The weak equivalence principle and the Dirac constant: A result from the holographic principle

Eiji Konishi

REVIEW 4 major objections 6 minor 25 references

The weak equivalence principle and the Dirac constant: A result from the holographic principle

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The weak equivalence principle is equivalent to the equality of two forms of the Dirac constant, derived from a classicalized holographic tensor network.

desk verdict A transparent but definitionally forced derivation: the claimed equivalence between WEP and ħ_E=ħ_L only goes through if you import the mass identifications from the author's earlier papers. read the letter →

arxiv 2501.07594 v2 pith:WMNYNBMN submitted 2025-01-09 physics.gen-ph

Eiji Konishi This is my paper · ORCID

classification physics.gen-ph

keywords holographicprincipleweakequivalenceDiracconstantWickrotationtensornetworksuperselectionruleinertialandgravitationalmass

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

The paper tries to show that the weak equivalence principle—the equality of inertial and gravitational mass—is not an independent law of general relativity but the same statement as a consistency condition in quantum mechanics: that the two roles of the Dirac constant, as the action of a spin degree of freedom and as the lower bound of uncertainty relations, coincide. The argument starts from a holographic tensor network whose ground state has been classicalized by a superselection rule, writes its Euclidean and Lorentzian actions in terms of Shannon entropy and two conceptually distinct constants $\hbar_E$ and $\hbar_L$, and then applies a Wick rotation. That rotation turns the equality of the two ratios $M_E/\hbar_E$ and $M_L/\hbar_L$ into the equivalence of the conditions $\hbar_E=\hbar_L$ and $M_E=M_L$, with $M_L$ the inertial mass and $M_E$ the active gravitational mass. If correct, the weak equivalence principle would be a derived consequence of holography, and quantum mechanics and general relativity would be two faces of a single principle.

What carries the argument

The central object is the classicalized holographic tensor network (cHTN): a scale-invariant tensor network (multi-scale entanglement renormalization ansatz) for the boundary CFT ground state, made classical by imposing a superselection rule that destroys quantum coherence. The identity that carries the argument is the Wick-rotation relation between Euclidean and Lorentzian world-line actions divided by the respective constants, $S_E/\hbar_E = -i S_L/\hbar_L$, which yields $M_E/\hbar_E = M_L/\hbar_L$; from there the condition $\hbar_E=\hbar_L$ (the requirement for consistent unitary bulk quantum mechanics) becomes the mass equality $M_E=M_L$. The two constants are distinguished conceptually throughout and only identified at the final step.

What would settle it

Compute $M_L$ from the Lorentzian on-shell energy uncertainty and $M_E$ from the Euclidean Gauss-law source for the Unruh acceleration independently, using the cHTN formalism; if the two are not forced equal by $\hbar_E=\hbar_L$, the claimed equivalence fails. At the experimental level, a measured violation of the weak equivalence principle for any test body—or a demonstration that spin action and uncertainty-bound action are governed by different constants—would directly contradict the paper's central claim.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that the weak equivalence principle in general relativity is equivalent to the equality of two forms of the Dirac constant: the action of the spin degree of freedom in a two-dimensional Hilbert space ($\hbar_E$) and the lower bound in quantum mechanical uncertainty relations ($\hbar_L$). The author derives this by writing the actions of a classicalized holographic tensor network (cHTN) as $I_E=-\hbar_E H$ and $I_L=-\hbar_L H$, where $H$ is the Shannon entropy of the classicalized ground state, and then applying the Wick rotation $t_E=i t_L$ to the world-line actions of a massive particle. The Wick rotation forces $M_E/\hbar_E=M_L/\hbar_L$; setting $\hbar_E=\hbar_L$ then forces $M_E=M_L$, which is the weak equivalence principle because $M_L$ is identified as inertial mass and $M_E$ as active gravitational mass. The paper concludes that quantum mechanics and general relativity are equivalent at the level of their principles.

