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REVIEW 3 major objections 5 minor 1 cited by

That Dot on the Screen: also, what about Born? and other objections to wavefunction physics

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A nonlinear wavefunction model can place a single dot on a detector screen without invoking point particles or probability rules, this paper argues.

desk verdict An honest, transparent toy-model essay whose central claim is undone by an unverified solver and engineered endpoints; worth peer review only if code and convergence are demanded. read the letter →

arxiv 2504.17808 v1 pith:4MYVD43P submitted 2025-04-22 physics.gen-ph

W. David Wick This is my paper · ORCID
classification physics.gen-ph
keywords wavefunctionrealismnonlinearequationmeasurementproblemWaveFunctionEnergydetectormodelquantumchaosprobabilityinterpretationdotonthescreen
topics The Measurement Problem
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that the standard objections to treating the wavefunction as the complete description of matter—the single dot on a screen, the click of a photon counter, and the line of droplets in a cloud chamber—do not force one to add point particles or probability rules. The proposed resolution is to keep a wavefunction-only ontology but replace the linear evolution equation with a nonlinear one, adding a WaveFunction Energy term that suppresses superposed macroscopic alternatives and, through sensitive dependence on initial conditions, makes outcomes appear random. The concrete evidence is a toy model of one particle position and three detectors: in 77–85 of 200 simulated runs exactly one detector fires, and when the nonlinear term is removed no detector ever fires. The paper does not claim to prove the mechanism; it offers the simulation as evidence that wavefunction-only physics can produce the appearance of a local dot.

What carries the argument

The load-bearing object is the detector-model Hamiltonian, defined on a wavefunction $ψ(x, y_1, \dots, y_n)$ in which $x$ is a discrete particle position and each $y_i$ is a detector variable. The Hamiltonian contains kinetic terms for the position and detector variables, a detector-energy term, a coupling between the position label and detector labels, and the nonlinear WaveFunction Energy term, which is quartic in $ψ$ and is applied separately to each distinguishable macroscopic detector so that it suppresses superpositions of triggered and untriggered states. The evolution is Hamilton's equation for this energy, and the simulated case has dimension 48 ($n=3$ positions, $d=1$ detector state) and is integrated with an explicit symplectic scheme designed for nonseparable Hamiltonians; the claimed dots appear in that numerical solution.

What would settle it

Run the identical 200-run experiment with an independent numerical integrator and a convergence check, such as halving the time step, and compare the one-dot counts. If the contrast between 77–85 one-dot runs at $w=20$ and zero at $w=0$ disappears under independent integration, or if energy and norm conservation fail badly, then the simulation evidence for the dot would collapse. A second check is to vary $w$ continuously from 0 to 20 and see whether the one-dot probability rises smoothly or through a sharp threshold, since the paper's energy-bound argument predicts a threshold tied to the cost of forming a cat state.

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Extended reading notes

Core claim

The central claim is that the dot on the screen is not evidence for particles or for the collapse of a wavefunction; it is a pattern produced by a deterministic, nonlinear wave equation. In the author's model, the wavefunction carries both a position label and detector labels, and a quartic energy term, WaveFunction Energy, penalizes superpositions in which detectors are triggered and untriggered at once. With a large enough WaveFunction Energy constant, the dynamics can end in a state in which the observable associated with one detector exceeds a threshold while all others stay low. The author further argues that the apparent randomness of which detector fires arises from chaos: under the nonlinear evolution, nearby initial wavefunctions separate rapidly, so uncontrollable small differences play the role of the hidden variables in a coin toss. The simulation results are mixed on the standard probability rule: a likelihood-based test cannot reject it, but a variance-based test rejects it because triggered detectors sit at the location of maximal probability too often. The author declares himself agnostic about the probability rule on the basis of this toy model.

Load-bearing premise

The central load-bearing premise is that the 20,000-step numerical integrations faithfully approximate the nonlinear Hamiltonian dynamics, so the simulated one-dot outcomes are properties of the model rather than artifacts of the solver; the author explicitly says he cannot prove that the program solves the model.

