Becoming classical: A possible influence on the quantum-to-classical transition

C. L. Herzenberg

REVIEW

Becoming classical: A possible influence on the quantum-to-classical transition

C. L. Herzenberg

General Physics · Submitted 23 Feb 2006 · 1 reference

Pith's verdict: A clean dimensional analysis built on a category error: Hubble-flow velocity spread is not a quantum uncertainty, so the 0.1 mm threshold has no physical basis.

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arXiv IDphysics/0602161 (version 1)

Pith IDWOQE3PY3, Pith's permanent record of this paper and its review

CitationC. L. Herzenberg. "Becoming classical: A possible influence on the quantum-to-classical transition." arXiv:physics/0602161 (2006). https://pith.science/paper/WOQE3PY3

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Editor's note

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Colleague — this is a short speculative note that has one genuinely new idea and one load-bearing misstep. The new idea is to let the Hubble-flow velocity gradient across an extended object define a quantum-classical boundary; solving Δx = L gives Lcr ~ 0.1 mm for density 1 g/cc, a number that lands in an interesting territory. The derivation is transparent, the arithmetic is correct, and the author is honest in the text that the limit is not stringent.

The trouble is the single sentence that makes the whole argument: the spread in Hubble velocities is treated as 'an uncertainty in velocity associated with the object.' That is not a quantum uncertainty. In quantum mechanics, Δp in the Heisenberg relation is the width of the momentum distribution of the object's center-of-mass wavefunction. A deterministic classical velocity field, especially one that is canceled in the rest frame of a bound object, does not produce such a width. Bound objects do not recede from themselves; the leading effect of cosmic expansion on a bound system is a tidal/curvature correction of order H0^2, not a relative velocity H0 L. So Eq. (2) is a category error, and Eqs. (3)-(5) inherit it.

The paper is not circular — it solves a self-consistency condition and doesn't fit parameters — but the missing physical identification is fatal. The abstract's 'real and significant influence' overstates what even the author concedes in the final paragraphs. No prior work is cited, so the idea appears original, but originality alone doesn't carry it.

Who is this for? A reader who wants a cautionary example of how dimensional analysis can dress a conceptual error. It might be a fun reading-group discussion piece, but not a paper I'd ask a referee to carefully evaluate. I'd desk reject; the central premise is wrong in a way referees can't fix.

Recommendation: reject, no external review.

Referee report

Major objections (3)

[After Eq. (1)] The load-bearing assumption is stated in the sentence: "Let us treat the spread in velocities at different locations in the object as providing an order of magnitude estimate of an uncertainty in velocity associated with the object." This identification is unjustified. In quantum mechanics, the velocity uncertainty entering the Heisenberg relation is the standard deviation of the velocity operator in the quantum state of the object's center of mass. A deterministic, classical Hubble-flow velocity field does not create such a quantum width. Moreover, bound objects do not recede with cosmic expansion: in the local inertial frame of a freely falling observer, the leading effect of FRW expansion on a bound system is a tidal/curvature correction of order H0^2 L, not a relative velocity H0 L. Thus Eq. (2) has no physical basis as a momentum uncertainty.
[Eq. (2)] Even if one grants a velocity spread Δv ≈ H0 L, the product m Δv with m the total mass of the object is not the momentum uncertainty of the object as a whole. The Hubble-flow spread is a differential motion between the constituent parts of the extended body; it contributes to the internal relative kinetic energy, not to the center-of-mass momentum uncertainty. Inserting the total mass conflates internal degrees of freedom with the collective quantum state of the object. This invalidates the subsequent derivation of Δx in Eqs. (3) and (4) and the threshold in Eq. (5).
[Eq. (5)] The self-consistency condition Δx = L is not circular, but it is a threshold condition that depends entirely on the invalid Δp. Furthermore, the derivation implies a universal, state-independent minimum position uncertainty for every object of given size and density, which is not a feature of standard quantum theory: the Heisenberg uncertainty for a center-of-mass state depends on how that state is prepared. The paper provides no mechanism by which the Hubble flow would prepare the required momentum spread, so the physical content of the threshold remains unsupported.

Minor objections (3)

[Throughout] The notation for the Hubble constant is inconsistent: "Ho" and "H o" are used interchangeably; H0 (with a subscript zero) is standard.
[Discussion] The paper mentions decoherence but does not cite the substantial literature on the quantum-classical transition (e.g., Zurek, Joos, or Zeh). A brief discussion of how the proposed limit relates to known decoherence mechanisms would strengthen the context, though it would not repair the main flaw.
[Introduction] The phrase "may be regarded as potentially moving apart" is hedged in a way that undercuts the derivation; the paper should either justify the physical reality of internal recession or remove the hedge.