Load-bearing premise

The load-bearing premise is that $M_L$ as it appears in the Lorentzian cHTN action is the inertial mass and $M_E$ as it appears in the Euclidean cHTN action is the active gravitational mass; these identifications are asserted from the author's earlier work, not derived in this paper, and without them the equality $M_E=M_L$ does not express the weak equivalence principle.

Editorial extensions

If this is right

If the equivalence holds, the weak equivalence principle is not an axiom of general relativity but a consequence of the holographic principle applied to a classicalized tensor network.
The Dirac constant then has two conceptually distinct roles—spin action in a two-dimensional Hilbert space and the lower bound in uncertainty relations—that coincide exactly when inertial and gravitational mass are equal.
A violation of the weak equivalence principle would, under this identification, be equivalent to a failure of the consistency condition $\hbar_E=\hbar_L$, meaning a breakdown of unitary quantum mechanics in the bulk.
The derivation gives concrete meaning to the idea that quantum mechanics and general relativity are two sides of the same coin: both follow from the same holographic action when the two forms of $\hbar$ are identified.

Reading between the lines

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

The author does not draw this conclusion explicitly, but if this derivation is right, the weak equivalence principle becomes a consistency condition rather than an independent postulate: a WEP violation would signal a breakdown of unitary bulk quantum mechanics, not merely a new force.
A natural extension would be to vary the superselection rule used for classicalization; the derivation's reliance on one particular choice (the Pauli Z operator) predicts that different classicalizations could yield different effective mass couplings, a claim testable in tensor-network toy models.
The identity suggests a laboratory target: measure the action per spin event and the uncertainty-bound action in the same system; any difference between $\hbar_E$ and $\hbar_L$ would translate into a predicted WEP-violation amplitude that existing torsion-balance and atom-interferometry tests could in principle bound.

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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

Short version: the paper is a clean, short, honest derivation that ends in the wrong place. The new bit is the explicit claim that the weak equivalence principle is equivalent to setting two conceptually distinct ħ-like parameters equal in the author's classicalized holographic tensor network. That phrasing is new relative to his prior papers; the underlying machinery is not.

What it does well: it is unusually transparent. The definitions of I_E and I_L are explicit, the Wick rotation step is flagged as an equivalence, and the paper states plainly that ℏ_E and ℏ_L are 'conceptually distinguished.' The footnotes and references point to exactly where each physical interpretation comes from. That is honest scholarship.

Where it falls down: the load-bearing step is the identification of M_L as inertial mass and M_E as active gravitational mass, after Eq. (7). That identification is not derived here. It is imported from Refs. [19] and [21], and without it, Eq. (7) is just an equality of two parameters in a speculative construction. The condition ℏ_E=ℏ_L is an input, not a result; the paper calls it a condition for consistency of unitary QM, but nothing forces it. So the claimed equivalence with WEP is semantically stipulated rather than demonstrated. The reader's circularity diagnosis is right: the equality M_E/ℏ_E = M_L/ℏ_L is built via definitions so that setting the ħ's equal yields M_E=M_L. This is restatement, not derivation.

Also note that Eq. (4) is asserted to follow from the Wick rotation through Eq. (5); that's a big jump. It may be fine within the author's framework, but the paper doesn't show the link between the world-line actions and the cHTN actions in enough detail for an outsider to check.

Verdict: The central claim does not hold up on its own terms. The paper is not incoherent, but it's a self-contained framework that becomes physically meaningful only via prior self-cited results. That makes it a poor candidate for a general journal. However, it is a serious attempt within a specific research program, and a referee who knows the prior work could quickly assess whether the mass identifications are justified. If I were an editor at a specialized holography/foundations journal, I would send it out for that check, expecting the referee likely to come back negative. For a general journal, desk reject.