Editorial extensions

If this is right

  • If the wavefunction is complete and nonlinear, no collapse postulate is needed: measurement outcomes are ordinary dynamical states of a larger wavefunction.
  • The random distribution of detector clicks can be traced to sensitive dependence on initial conditions, so probability enters physics the same way it enters roulette or coin flips.
  • Macroscopic superpositions, the 'cats' of the measurement problem, are blocked whenever the total energy is below the cost of forming one, so quantum superpositions remain at microscopic scales.
  • The toy model gives a concrete, testable prediction: removing the nonlinear WaveFunction Energy term makes dots disappear, since zero detectors fired in 200 runs at $w=0$.
  • If the variance-based rejection of the probability rule persists in larger models, correlations now attributed to quantum randomness would need to be re-examined.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural experimental extension is to look for energy thresholds in real detectors: if WaveFunction Energy exists, there should be a sharp boundary below which no dot forms and above which dot probability rises steeply, a signature absent from linear quantum mechanics.
  • The paper's own account implies dots may be transient and recurrent rather than permanent records, which suggests that testing the model would require timing measurements sensitive to the brief appearance of a dot.
  • The variance-based rejection of the standard probability rule is the point most worth pursuing: if real experiments with better statistics show triggered detectors preferentially at maximal-probability locations, small corrections to the usual rule might become visible.
  • If the one-dot results survive independent integration, they would strengthen a particle-free realist reading of the wavefunction and make 'finding' language optional in quantum measurement.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper argues that the 'dot on the screen', the cloud-chamber droplet track, and the detector click can be accounted for by Schrödinger's wavefunction alone if the linear equation is augmented by a nonlinear 'Wave-Function Energy' (WFE) term, without invoking particles or Born probabilities. After introducing a finite-dimensional toy model of one particle and n two-state detectors with Hamiltonian (2)-(5), the author proposes per-detector WFE (16), shows that WFE assigns energy w(1-1/n) to the cat state (20), and reports simulations (Table 2) in which, with w=20, one detector fires in 77-85 of 200 runs and none fire when w=0. The paper interprets the random dot location as sensitive dependence on initial conditions and uses the culled single-dot runs to test Born's rule. The final sections are Q&A and discussion.

Significance. If the simulation result were robust, the paper would constitute a serious challenge to the standard view that measurement outcomes require either collapse, hidden variables, or Born probabilities. The author deserves credit for making the toy model explicit, for stating the model Hamiltonian in full, and for candidly flagging the limitations of the numerical work: no proof that the solver is faithful, no code, no convergence data, and no formal chaos study. These admissions are strengths in that they make the evidential status transparent. However, the evidence currently on offer is not sufficient to support the abstract's strong claim.

major comments (3)
  1. [§6 Q&A; §8 Appendix] The central empirical claim rests on an unverified numerical solver. The runs in Table 2 are the only evidence that WFE localizes the wavefunction into a dot, yet the manuscript provides no code, no random seeds, no energy/norm conservation tolerances, and no convergence study, and the author states in the Q&A: 'Prove to me that your program actually solves, approximately, your model? Answer: I cannot.' Without independent verification, the w=20 versus w=0 contrast cannot be distinguished from a solver artifact or integration error.
  2. [§4, Eq. (20); §5, Table 1] The one-detector endpoint is built into the model's parameters. For n=3, w=20, v=10, the cat state of Eq. (19) has energy v + w(1-1/n) = 10 + 40/3 ≈ 23.3, exceeding the stated initial energy ≈20, while the all-detectors state (17) has energy 30. Energy conservation therefore excludes both cat and multi-detector final states a priori, leaving only the single-detector or no-detector outcomes reported in Table 2. The simulation thus demonstrates the energy bookkeeping, not a dynamical mechanism for dot formation.
  3. [§5; §7] The chaos explanation is not tested for this model. The author writes that he 'did not make a formal study of this question', and the only diagnostic offered is Figure 2, a plot of det M versus time. Since the initial conditions in Eq. (6) are randomized run-to-run via z and θ, the scatter of dot locations may simply reflect the random draws rather than sensitive dependence on initial conditions. No separation experiment, Lyapunov estimate, or quantitative instability analysis for this model is presented.
minor comments (5)
  1. [Table 2] The ranges 77-85 and 115-122 do not sum to 200 in any combination; please report exact counts or explain the uncertainty range.
  2. [Figure 3] The strong suppression of dots at position 2.0 is unexplained; since the toy model has only three positions, this behavior should be understood before the histograms are presented as evidence of approach to a limiting distribution.
  3. [§3] The step from the distinguishability argument to Eq. (16) is not fully derived; state explicitly why each detector's WFE uses only the marginal over y_j and not the joint distribution.
  4. [References] Reference [10] lists 'arXiv 1980.02352', which appears to be a typo; the actual year/identifier should be corrected.
  5. [Eq. (9)] The quantity Born_i is called a probability, although the paper's thesis denies the fundamental status of probabilities; a neutral term such as 'Born functional' would avoid confusion.

