On a recent explanation of the dynamics of the Meissner effect within the conventional theory of superconductivity

J. E. Hirsch

REVIEW 4 major objections 6 minor 11 references

On a recent explanation of the dynamics of the Meissner effect within the conventional theory of superconductivity

T0 review · 4 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read A recent explanation of the Meissner effect's dynamics is a tautology, this paper argues, and a cavity experiment can prove it.

desk verdict A pointed reply whose core critique of Markos-Hlubina's prescribed f(r,t) is correct, but whose proposed experiment and 'nonexistent force' charge are not yet secured. read the letter →

arxiv 2512.16938 v2 pith:2ZNDC4N3 submitted 2025-12-12 cond-mat.supr-con

J. E. Hirsch This is my paper · ORCID

classification cond-mat.supr-con

keywords MeissnereffectLondonequationsuperconductivitydynamicaltransitioncavityexperimentradialchargeflowmagneticfieldexpulsionconventionaltheory

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 a recently proposed explanation of the Meissner effect's dynamics within conventional superconductivity theory is not an explanation at all. The proposal inserts a time-dependent superconducting fraction f(r,t) into the London equation and shows that any such function that goes from zero to one expels the magnetic field. The author's point: that just restates the problem, since the physics that creates f(r,t) is exactly what is unexplained. The paper also proposes a concrete experiment—a superconductor with a small empty cavity—where the two theories give different final states, so the disagreement can be tested.

What carries the argument

The argument turns on the generalized London equation, which replaces the constant superconducting density with an arbitrary spacetime-dependent fraction f(r,t). The paper shows this equation contains a term proportional to ∂f/∂t times the vector potential, which acts as a nonexistent force, and that the entire dynamical content is absorbed into the hand-chosen f(r,t). The proposed experimental discriminator is a long superconducting cylinder with a small empty cylindrical cavity at its center, cooled in a uniform axial field.

What would settle it

Cool a superconducting cylinder with a small empty cavity in a uniform magnetic field and observe the final magnetic field distribution. If the field in the cavity is fully expelled and the entire metal becomes superconducting, the paper's central objection is falsified; if normal regions persist above and below the cavity, the standard theory's prediction is falsified.

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Extended reading notes

Core claim

The paper's central claim is that the generalized London equation with an externally prescribed superconducting fraction cannot account for the Meissner effect's dynamics. Whatever function f(r,t) one chooses, as long as it interpolates between the normal and superconducting states, the equations will describe field expulsion; the choice of f(r,t) encodes the entire missing physics. The paper further claims that because expelling a magnetic field requires outward radial charge flow, an empty cavity cannot expel its field, so a cylinder with a cavity should end up with normal regions above and below the cavity, opposite to the prediction of the standard theory.

Load-bearing premise

The prediction that normal regions persist relies on the premise that a magnetic field cannot be expelled from a region unless electric charge can flow outward from that region, and that premise is asserted rather than derived in this paper.

Editorial extensions

If this is right

If the critique holds, the recent generalized-London-equation approach leaves the four central questions about forces, momentum conservation, and reversibility unanswered.
The proposed cavity experiment offers a clean binary outcome: either the field in the cavity is fully expelled (supporting the standard view) or normal regions persist above and below the cavity (supporting the author's charge-expulsion view).
The same logic applies to the Becker-London effect in rotating superconductors, so the critique extends beyond the Meissner case.
If the standard theory's prediction of full expulsion is confirmed, the author's long-standing objections would be shown to be unfounded.

Reading between the lines

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

The cavity experiment may be hard to realize in practice because a truly empty cavity with no material walls is difficult; but even an approximate version could be informative.
The charge-expulsion premise, if correct, implies the Meissner effect is inherently a dynamical charge-separation phenomenon, which would connect to surface and transport properties in ways not captured by static London theory.
The logical structure of the critique—that inserting a time-dependent order parameter as an input is a tautology—applies to any theory that parameterizes a phase transition without deriving the parameter's evolution.
A positive result for the standard theory (full expulsion) would not necessarily validate the generalized London equation's dynamical details, only its final-state prediction; the dynamics would remain a separate question.

