Can the Infamous Boundary Be Found in Macromolecules? Also, von Neumann vs. Schroedinger ensembles, and `Hund's Paradox' in quantum chemistry

W. David Wick

REVIEW 3 major objections 4 minor 10 references

Can the Infamous Boundary Be Found in Macromolecules? Also, von Neumann vs. Schroedinger ensembles, and `Hund's Paradox' in quantum chemistry

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The quantum-classical split could be located at the scale of macromolecules, and the paper proposes two experiments that could reveal it.

desk verdict An honest, clearly written speculative essay that extends the author's own unparameterized nonlinear wavefunction idea to macromolecules; the experimental proposal cannot discriminate the mechanism because w is free. read the letter →

arxiv 2506.02227 v1 pith:X74CATQN submitted 2025-06-02 quant-ph physics.chem-ph

W. David Wick This is my paper

classification quant-phphysics.chem-ph

keywords InfamousBoundaryquantum-classicalsplitmacromoleculeschiralityHund'sparadoxthermalensemblesmeasurementproblemnonlinearwavefunctionenergy

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 split between quantum and classical behavior might occur at the scale of large organic molecules, not at the scale of laboratory apparatus. The location is tied to a choice between two thermal ensembles: one built only from energy eigenstates and one that admits superpositions of those states. The paper connects this choice to the old puzzle of why handed molecules are always observed in one localized form even though such forms are not exact energy eigenstates. It then proposes two experimental signatures, substrate conversion by a cooled enzyme and the polarization of light passing through a sample of enantiomers, that would reveal whether a cooled ensemble is a statistical mixture of the two forms or a superposition.

What carries the argument

The load-bearing object is a nonlinear energy functional $W_{FE}(\psi) = w N^2 D_N(\psi)$, in which $N$ is the number of degrees of freedom and $D_N$ is the center-of-mass dispersion of the wavefunction, with $w$ an unknown positive parameter. This term is added to the ordinary energy expectation in the wavefunction-based thermal ensemble. Because $D_N$ is taken to be much larger for $\psi_0$ and $\psi_1$ than for $\psi_A$ and $\psi_B$, the term can make the localized forms energetically preferred even when their ordinary quantum energies are higher. That reversal is what selects case I (mixture) versus case II (superposition) after cooling.

What would settle it

Cool a collection of a carefully chosen asymmetric enzyme nearly to its ground state and measure substrate conversion; if the substrate is always either fully converted or untouched, case I is supported, while any partial conversion would reveal case II superpositions, and finding only ordinary quantum behavior with no dependence on molecular size would rule out the mechanism.

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Extended reading notes

Core claim

The paper's central claim is that the 'Infamous Boundary' could be a property of macromolecules: if an extra nonlinear energy term grows with molecular size and with how spread out the molecule's center of mass is, then the normal energy ordering between localized and delocalized states can be reversed. Writing the localized chiral forms as $\psi_A$ and $\psi_B$ and their symmetric and antisymmetric superpositions as $\psi_0$ and $\psi_1$, the paper assumes the delocalized states have much larger center-of-mass dispersion. If the new term makes the localized forms lower in total energy, cooling yields a statistical mixture of the two forms (case I); if not, cooling leaves superpositions (case II). The paper's proposed experiments are designed to tell these two cases apart.

Load-bearing premise

The argument rests on an unmeasured extra energy term, never directly observed, whose strength is unknown; if that term is absent or only becomes significant at apparatus scale, the proposed boundary and the case I versus case II distinction both collapse.

Editorial extensions

If this is right

If case I is realized, cooling a sample of an enzyme whose only one isoform is active should yield either complete substrate conversion or none at all, never partial conversion.
If case II is realized, the same preparation should convert about half of the substrate, because the cooled ensemble would contain superpositions of the active and inactive forms.
For enantiomers, case I would show linearly polarized light after passing through the sample, whereas case II would show a superposition of opposite polarization states, which can appear as circularly polarized light.
Carrying out the experiment, or re-examining existing data on large molecules in interferometers, would let molecules be ranked by size and center-of-mass dispersion and would estimate the unknown strength parameter $w$.
If the boundary is set by molecular size and dispersion, molecules that are too large to sustain superpositions should exist, and finding them would place the quantum-classical split at a concrete, measurable scale.