Circularity Check

1 steps flagged · score 5.0 of 10

The single-dot endpoint is largely built into the model: the WFE parameter w is hand-fitted to make the cat state energetically impossible, so the simulation's 'one dot, not a spray' is an anticipated construction rather than an independent prediction.

  1. fitted input called prediction [Section 5, Table 1 and Table 2; cf. Section 4, Eq. (20)]
    "The parameters were chosen by experimentation, with some goals in mind. First, there should be some wavefunction spread over spatial positions (“movement of the particle”) and detections (“some detectors should be triggered”). As for WFE, controlled by parameter ‘w’, the computed energy with the parameters in the Table and the initial conditions described in section 2, came out to around 20; hence the choice made was to render the cat state (section 4) almost impossible."

    Eq. (20) shows the cat state carries WFE = w(1−1/n). The paper then fixes w=20 so that this cat-state energy exceeds the initial energy, and Section 4 states that this 'will disabuse the cat, leaving only (b) as a possible endpoint.' The simulation's central qualitative output—a single triggered detector, i.e., 'that dot on the screen'—is therefore an energy-allowed endpoint selected by a WFE parameter explicitly fitted to make the cat impossible. The 'one dot, not a spray' feature of the claimed explanation is built into the model's energy landscape and fitted parameter values rather than being an independent, parameter-free prediction. The paper does not claim to predict the dot frequency, which softens the circularity, but the qualitative single-dot endpoint is constructed by design.

full rationale

The paper is transparent about its exploratory character: parameters are 'chosen by experimentation,' and the author concedes in §6 that he cannot prove the numerical program solves the model. These admissions are relevant to reliability but are not themselves circularity. The clearest circular aspect is that the headline phenomenon—a single dot as opposed to a cat—is enforced by the definition of WFE (which penalizes variance in detector variables) and by the hand-set choice w=20, which makes the cat state energetically inaccessible. In that narrow sense, the simulation confirms what the model was designed to do. However, the dynamical fact that a dot appears at all (rather than the system remaining in the no-dot state), and the random distribution of dot locations, are not forced by the definitions; they emerge from the numerical integration, though that integration is unverified and no code or convergence study is provided. Self-citations to the author's prior papers [7], [9], [11] supply the WFE program and the DCI chaos criterion, but the present paper also supplies its own det-M plot and histograms, so the self-citations are not the sole support for every claim. Overall, the central derivation has substantial fitted-input structure but retains independent dynamical content, justifying a moderate partial-circularity score rather than a finding of complete circularity.

Assumptions & free parameters 9 free parameters · 6 assumptions · 1 invented entities

The paper rests on a large set of tuned constants and on the WFE postulate from the author's earlier work. The central demonstration, one dot, is produced by adjusting the parameters so that the only allowed endpoint is a single triggered detector; the chaos mechanism is asserted, not tested. There are no externally benchmarked predictions in this preprint.