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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

Colleague,

The thing to know: this is a reply piece, not a new result. Hirsch's central objection to Markos-Hlubina is well placed and worth taking seriously: if you prescribe f(r,t) evolving from 0 to 1, you've already built in the Meissner expulsion, and that tells you nothing about the mechanism. MH themselves concede they can't address how phase coherence forms. On that core point, the paper is right.

Where it gets soft: the paper calls the -∂f/∂t A term in MH's acceleration equation a nonexistent force. That's too quick. MH's equation is a London-type constitutive relation written in canonical momentum language; whether it represents a physical force is exactly what's at issue, and Hirsch hasn't dismantled that formulation by assertion. The four objections in Sec. III are mostly a re-run of his earlier papers, and the only genuinely new element is the cavity experiment. But that experiment is not actually solved. The MH prediction in Fig. 2 is left as 'an exercise for the reader,' and since f is an external input in MH's formalism, the final state depends on the assumed f. The Hirsch prediction in Fig. 4 rests entirely on the premise, from Ref. [8], that expelling a field requires outward radial charge flow in that region. That premise may be right, but it's not derived or independently verified here. So the proposed test is conditional: if the premise holds and the computation is done, it discriminates; as written, it doesn't.

Who should read it: anyone following the Hirsch conventional-theory debate, especially the MH response. It's not a standalone contribution, but as a comment it's a legitimate challenge. A serious referee should send it out, but the referee should insist the cavity computation be supplied and the charge-expulsion premise be backed by something other than self-citation. I wouldn't cite it in my own work; I'd probably read it and the MH paper together in a reading group.

Referee Report

4 major / 6 minor

Summary. This manuscript responds to Markos and Hlubina (arXiv:2511.03384), who argued that a generalized time-dependent London equation with an externally prescribed superconducting fraction f(r,t) accounts for the dynamics of the Meissner effect within conventional theory. Hirsch's main critical claim is that any f(r,t) interpolating between the normal and superconducting states automatically expels the magnetic field, so the assumed f carries the entire explanatory burden and MH's four answers to his earlier questions are circular or incomplete. The paper further proposes a cylindrical-cavity experiment intended to discriminate between the MH/conventional prediction and Hirsch's own charge-expulsion scenario. It concludes that the conventional theory still lacks a dynamical explanation of the Meissner effect and that charge expulsion, possibly involving negative effective mass, is indispensable. The manuscript also argues that the term −(∂f/∂t)A in MH's Eq. (3) is a nonexistent force.

Significance. The paper makes one genuinely useful logical observation: if f(r,t) is prescribed a priori and simply interpolates from 0 to 1, then Maxwell's equations plus the London relation will indeed produce field expulsion, and the formalism by itself supplies no microscopic mechanism for the appearance or momentum of the supercurrent. This is a fair and clearly stated limitation of MH's approach, and the paper honestly quotes MH's own concessions that the appearance of phase coherence is outside their formalism. If this were the whole paper, it would be a reasonable, if somewhat combative, comment. However, the manuscript's positive program is not secured. The proposed cavity experiment is not actually solved; the predicted final state under MH's theory is asserted after being left as an exercise. The alternative Hirsch prediction rests on a premise about charge expulsion that is cited from the author's prior work rather than derived here. The 'nonexistent force' objection is also stated too strongly and appears to conflate a constitutive relation with a force law. The paper therefore contains a valuable critical kernel but overreaches in its conclusions and in the claimed discriminating p

major comments (4)