Reading between the lines

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

A natural extension is that the transition between case I and case II should appear as a smooth crossover in molecular mass or center-of-mass dispersion, so existing and future interferometry data could be plotted to search for a threshold.
If case I is confirmed, the measurement problem enters biochemistry directly: active sites of large enzymes could behave quantum mechanically while their structural scaffolding behaves classically, which would change how enzyme catalysis is modeled.
Existing molecule-interference results already set an upper bound on where the boundary cannot be; re-analyzing them with the dispersion criterion could yield a first estimate of the unknown parameter $w$ without new experiments.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

You should know this is a speculative essay, not a research result. The author takes his 2017 nonlinear wavefunction term W_FE and asks what would happen if it switched on at the macromolecular scale instead of apparatus scale. That is the genuinely new move; everything else—the von Neumann vs Schrödinger ensemble clash, Hund's paradox, and the molecular-structure/measurement-problem link—restates earlier work, including his own.

The paper is well written and more honest than most: it explicitly says 'suggesting (certainly not proving)' in Section 1, flags the free parameter w in Section 7, and admits it has no practical experimental protocol. It also does a useful service by framing the question of whether Bell's boundary might sit at macromolecular scales and pointing to a possible research program (rank molecules by size and COM dispersion).

The soft spot is as big as the central claim. W_FE = w N² D_N(psi) is a postulate from the author's own 2017 arXiv paper, with w of unknown magnitude. Inequality (13), which assumes psi_0 and psi_1 have much larger COM dispersion than psi_A and psi_B, is asserted with no molecule and no calculation. And the proposed experiments cannot discriminate: complete conversion is case I, half conversion is case II, and the paper itself notes that standard decoherence, tunneling, or parity-violating energy differences give the same appearances. Since w can be adjusted to fit any outcome, the experiment is not a test of the mechanism; at best it might estimate w if the rest of the theory is presupposed.

None of this makes the paper incoherent or dishonest. It is a clearly-labeled suggestion. But it is not a derived result, and the advertised deliverable—an experimental setup that could reveal the Infamous Boundary—is not supported as stated.

Who is this for? Readers interested in foundations of quantum mechanics and the quantum-classical boundary, particularly in chemistry, may find it a thought-provoking pointer. It could be a useful reading-group piece to spark discussion about ensemble choice and Hund's paradox.

My recommendation: do not send this to a regular quant-ph referee as a research paper. If the venue has a speculative/essay track, it might merit peer review for the clarity of the question, but for a standard journal it is a desk reject. I would not cite it as evidence for anything, though I might mention it as an example of a self-cited, unparameterized proposal.

Referee Report

3 major / 4 minor

Summary. The paper asks whether Bell's 'Infamous Boundary' between quantum and classical behavior might lie at the scale of macromolecules rather than at the scale of laboratory apparatus. It contrasts von Neumann thermal ensembles, which contain only energy eigenstates, with Schrödinger thermal ensembles, which contain superpositions, and connects this distinction to Hund's paradox for chiral or isomeric molecules. The central mechanism is a nonlinear wavefunction-energy term W_FE(ψ)=w N^2 D_N(ψ) (Eq. 9) introduced from the author's 2017 theory. Section 5 defines two regimes: case I, where W_FE favors localized wavefunctions ψ_A and ψ_B, and case II, where superpositions ψ_0 and ψ_1 remain. Section 6 proposes enzyme-conversion and polarization experiments to distinguish the regimes. Section 7 acknowledges that w is a free parameter and that the proposed experiments may only allow an estimate of w.

Significance. The paper makes a useful conceptual connection between the choice of thermal ensemble, Hund's paradox, and the measurement problem, and it is candid about the conditional nature of its proposal. If the W_FE mechanism were independently established, locating the boundary at macromolecular scale would be a significant advance. However, the paper supplies no derivation or independent evidence for W_FE, no estimate of w or of the dispersion D_N, and no specific molecule for which the central inequality is shown to hold. The proposed experiments also fail to discriminate W_FE from standard alternatives such as decoherence, tunneling, or parity-violating energy differences, as the paper itself notes. The significance is therefore speculative rather than established.

major comments (3)

