On blocking Dispersion of Matter by Energy conservation

Leonardo De Carlo

arxiv: 2403.13699 · v11 · submitted 2024-03-20 · 🪐 quant-ph · cond-mat.stat-mech

On blocking Dispersion of Matter by Energy conservation

Leonardo De Carlo This is my paper

Pith reviewed 2026-05-24 03:35 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech

keywords nonlinear termsenergy conservationwavefunction dispersionmacroscopic superpositionscommutation relationsspin modelsmeasurement problemcollapse models

0 comments

The pith

Nonlinear terms that block spatial wavefunction dispersion by energy conservation satisfy the derived commutation relations, but their generalization to non-pure spin models does not.

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

The paper reviews a mechanism in which nonlinear terms added to the Schrödinger equation suppress macroscopic superpositions through energy conservation. It derives the commutation relations these terms must obey to remain physically admissible. The original terms that confine the wavefunction in space meet the relations, while the generalized versions intended for spin models to produce finite-temperature magnetization do not. A toy model illustrates that spatial cats encounter an energy barrier. The work ends with a comparison to standard collapse models.

Core claim

The nonlinear terms confining the wavefunction in space satisfy the commutation relations required for physical admissibility under energy conservation. When these terms are generalized to non-pure spin models, they fail to satisfy the same relations, which may account for earlier observations about magnetization at finite temperature.

What carries the argument

Commutation relations that nonlinear terms must satisfy to preserve physical admissibility when energy conservation is used to suppress macroscopic superpositions.

If this is right

Spatial confining terms remain consistent with energy conservation.
Generalized spin terms violate the commutation relations needed for admissibility.
Formation of spatial cats is blocked by an energy barrier in the toy model.
The failure for non-pure states supplies an interpretation of prior magnetization results.

Where Pith is reading between the lines

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

Only a restricted class of nonlinear modifications can block dispersion while respecting energy conservation.
The mechanism may require pure-state assumptions to function for spin systems.
Direct tests could search for the predicted energy cost when superpositions attempt to form across separated locations.

Load-bearing premise

The nonlinear terms must obey specific commutation relations derived from energy conservation to count as physically admissible.

What would settle it

An explicit check, for a chosen non-pure spin Hamiltonian, of whether the generalized nonlinear term commutes with the total energy operator in the manner required by the derived relations.

Figures

Figures reproduced from arXiv: 2403.13699 by Leonardo De Carlo.

read the original abstract

In [L. De Carlo and W. D. Wick, Entropy 25, 564 (2023)], we considered the problem of wavefunction ensembles for spin models. To observe magnetization at finite temperature, we had to add macroscopic nonlinear terms that suppress macroscopic superpositions by energy conservation. The nonlinear terms were of the kind introduced in [W. D. Wick, arXiv:1710.03278 (2017)] to block spatial cats by energy conservation, proposed as a solution to the Measurement Problem. Reviewing this theory, I derive commutation relations that these nonlinear terms have to satisfy to be physically admissible, and show that the ones confining the wavefunction in space do indeed satisfy these relations. I generalize the terms of [L. De Carlo and W. D. Wick, Entropy 25, 564 (2023)] for non-pure spin models and check if they also satisfy the constraints, concluding with a negative answer and possibly giving an interpretation of the previous results. With a toy model I present the main experimental idea, that is that forming spatial cats meets an energy barrier. A comparison with Collapse Models is at the end.

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.

Desk Editor's Note private letter to a colleague

This paper derives commutation relations for the nonlinear terms and reports that the spatial versions satisfy them while the generalized non-pure spin versions do not.

read the letter

The core point is a consistency check: the nonlinear terms meant to block spatial superpositions via energy conservation pass the derived commutation relations, but extending them to non-pure spin models fails that test. The paper also sketches a toy model for the energy barrier idea and compares briefly to collapse models. That negative result on the spin generalization is the main new piece, along with spelling out the commutation conditions themselves. The spatial terms get a clean pass, which at least confirms internal consistency in that case. The work stays tightly focused on the framework from the 2023 Entropy paper and the 2017 arXiv preprint, so the algebra is an extension rather than a fresh start. The negative finding for the spin case is stated plainly and could be useful to anyone trying to build on those earlier nonlinear terms. The main limitation is that the whole exercise sits inside the same author-overlapping setup, so the commutation relations are not independently motivated from outside that line of work. Without the explicit steps in front of me it is hard to judge how tight the negative conclusion really is or whether a different generalization might slip through. This is niche material aimed at people already tracking nonlinear modifications to quantum mechanics for the measurement problem. A reader working on energy-conservation constraints or collapse-model alternatives might find the negative result and the toy model worth a look, but it will not move the broader discussion. The paper is coherent enough on its own terms to deserve referee time rather than a desk rejection; the negative claim is checkable in principle even if the overall approach remains debatable.

Referee Report

2 major / 1 minor

Summary. The manuscript reviews the theory of nonlinear terms introduced to block spatial superpositions of matter via energy conservation, as proposed in prior works. It derives commutation relations required for these terms to be physically admissible, verifies that the spatial-confining terms satisfy the relations, generalizes the terms from the 2023 De Carlo-Wick paper to non-pure spin models, and reports that the generalizations fail the constraints. A toy model illustrates the experimental idea of an energy barrier preventing spatial cats, with a final comparison to collapse models.