[§II, Eq. (3); §VII] The claim that the second term in MH's Eq. (3) is a 'nonexistent force' is not established. The term −(∂f/∂t)A arises simply by differentiating the constitutive relation (2) when f varies in time. It is not introduced by MH as a force; it is a source term describing the change in supercurrent due to the changing superconducting fraction. In a canonical-momentum formulation, this term is a natural consequence of the London relation, not an invented force. The paper should either engage the canonical-momentum reading of MH's equations or soften this objection. The valid point is that f is externally prescribed, but that is a different argument from the claim that MH invoke a fictitious force.
[§V, after Eq. (10)] The central experimental prediction attributed to MH is not derived. The paper states that solving MH's Eq. (2) together with Maxwell's equations for the staged f in Eqs. (8)–(10) is 'left as an exercise for the reader,' yet the next paragraph asserts that 'according to the MH theory' the final state is Fig. 2. Since in MH's formalism f is an external input, the final state depends on the assumed f; different plausible choices can lead to different outcomes. Without actually performing the stated computation, the claim that MH predict full expulsion from the cavity is an assertion, not a demonstrated consequence. This undermines the experiment's power to test MH's theory.
[§VI] The Hirsch scenario (Fig. 4) rests entirely on the premise, taken from Ref. [8], that 'to expel the magnetic field from any given region of space requires outward motion of charge in that region of space,' and that because the cavity contains no charge, the field inside it cannot be expelled. This premise is asserted, not derived or independently verified in this manuscript. If the premise is false, Fig. 4 has no basis. The proposed experiment therefore only discriminates between the two theories conditional on a premise that is itself part of the author's contested theory. The manuscript should either provide a self-contained derivation of the premise or explicitly frame Fig. 4 as a prediction of the author's model rather than a direct consequence of standard electrodynamics.
[§VI–VII] The conclusions that 'charge expulsion is indispensable' and that the conventional theory 'will have to be discarded or amended' are disproportionately strong relative to the evidence presented in this paper. The argument depends on (a) the negative critique of MH, (b) the unsolved cavity experiment, and (c) the author's prior results in Refs. [6] and [8]. Because the force objection is overstated and the experiment is not computed, the manuscript does not establish that the conventional theory fails; at most it shows that MH's particular f-based model does not answer the microscopic questions. I recommend a more measured conclusion that clearly separates what is proven here from what is a research program.

minor comments (6)

[§II heading] The heading and text use 'Markus' where the correct spelling is 'Markos'.
[Eq. (3)] There is a typographical error: 'fr, t)' should be 'f(r, t)'.
[§V] Two typos: 'exceeds de radius' should be 'exceeds the radius', and 'analogous the the one' should be 'analogous to the one'.
[§I and §II] The words 'fatal flaws' and 'exactly nothing' are rhetorical and stronger than the technical content supports. Consider calibrating the language to the logical substance, especially since the paper's own positive scenario is not fully worked out.
[Fig. 2 and Fig. 4] The text refers to 'the right panel of Fig. 2' and 'the right panel of Fig. 4,' but the figures as presented appear to have a single panel each. Clarify the figure layout or adjust the references.
[§VII] The London quotation is interesting and relevant, but it is not integrated into the technical argument; it could be shortened or used more explicitly to support the point about explanatory scope.

Circularity Check

2 steps flagged · score 4.0 of 10

Negative critique is self-contained; the Hirsch-prediction experiment rests on the author's own unverified charge-expulsion premise.

uniqueness imported from authors [Sec. VI, 'ALTERNATIVE VIEW']
"to expel the magnetic field from any given region of space requires outward motion of charge in that region of space [8]. Because there is no electric charge in the interior of the cavity, the magnetic field in the interior of the cavity cannot be expelled. Therefore, the final state of the process has to be what is depicted in the right panel of Fig. 4"

The 'requires ... cannot be expelled ... therefore has to be' chain is a necessity claim cited only to the author's own Ref. [8]. The disputed question—whether charge expulsion is indispensable for the Meissner effect—is exactly what MH deny. The Hirsch-side outcome of the proposed experiment is therefore not derived from independent physics in this paper; it is forced by the author's own prior assumption. Without Ref. [8], no basis for Fig. 4 is given.
self citation load bearing [Sec. VII, CONCLUSION]
"As of today, the conventional theory has not provided answers, the only existing proposed answers are provided by the theory of hole superconductivity [6]."