Referee Report

4 major / 6 minor

Summary. The paper claims to prove that the weak equivalence principle (WEP) in general relativity is equivalent to the equality of two Dirac-like constants, ℏ_E and ℏ_L, in a 'classicalized holographic tensor network' (cHTN). The author defines Euclidean and Lorentzian actions for the cHTN, introduces a superselection rule that classicalizes the tensor network, and uses a Wick rotation to derive a relation M_E/ℏ_E = M_L/ℏ_L. Imposing ℏ_E = ℏ_L then gives M_E = M_L, with M_L interpreted as inertial mass and M_E as active gravitational mass. The paper concludes that quantum mechanics and general relativity are two sides of the same coin at the level of their principles.

Significance. If the claimed result were established, it would be a striking derivation of the WEP from holographic/tensor-network ideas and would suggest a new foundational link between quantum mechanics and gravity. The holographic setup is interesting, and the paper is concise and readable. However, the central claim is not supported by the derivation as written: the mass identifications are imported from the author's earlier work rather than derived, and the key equality is close to definitional. The paper is best read as a speculative interpretive proposal, not as a proof of an equivalence between known principles.

major comments (4)

[Text after Eq. (7) and footnote [25]] The identification of M_L as inertial mass and M_E as active gravitational mass is the load-bearing step of the paper, but it is not derived here. The text asserts that M_L appears in the rest energy as the energy uncertainty of the cHTN (citing Refs. [21,23]) and that M_E is the source quantity in Gauss's theorem for the gravitational proper acceleration (citing Ref. [19]); footnote [25] only equates active and passive gravitational mass via Eq. (21) of Ref. [19]. These identifications are taken from prior self-cited work and are not independently established in this manuscript. Without them, Eq. (7) is merely an equality of two model parameters and has no demonstrated connection to the WEP. To support the central claim, the paper must either derive these mass identifications from the cHTN model or explicitly state that the WEP is an input assumption.
[Eqs. (3)-(5)] The claimed equivalence between the Wick rotation (3) and Eq. (4) is not demonstrated. The text states that the relation (3) is equivalent to (4) 'from the definitions (1) and (2)', and that this equivalence follows from Eq. (5). But Eq. (5) is itself an assumed relation between the world-line actions S_E, S_L and the cHTN actions; the manuscript does not define these world-line actions or show that they are linear in the mass parameters M_E and M_L. Therefore Eq. (4) functions as an additional, unexplained assumption rather than a consequence of Wick rotation.
[Eqs. (1)-(2) and Eq. (6)] The result is substantially definitional. Since ℏ_E and ℏ_L are introduced as the unit actions of a cHTN pixel via Eqs. (1)-(2), the condition ℏ_E = ℏ_L fixes a relation between the Euclidean and Lorentzian action scales. The subsequent equality M_E = M_L then expresses that the same mass parameter appears in both world-line actions. This is close to a restatement of the author's chosen definitions rather than an independent physical equivalence, unless the mass identifications are independently justified. As written, the derivation does not provide new information about the relation between inertial and gravitational mass.
[Paragraph 2 (classicalization)] The existence of a superselection rule that classicalizes the tensor network is assumed without independent evidence. The paper does not explain why such a superselection rule should hold in a holographic ground state, nor does it derive the cHTN actions (1)-(2) from a more fundamental principle. Consequently, the entire argument is conditional on a speculative model. This is not objectionable for a theory paper, but it weakens the claim that a fundamental equivalence has been established.

minor comments (6)

[Title/abstract] The title contains a typo: 'res ult' should be 'result'.
[Abstract] The word 'formularization' is nonstandard; consider 'formulation'.
[Text after Eq. (7)] The inline expression dI = dτ_E S_E/ℏ_E is not numbered, and the symbol τ_E is not defined before use; please clarify its meaning.
[Eq. (5)] The sign conventions and domain of validity of the Wick rotation in the presence of the cHTN background are not explained; a reference or a brief derivation would help the reader assess Eq. (5).
[Refs. [19]-[21], [23]] The physical interpretation after Eq. (7) depends heavily on four self-citations to a niche journal; the manuscript is not self-contained. Please state the relevant results or definitions explicitly, or at least quote the equations being invoked.
[Paragraph 2] The phrase 'the quantum ground state becomes equivalent to a diagonal quantum mixed state' uses 'equivalent' without a precise definition; clarify whether the equivalence is with respect to the restricted observable algebra A.

