-phase / scattering arguments and interchange of limits (left unproved).
    Section IV.B labels the resulting formulas “numerically supported conjectures.”

pith-pipeline@v1.1.0-grok45 · 26688 in / 2505 out tokens · 24281 ms · 2026-07-12T01:45:47.141646+00:00 · methodology

0 comments
read the original abstract

The problem of making unambiguous probabilistic predictions about experiments involving waiting "always on" detectors remains a challenge for quantum theory. While most research on this problem studies arrival time, i.e., predicting the distribution of when detection events occur, this paper studies the arrival position problem, which is the complementary challenge of predicting the distribution of where detection events occur. Despite the widespread recognition of the arrival time problem, the inability of standard quantum theory to address the arrival position problem remains a pervasive theoretical blind spot. In this paper, we compare quantitative arrival position predictions derived from prominent proposed solutions to the screen problem. As we show, these models yield distinguishable predictions even in relatively simple experiments achievable with current technology. Notably, many of these discrepancies persist even in the far-field limit, where standard semiclassical approximations are typically assumed to be valid.

Figures

Figures reproduced from arXiv: 2607.03538 by Ali Ayatollah Rafsanjani, Will Cavendish.

Figure 1
Figure 1. Figure 1: FIG. 1. A realization of the proposed experimental scheme and arrival position distributions for two proposals. Panel A shows [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of the arrival position distributions [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The total detection probabilities for a Gaussian ini [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

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Reference graph

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    Note that conditional distributiongiventhat a detec- tion has occurred is all that is available in some closely related experimental protocols, e.g., the standard dou- ble slit experiment where particles are not prepared one at a time, but are produced at a variable rate by an oven or electrode or with variable count in a conden- sate or atom array. For t...

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