The uniqueness claim 'only existing proposed answers' is justified exclusively by the author's own Ref. [6] and its references. It is load-bearing for the conclusion that the conventional theory 'will have to be discarded or amended,' but no independent derivation, proof, or external experimental benchmark is supplied here; it is an appeal to the author's own body of work.

full rationale

The paper's main critical argument—that MH's generalized London equation with an externally prescribed f(r,t) has the Meissner expulsion built into the boundary conditions (Eqs. 4a-4c)—is self-contained and not circular: it points out that any interpolating f between f=0 and f=1 will force the field to evolve from uniform to expelled, so the 'prediction' is a tautology of the assumed input. That is a genuine reduction of MH's claim by construction, but it is a criticism of the target paper, not a flaw in this paper's own derivation. The proposed experiment, however, has a load-bearing step that is not independently secured: the Hirsch-side prediction (Fig. 4) rests on the premise, cited only to Hirsch's own Ref. [8], that expelling field requires radial charge flow and that an empty cavity cannot therefore expel its field. That premise is the very point at issue, and no derivation or external evidence is given. The conclusion that the conventional theory must be discarded also leans on Ref. [6] for the 'only existing proposed answers' claim. Thus the paper's negative point is independent, but the positive/alternative prediction is supported by self-citation rather than by a derivation, giving a partial circularity score of 4.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim depends on the standard electromagnetic framework plus several contested assertions imported from Hirsch's earlier work. No numbers are fitted to data; the only free parameters are arbitrary front speeds in the illustrative scenario.

free parameters (1)

condensate front speeds v1, v2 = not fitted; arbitrary constants
Introduced in Sec. V as rates in the illustrative staged f(r,z,t). They do not enter the conclusion, but they are unconstrained inputs to the thought experiment.

assumptions (5)

domain assumption Maxwell's equations and the London equation in the London gauge are the correct framework.
Used throughout (Sec. II) to frame both MH's calculation and Hirsch's critique.
ad hoc to paper A valid explanation of Meissner dynamics must identify a real force that gives electrons their initial momentum.
This epistemic requirement underlies objections (i)-(iii) and is not a theorem of electrodynamics.
ad hoc to paper There is no physical force proportional to the vector potential A; the term -(∂f/∂t)A in MH's Eq. (3) is therefore fictitious.
Central to the critique (Sec. II), but contested because canonical momentum can depend on A.
ad hoc to paper Expelling magnetic field from a region requires outward radial charge flow in that region.
Imported from Ref. [8] in Sec. VI; it is what makes the cavity prediction differ from the conventional one.
ad hoc to paper Reversible momentum transfer between electrons and the body requires negative effective mass.
Invoked in Sec. VII from Hirsch's hole-superconductivity program [6]; no independent evidence in this paper.

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Cite this review

Pith. "Pith review of On a recent explanation of the dynamics of the Meissner effect within the conventional theory of superconductivity." pith.science (2026). https://pith.science/paper/2ZNDC4N3

@misc{pith2026251216938,
  author       = {Pith},
  title        = {Pith review of: On a recent explanation of the dynamics of the Meissner effect within the conventional theory of superconductivity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2ZNDC4N3}},
  note         = {Machine review of arXiv:2512.16938}
}

read the original abstract

In Ref. [1], arXiv:2511.03384, Markos and Hlubina argue that "contrary to the expectations of Hirsch" [2] the conventional theory of superconductivity correctly describes the dynamics of the Meissner effect. Here I point out the flaws in their arguments that render them invalid, and propose an experiment to shed further light on these issues.