[Sec. 4, Eq. (9)] The entire argument depends on the nonlinear energy term W_FE(ψ)=w N^2 D_N(ψ), imported from the author's 2017 preprint [3] with w 'of unknown magnitude.' No physical derivation or empirical anchor is given for this term, and no argument is provided for why it should become significant at macromolecular sizes (N~10^3–10^5) rather than at apparatus scales (N~10^20). Because w is a free parameter, inequalities (13) and (16) can be satisfied in either direction by choosing w appropriately; the theory is therefore unfalsifiable in the form presented. Section 7's statement that the experiment 'may allow for an estimate of the magnitude of w' concedes that the experiment calibrates the model rather than tests its existence.
[Sec. 5, Eq. (13)] The classification into case I and case II rests entirely on inequality (13), which asserts that ψ_0 and ψ_1 have much larger center-of-mass dispersion than ψ_A and ψ_B, together with inequalities (14)–(16), which assert that the W_FE differences dominate the ordinary Hamiltonian energy differences. No specific molecule or substrate is identified, no dispersion or size estimate is computed, and no physical argument is supplied for the required ordering. Without an independent derivation or at least a concrete numerical estimate, the central conditional claim has no load-bearing support.
[Sec. 6] The proposed experimental signatures are not discriminating. Complete versus half conversion of a substrate, or linear versus circular polarization of transmitted light, can be accounted for not only by case I and case II but also by standard mechanisms that the paper itself lists in Section 7: decoherence, tunneling, and parity-violating energy differences. Since w is adjustable, the W_FE theory can accommodate every possible outcome in both regimes, so no experiment described in Section 6 would confirm the W_FE mechanism over these alternatives.

minor comments (4)

[Sec. 2] The phrase 'Avon Neumann Thermal Ensemble' appears to be a typo and should read 'A von Neumann Thermal Ensemble.'
[Sec. 2, Eq. (4)] The integration domain designated as '[P |a_n|^2=1]' is not defined as a measure space; please specify the uniform measure on the unit sphere in the coefficient space.
[Sec. 4] In the discussion of possibility (a), 'nothing happens (no registrations)' is unclear; it should specify whether the apparatus pointer remains in its initial state or whether no measurement outcome is produced.
[References] References [3], [4], [5], and [10] are arXiv preprints; please update their publication status or provide DOIs in a journal version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the macromolecular-boundary claim is an openly conditional hypothesis built on an explicit free parameter, not a derivation that reduces to its own inputs.

full rationale

The paper's central mechanism is W_FE(ψ) = w N^2 D_N(ψ) (Eq. 9), introduced in Section 4 as an assumption from the author's own 2017 work, with w explicitly described as 'a positive parameter (of unknown magnitude)'. Section 5 asks 'What if it is functional at the level of macromolecules?' and then derives conditional consequences: under inequality (13) and energy comparison (14), case I yields a statistical mixture of A and B; under inequality (16), case II yields superpositions. The experimental outcomes in Section 6 (complete vs. half conversion, linear vs. circular polarization) are consequences of these cases, not definitions of the cases themselves. Section 7 openly admits that the theory contains a free parameter w and that the proposed experiment 'may allow for an estimate of the magnitude of w'. The self-citation to [3] is load-bearing in the sense that the nonlinear term is taken from that prior paper, but the present paper does not present that term as an independent external proof; it labels it as an assumption. There is no fitted parameter renamed as a prediction, no equation where the predicted quantity is identical by construction to an input, and no uniqueness theorem imported from the author's own work. The case I/II dichotomy does make the proposal weakly falsifiable, and the unconstrained w and assumed inequality (13) are substantive scientific weaknesses, but these are testability and support concerns, not circularity. Accordingly, no circular step can be exhibited with a specific equation-to-equation reduction, and the honest finding is no significant circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 1 invented entities

The predictive content of the paper rests on the author's own WFE energy term with a free parameter w, an assumed shift of its activation scale from apparatus to macromolecules, and an assumed dispersion inequality for isoform states. The ensemble formalism is standard or drawn from prior work including the author's ref [10]. There are no data fits, but w is free to accommodate any experimental outcome, which is the paper's central weakness.