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The paper

The paper claims

The paper claims that cosmic expansion sets a fundamental quantum-classical boundary at about 0.1 millimeter (roughly a microgram of mass), above which whole objects must behave classically.

The reading

This paper tries to establish that the expansion of the universe leaves a mark on everyday objects: the Hubble flow across any extended body gives it a tiny spread of velocities, and treating that spread as a quantum uncertainty generates a minimum uncertainty in position. Requiring that this position uncertainty not exceed the object's own size yields a threshold length of about 0.1 millimeter, or a mass of about a microgram, at ordinary density. Above that threshold, the paper argues, an object should behave classically as a whole; below it, quantum behavior as a whole object is not ruled out. The author presents the result as an order-of-magnitude, fundamental limit rather than a precise boundary, offering a cosmic source for classical behavior that would operate even without environmental decoherence.

What carries the argument

The load-bearing device is the substitution of the Hubble-flow velocity spread for a quantum velocity uncertainty. The identity $\Delta v \approx H_0 L$, where $H_0$ is the Hubble constant and $L$ the object's size, is combined with the Heisenberg inequality through $\Delta p = m\Delta v$; imposing $\Delta x \approx L$ then produces the threshold formula $L_{\rm cr} \approx [h/(4\pi\rho H_0)]^{1/5}$. This one formula turns a very small classical expansion rate into a macroscopic cutoff near 0.1 millimeter.

Extended reading notes

Core claim

The central claim is that cosmic expansion itself supplies the dividing line between quantum and classical behavior. For an object of size $L$ and density $\rho$, the spread of recessional velocities across the object is $\Delta v \approx H_0 L$; multiplying by the mass turns this into a momentum uncertainty $\Delta p \approx m H_0 L$. The Heisenberg relation then implies a position uncertainty $\Delta x \approx h/(4\pi m H_0 L)$, and setting $\Delta x = L$ gives a critical size $L_{\rm cr} \approx [h/(4\pi\rho H_0)]^{1/5}$. With $\rho \approx 1\,\mathrm{g/cm^3}$ and $H_0 \approx 2.3\times 10^{-18}\,\mathrm{s^{-1}}$, this is about 0.1 millimeter, so objects larger than that (or more massive than about a microgram) are predicted to behave classically as whole objects.

Load-bearing premise

The whole derivation rests on treating the Hubble-flow spread across a bound object as a genuine quantum uncertainty in velocity, when cosmic expansion is a coherent classical motion and bound objects do not actually recede from themselves.

Editorial extensions

If this is right

If the claim is correct, objects larger than roughly 0.1 millimeter (or heavier than about a microgram) at ordinary density should show classical center-of-mass behavior even in the absence of environmental decoherence.
The mechanism depends only on density and the Hubble constant, so it would apply universally to any extended body regardless of composition.
Below the threshold, quantum behavior of an entire object is not excluded by this effect, so the proposal is a size-and-mass cutoff rather than a sharp universal law.
The threshold does not conflict with observed quantum behavior of molecules, which are far smaller than 0.1 millimeter.
For objects above the threshold, quantum effects would be expected only among internal constituents, not for the object's motion as a whole.

Reading between the lines

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

If the argument were correct, a concrete testable consequence is that center-of-mass interference experiments on objects approaching the microgram scale should encounter a fundamental classical floor; current levitated-interference experiments are moving toward that scale.
A natural extension the paper does not develop is the density scaling: because the threshold scales as $\rho^{-1/5}$, changing the density by a factor of 1000 shifts the cutoff by only a factor of about 4, which could serve as a distinctive signature across materials.
The same Hubble-flow logic, applied to internal coordinates, would suggest a universal coherence length in matter that is independent of temperature, an effect distinct from ordinary thermal decoherence.

Original abstract

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using an uncertainty in position estimated from the spread in velocities associated with its size, the criterion that the uncertainty in position should be smaller than the extension of the object leads to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,032 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using an uncertainty in position estimated from the spread in velocities associated with its size, the criterion that the uncertainty in position should be smaller than the extension of the object leads to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world.	background 0.88	0.11	0.18	hedged possibility 1.00
s1	Calculations suggest that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior.	result 0.40	0.50	0.60	hedged possibility 1.00
s2	Using an uncertainty in position estimated from the spread in velocities associated with its size, the criterion that the uncertainty in position should be smaller than the extension of the object leads to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.	result 0.51	0.77	0.68	hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.50.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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Papers whose main result relates to this one's

How each label was checked · JSON

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper

A calculation suggests that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior.

A possible cosmological effect on the quantum-to-classical transition · 1.00

Discussion

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[1] [1]

Chicago, IL 60637-5092 carol@herzenberg.net quantum to classical.doc 20 February 2006 draft, revised

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