Figures

Figures reproduced from arXiv: 2512.16938 by the authors.

**Figure 3.** FIG. 3: Schematic depiction of the initial stages of the tran [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** FIG. 4: Final state when the system is cooled into the super [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

11 extracted references · 1 linked inside Pith

[8]

What holes in superconductors reveal about superconductivity

J.E. Hirsch, “What holes in superconductors reveal about superconductivity”, arXiv:2506.07361 (2025)

arXiv 2025
[6]

The Meissner effect in superconduc- tors: emergence versus reductionism

J. E. Hirsch, “The Meissner effect in superconduc- tors: emergence versus reductionism”, arXiv:2510.17805 (2025) and references therein

arXiv 2025
[1]

On the dynamics of the Meissner and the Becker-London effects

P. Markos and R. Hlubina, “On the dynamics of the Meissner and the Becker-London effects”, arXiv:2511.03384 (2025), Physica C 639, 1354814 (2025)

arXiv 2025
[2]

Superconductivity begins with H

J. E. Hirsch, “Superconductivity begins with H”, World Scientific, Singapore, 2020 and references therein

2020
[3]

Introduction to superconductivity

M. Tinkham, “Introduction to superconductivity”, Sec- ond Edition, McGraw Hill, New York, 1996

1996
[4]

J. E. Hirsch, references in https://jorge.physics.ucsd.edu/meissner.html
[5]

The Lorentz force and superconductivity

J.E. Hirsch, “The Lorentz force and superconductivity”, Phys. Lett. A 315, 474 (2003)

2003
[7]

How do supercurrents die down when a superconductor goes normal?

J. E. Hirsch, “How do supercurrents die down when a superconductor goes normal?”, Physica C 635, 1354747 (2025)

2025

Show all 11 references

[9]

Introduction to Many-Body Physics

Piers Coleman, “Introduction to Many-Body Physics”, Cambridge University Press, Cambridge, 2015, Chapter 11

2015
[10]

Superconductivity

“Superconductivity”, Third Edition, edited by C.P. Poole, Jr, Ruslan Prozorov, Horacio A. Farach and Richard J. Creswick, Elsevier, Amsterdam, 2014, Chpt. 2 Sect. IX Fig. 2.34, and Chpt. 5, Sect. V Figs. 5.8, 5.9, and associated text

2014
[11]

Superfluids

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1961

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

[1] [8]

What holes in superconductors reveal about superconductivity

J.E. Hirsch, “What holes in superconductors reveal about superconductivity”, arXiv:2506.07361 (2025)

arXiv 2025

[2] [6]

The Meissner effect in superconduc- tors: emergence versus reductionism

J. E. Hirsch, “The Meissner effect in superconduc- tors: emergence versus reductionism”, arXiv:2510.17805 (2025) and references therein

arXiv 2025

[3] [1]

On the dynamics of the Meissner and the Becker-London effects

P. Markos and R. Hlubina, “On the dynamics of the Meissner and the Becker-London effects”, arXiv:2511.03384 (2025), Physica C 639, 1354814 (2025)

arXiv 2025

[4] [2]

Superconductivity begins with H

J. E. Hirsch, “Superconductivity begins with H”, World Scientific, Singapore, 2020 and references therein

2020

[5] [3]

Introduction to superconductivity

M. Tinkham, “Introduction to superconductivity”, Sec- ond Edition, McGraw Hill, New York, 1996

1996

[6] [4]

J. E. Hirsch, references in https://jorge.physics.ucsd.edu/meissner.html

[7] [5]

The Lorentz force and superconductivity

J.E. Hirsch, “The Lorentz force and superconductivity”, Phys. Lett. A 315, 474 (2003)

2003

[8] [7]

How do supercurrents die down when a superconductor goes normal?

J. E. Hirsch, “How do supercurrents die down when a superconductor goes normal?”, Physica C 635, 1354747 (2025)

2025