free parameters (9)
  • w (WFE coupling) = 20.0
    Chosen by experimentation so that the cat state's WFE cost w(1-1/n) is almost impossible; central to producing a single dot.
  • v (detector energy) = 10.0
    Tuned to allow detector triggering within energy bounds.
  • alpha (particle-detector interaction) = 15.0
    Tuned to create an interaction that localizes the particle.
  • M (particle mass) = 0.2
    Sets the kinetic energy scale in the tight-binding Hamiltonian.
  • DM (detector mass) = 0.5
    Sets the detector pointer kinetic energy scale.
  • delta (trigger threshold) = 0.7
    Converts continuous observable Ob_i into a binary 'triggered' decision; materially affects dot counts.
  • FT (final time) = 20.0
    Choice of integration horizon; histograms at FT=5.0 and 20.0 differ, indicating the outcome depends on when the snapshot is taken.
  • TS (time steps) = 20,000
    Chosen for numerical stability; no convergence study is provided.
  • epsilon (initial perturbation amplitude) = not tabulated
    Appears in Eq. (6) and controls the initial wavefunction spread; its value is not given in Table 1.
assumptions (6)
  • domain assumption The wavefunction is the complete description of atomic phenomena; there are no point particles and no irreducible probabilities.
    Stated in the abstract and Section 1; the entire program presupposes this.
  • ad hoc to paper A quartic WFE term proportional to the variance of each detector variable should be added to the Hamiltonian.
    Introduced in Section 3, Eq. (16); no derivation from experiment or first principles is given.
  • ad hoc to paper Distinguishable subsystems each carry their own WFE, rather than a single joint WFE.
    Proposed in Section 3 based on separability of Alice and Bob devices; not tested.
  • domain assumption The Tao explicit symplectic method with 20,000 time-steps accurately integrates the nonseparable nonlinear Hamiltonian.
    Section 5 and the Computational Appendix; the author says no proof exists that the program solves the model.
  • domain assumption A detector click is modeled by a threshold on the expectation value Ob_i = <psi|y_i|psi>.
    Section 2, Eq. (8), and Q&A; no microscopic amplifier mechanism is included.
  • ad hoc to paper Random outcomes across runs can be explained by sensitive dependence on initial conditions, or chaos, a la Poincare.
    Section 5 admits no formal chaos study for this model; the runs simply sample random initial z and theta.
invented entities (1)
  • Wave-Function Energy (WFE)
    purpose: Nonlinear quartic term added to the Hamiltonian to suppress macroscopic superpositions and force localized detector outcomes.
    WFE is a new physical energy term; the paper gives no independent measurement or experimental signature. It is the key device that makes dots appear.

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Cite this review

Pith. "Pith review of That Dot on the Screen: also, what about Born? and other objections to wavefunction physics." pith.science (2026). https://pith.science/paper/4MYVD43P

@misc{pith2026250417808,
  author       = {Pith},
  title        = {Pith review of: That Dot on the Screen: also, what about Born? and other objections to wavefunction physics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4MYVD43P}},
  note         = {Machine review of arXiv:2504.17808}
}
read the original abstract

In this paper I address the most common objections to the claim that Schrodinger was right in 1926: the wavefunction provides the correct, and complete, description of atomic phenomena. I suggest that the line of droplets in the Wilson cloud chamber, the click of the ``photon detector", and ``that dot on the screen" can all be explained within a context of wavefunction models and Schrodinger's-type equations, albeit nonlinear. No auxiliary hypotheses about point particles or probabilities are required. The random locations of the triggered ``particle detectors" can be explained by ``chaos" (meaning sensitive dependence on initial conditions). Even Born's ad hoc invocation of probabilities may be justifiable in certain circumstances. As an illustration, I present simulations from a (toy) wavefunction ``particle-detectors" model.

Figures

Figures reproduced from arXiv: 2504.17808 by the authors.

Figure 2
Figure 2. (slog(x) = sign(x) log(|x|).) [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 1
Figure 1. Results for two typical runs, using parameters from Table 1. Ob [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Plot of det M vs. time, with parameters from [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figures from the paper (1 more)
Figure 3
Figure 3. Figure 3: Histograms of That Dot on the Screen [PITH_FULL_IMAGE:figures/full_fig_p018_3.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Nonlinear Nonlocal: Comparing A. O. Barut's Theory to Mine with special emphasis on That Dot on the Screen

    quant-ph 2025-05 conditional novelty 4.0 of 10

    Barut's nonlinear self-energy term and the author's wavefunction energy term are shown to differ in distance behavior, and the author argues Barut's theory cannot explain single events.

Reference graph

Works this paper leans on

16 extracted references · 11 canonical work pages · cited by 1 Pith paper

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