free parameters (1)

w (WFE coupling constant) = unknown; 'positive parameter (of unknown magnitude)' per Section 4
Sets the strength of the nonlinear term W_FE = w N^2 D_N(psi). Which branch (case I or case II) applies at macromolecule scale is governed by w; Section 7 says the proposed experiment 'may allow for an estimate of the magnitude of w', so w is free to absorb any observed outcome.

assumptions (5)

ad hoc to paper The nonlinear energy term W_FE(psi) = w N^2 D_N(psi) exists and adds to the Hamiltonian energy.
Postulated in the author's 2017 theory (ref [3]) and restated in Section 4, Eq. 9; no derivation or independent evidence is provided here, and every later prediction depends on it.
ad hoc to paper W_FE may become significant at macromolecular scales, not only at apparatus scales (N about 10^20).
Section 5 introduces this by asking 'What if it is functional at the level of macromolecules?'; it is a change of scale assumption without new evidence.
domain assumption For enantiomers/isoforms, psi_A and psi_B have small center-of-mass dispersion, while psi_0 and psi_1 have large dispersion.
Inequality (13) in Section 5 is stated as a supposition ('Suppose...'); it is the mechanism that makes cooling favor mixtures over superpositions.
domain assumption The von Neumann and Schrodinger thermal ensembles are physically distinct and the difference is observable in principle.
Defined in Section 2; whether the ensemble choice matters at macromolecule scale is the paper's hypothesis, supported only by the author's own ref [10].
standard math The Hamiltonian in a finite box has purely discrete spectrum.
Section 2, Eq. (2); standard background assumption for confined systems.

invented entities (1)

W_FE, a nonlinear wavefunction energy functional w N^2 D_N(psi)
purpose: To penalize superpositions with large center-of-mass dispersion, converting Schrodinger superpositions into statistical mixtures at some length scale; the central mechanism behind case I.
Introduced in the author's prior work (ref [3]) and central to this paper (Eq. 9). Its strength is set by the free parameter w and its activation scale is assumed, so it has no falsifiable handle outside the author's own framework; the proposed experiment would only estimate w (Section 7).

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Cite this review

Pith. "Pith review of Can the Infamous Boundary Be Found in Macromolecules? Also, von Neumann vs. Schroedinger ensembles, and `Hund's Paradox' in quantum chemistry." pith.science (2026). https://pith.science/paper/X74CATQN

@misc{pith2026250602227,
  author       = {Pith},
  title        = {Pith review of: Can the Infamous Boundary Be Found in Macromolecules? Also, von Neumann vs. Schroedinger ensembles, and `Hund's Paradox' in quantum chemistry},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/X74CATQN}},
  note         = {Machine review of arXiv:2506.02227}
}

read the original abstract

John Bell coined the phrase ``Infamous Boundary" for the point where classical physics splits off from quantum physics. Many authors, including the present one, have advanced theories with the intention of defining and locating this ``shifty split"; most propose that it lies somewhere on the scale of apparatus. But what if it resides at the level of macromolecules? I show here that this question is intimately connected to the choice of thermal ensembles and to the so-called `Hund's Paradox' in quantum chemistry. I propose an experimental set-up that could in principle reveal the IB lurking in asymmetric macromolecules.

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Reference graph

Works this paper leans on

10 extracted references · 8 canonical work pages

[3]

On Non-Linear Quantum Mechanics and the Measurement Problem I: Blocking Cats

Wick, W. D. “On Non-Linear Quantum Mechanics and the Measurement Problem I: Blocking Cats”, ArXiv 1710.03278 (October 2017)

arXiv 2017
[1]

English translation of the original German text (1932), published by Princeton University Press (1955)

von Neumann, J.The Mathematical Foundations of Quantum Mechan- ics. English translation of the original German text (1932), published by Princeton University Press (1955)

work page 1932
[2]

On the Explanation of Molecular Spectra, II

Hund, F. “On the Explanation of Molecular Spectra, II”, Zeitschrift fur Physik, 42, 43-120 (1927). The Infamous Boundary and macromolecules12

work page 1927
[4]

On Non-Linear Quantum Mechanics and the Measurement Problem III: Poincar´ e Probability and ... Chaos?