Significance. If the algebraic verification holds, the work supplies a consistency check on the nonlinear terms from the 2023 Entropy paper, supporting their use for suppressing macroscopic superpositions while highlighting limitations when extending to generalized spin models. The negative result for the generalizations may interpret prior findings on magnetization. The toy model is a strength, as it points toward a concrete, falsifiable experimental test involving energy barriers. These elements add to the literature on energy-conservation-based approaches to the measurement problem.

major comments (2)

[Review of the theory and derivation of commutation relations] The commutation relations are obtained by reviewing the 2023 De Carlo-Wick paper and the 2017 Wick arXiv preprint. To permit independent assessment of the claim that the generalized terms fail the constraints, the explicit algebraic steps computing the commutators for the generalized nonlinear terms (including their action on non-pure states) should be supplied in the manuscript rather than referenced externally.
[Toy model for experimental idea] The toy model section presents the experimental idea that forming spatial cats meets an energy barrier, but provides no quantitative estimates (e.g., barrier height in energy units, relevant timescales, or coupling parameters) that would allow evaluation of experimental feasibility or direct comparison with the commutation-relation constraints.

minor comments (1)

[Abstract] The abstract and introduction use first-person singular ('I generalize', 'I derive'); for journal style, consider consistent use of 'we' or passive voice.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback on our manuscript. We address each major comment below and will incorporate the suggested improvements in a revised version.

read point-by-point responses

Referee: [Review of the theory and derivation of commutation relations] The commutation relations are obtained by reviewing the 2023 De Carlo-Wick paper and the 2017 Wick arXiv preprint. To permit independent assessment of the claim that the generalized terms fail the constraints, the explicit algebraic steps computing the commutators for the generalized nonlinear terms (including their action on non-pure states) should be supplied in the manuscript rather than referenced externally.

Authors: We agree that explicit algebraic details would strengthen the manuscript and allow independent verification. In the revised version, we will add an appendix providing the full step-by-step computation of the commutators for the generalized nonlinear terms, including their explicit action on non-pure states and demonstration that the constraints are not satisfied. revision: yes
Referee: [Toy model for experimental idea] The toy model section presents the experimental idea that forming spatial cats meets an energy barrier, but provides no quantitative estimates (e.g., barrier height in energy units, relevant timescales, or coupling parameters) that would allow evaluation of experimental feasibility or direct comparison with the commutation-relation constraints.

Authors: We acknowledge that quantitative estimates would improve the toy model's utility for assessing feasibility. In the revision, we will add order-of-magnitude estimates for the energy barrier height (relative to typical spin-interaction scales), relevant timescales, and coupling parameters, using standard values from condensed-matter systems to permit comparison with the commutation constraints. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper reviews prior self-cited works to derive commutation relations for physical admissibility under energy conservation, then performs a consistency check showing that spatial-confining nonlinear terms satisfy them while a generalization to non-pure spin models does not. No explicit equations, derivation steps, or reductions are supplied in the provided text that would allow exhibiting a specific reduction of the central claim to its inputs by construction (e.g., a fitted parameter renamed as prediction or a self-citation chain that is itself unverified). The consistency test on the generalized terms is presented as an independent computational verification, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the work rests on the prior nonlinear terms and the assumption that energy conservation imposes commutation constraints; no new free parameters or invented entities are explicitly introduced in the provided text.

axioms (1)

domain assumption Nonlinear terms must satisfy specific commutation relations to be physically admissible under energy conservation
Stated when the paper reviews the theory and derives the conditions the terms have to obey

pith-pipeline@v0.9.0 · 5723 in / 1238 out tokens · 27923 ms · 2026-05-24T03:35:53.927283+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the term E_WFE(ψ)=wN^{2}D_X(ψ,ψ*) ... to forbid the states (3) by energy conservation
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean J_uniquely_calibrated_via_higher_derivative echoes

?

echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

derive commutation relations that these nonlinear terms have to satisfy to be physically admissible

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · 2 internal anchors

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author author E. Schrödinger ,\ title The exchange of energy according to wave-mechanics , \ in\ @noop booktitle Collected Papers on Wave Mechanics \ ( publisher Blackie & Son Limited ,\ address London and Glasgow ,\ year 1928 )\ pp.\ pages 137--146 NoStop

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work page 2016

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author author W. D. \ Wick ,\ @noop title That dot on the screen: also, what about born? and other objections to wavefunction physics , \ howpublished arXiv:2504.17808 ( year 2025 b ) NoStop

work page arXiv 2025

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author author A. Ashkin , author J. M. \ Dziedzic , author J. E. \ Bjorkholm , \ and\ author S. Chu ,\ title title Observation of a single-beam gradient force optical trap for dielectric particles , \ @noop journal journal Opt. Lett. \ volume 11 ,\ pages 288--290 ( year 1986 ) NoStop

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Sadler , author J

author author L. Sadler , author J. Higbie , author C. Hetherington , author S. Schmid , author M. Pasienski , \ and\ author D. M. \ Stamper-Kurn ,\ title Periodically-dressed Bose-Einstein condensate in ^ 87 Rb , \ NoStop

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title author author G. C. \ Ghirardi , author A. Rimini , \ and\ author T. Weber ,\ title title Unified dynamics for microscopic and macroscopic systems , \ @noop journal journal Phys. Rev. D \ volume 34 ,\ pages 470 ( year 1986 ) NoStop

work page 1986

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