Wick, W. D. “On Non-Linear Quantum Mechanics and the Measurement Problem III: Poincar´ e Probability and ... Chaos?” ArXiv 1803.1126v1 published March 2018

work page arXiv 2018
[5]

Chaos in a Nonlinear Wavefunction Model: An Alternative to Born’s Probability Hypothesis

Wick, W. D. “Chaos in a Nonlinear Wavefunction Model: An Alternative to Born’s Probability Hypothesis”. ArXiv 2502.02698. (4 Feb. 2025)

arXiv 2025
[6]

The Problem of Molecular Structure Just is the Measurement Problem

Franklin, A and Seifert, V. A. “The Problem of Molecular Structure Just is the Measurement Problem”. Brit J Phil Science, 75(1) 2024, also available over the Internet

work page 2024
[7]

Quantum superposition of molecules beyond 25 kDa

Fein, Y. Y.et al.“Quantum superposition of molecules beyond 25 kDa”. Nat Phys. 15, 1242-1245 (2019)

work page 2019
[8]

D.The Infamous Boundary: Seven Decades of Heresy in Quantum Physics.With a mathematical appendix by William Faris

Wick, W. D.The Infamous Boundary: Seven Decades of Heresy in Quantum Physics.With a mathematical appendix by William Faris. Birkh¨ auser, 1995 (hard-bound, with a different subtitle) and Coperni- cus, 1996 (paperback, with an index)

work page 1995

Show all 10 references

[9]

hectograph

Schr¨ odinger, E.Statistical Thermodynamics. 2nd edition (1952); reprinted, except for a Note to the reader and a new Appendix, from a “hectograph” of a lecture he gave in 1944 in Dublin

1952
[10]

On Schr¨ odingerist Quantum Thermody- namics

De Carlo, L. and Wick, W. D. “On Schr¨ odingerist Quantum Thermody- namics”. ArXiv 2208.07688 (2022, revised in 2024). Journal publication: “On Magnetic Models in Wavefunction Ensembles”. Entropy 25(4) 564 (2023)

2023 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [3]

On Non-Linear Quantum Mechanics and the Measurement Problem I: Blocking Cats

Wick, W. D. “On Non-Linear Quantum Mechanics and the Measurement Problem I: Blocking Cats”, ArXiv 1710.03278 (October 2017)

arXiv 2017

[2] [1]

English translation of the original German text (1932), published by Princeton University Press (1955)

von Neumann, J.The Mathematical Foundations of Quantum Mechan- ics. English translation of the original German text (1932), published by Princeton University Press (1955)

work page 1932

[3] [2]

On the Explanation of Molecular Spectra, II

Hund, F. “On the Explanation of Molecular Spectra, II”, Zeitschrift fur Physik, 42, 43-120 (1927). The Infamous Boundary and macromolecules12

work page 1927

[4] [4]

On Non-Linear Quantum Mechanics and the Measurement Problem III: Poincar´ e Probability and ... Chaos?

Wick, W. D. “On Non-Linear Quantum Mechanics and the Measurement Problem III: Poincar´ e Probability and ... Chaos?” ArXiv 1803.1126v1 published March 2018

work page arXiv 2018

[5] [5]

Chaos in a Nonlinear Wavefunction Model: An Alternative to Born’s Probability Hypothesis

Wick, W. D. “Chaos in a Nonlinear Wavefunction Model: An Alternative to Born’s Probability Hypothesis”. ArXiv 2502.02698. (4 Feb. 2025)

arXiv 2025

[6] [6]

The Problem of Molecular Structure Just is the Measurement Problem

Franklin, A and Seifert, V. A. “The Problem of Molecular Structure Just is the Measurement Problem”. Brit J Phil Science, 75(1) 2024, also available over the Internet

work page 2024

[7] [7]

Quantum superposition of molecules beyond 25 kDa

Fein, Y. Y.et al.“Quantum superposition of molecules beyond 25 kDa”. Nat Phys. 15, 1242-1245 (2019)

work page 2019

[8] [8]

D.The Infamous Boundary: Seven Decades of Heresy in Quantum Physics.With a mathematical appendix by William Faris

Wick, W. D.The Infamous Boundary: Seven Decades of Heresy in Quantum Physics.With a mathematical appendix by William Faris. Birkh¨ auser, 1995 (hard-bound, with a different subtitle) and Coperni- cus, 1996 (paperback, with an index)

work page 1995