Circularity Check

2 steps flagged · score 8.0 of 10

The central 'WEP = Dirac-constant equivalence' is an algebraic restatement of the author's own action-ratio ansatz, with the inertial/gravitational mass labels imported from self-cited prior work.

self definitional [Eqs. (4) and (5), after Eq. (3)]
"From the definitions (1) and (2) of the unit actions −ℏ_E and −ℏ_L, respectively, this relation (3) is equivalent to the following relation: M_E/ℏ_E = M_L/ℏ_L. (4) ... this equivalence follows from the equivalence [22] S_E/ℏ_E = −iS_L/ℏ_L |_{t_L→−it_E}. (5)"

The claimed derivation of Eq. (4) from the Wick rotation passes through Eq. (5), which is an assumed equality of the Euclidean and Lorentzian world-line actions divided by ℏ_E and ℏ_L. Since M_E and M_L are defined as the masses appearing in S_E and S_L, substituting the world-line actions and using τ_E = iτ_L turns Eq. (5) algebraically into exactly Eq. (4). The subsequent biconditional (6)⇔(7) is then elementary algebra: from M_E/ℏ_E = M_L/ℏ_L, setting ℏ_E = ℏ_L gives M_E = M_L. Thus the central 'result' is built into the ansatz (5) by construction rather than derived as a new physical consequence.
self citation load bearing [After Eq. (7) and footnote [25]]
"Here, M_L appears in the rest energy M_L c^2 as the energy uncertainty ∆E of the cHTN (2) in the ground state. So, M_L is the inertial mass. ... Thus, M_E is the active gravitational mass.[25] [25] Here, the active gravitational mass is the passive gravitational mass due to Eq. (21) in Ref. [19]."

The physical identification that converts the algebraic statement M_E = M_L into the weak equivalence principle is not derived in this paper. It is asserted by attaching the labels 'inertial mass' to M_L and 'active gravitational mass' to M_E, with both identifications and the active=passive equivalence referred to the author's own Refs. [19], [21], [23] (footnote [25] cites Eq. (21) of Ref. [19]). These self-citations are load-bearing: without them, Eq. (7) is merely an equality of two model parameters in a speculative Euclidean/Lorentzian tensor-network construction. The claimed result is therefore forced by the author's prior definitions rather than by the holographic principle or by any independent evidence.

full rationale

The derivation chain is: Eqs. (1)-(2) define cHTN actions; Eq. (5) imposes S_E/ℏ_E = −iS_L/ℏ_L; substituting the world-line actions makes this identical to Eq. (4), M_E/ℏ_E = M_L/ℏ_L; then Eq. (6), ℏ_E = ℏ_L, yields Eq. (7), M_E = M_L. The final step from Eq. (7) to the weak equivalence principle is made only by the sentences after Eq. (7) that declare M_L inertial and M_E active gravitational, citing Refs. [19], [21], [23] and Eq. (21) of Ref. [19] in footnote [25]. These are self-citations by the sole author, and the paper does not independently derive those physical identifications. The formal biconditional is valid conditional on the model, but as a paper-internal derivation the claimed 'result from the holographic principle' reduces to the author's definitions and prior labels. No data are fitted, so no fitted-input prediction occurs; the circularity is definitional and self-citational.

Assumptions & free parameters 1 free parameters · 4 assumptions · 1 invented entities

The central claim rests on the author's own framework: the superselection rule classicalization, the action-entropy relations, and the identification of the two masses. None of these are independently established in this paper, and the two constants hbar_E and hbar_L are free labels that are later set equal by assumption.

free parameters (1)

hbar_E and hbar_L (conceptually distinct Dirac-like constants)
Two constants are introduced to label the Euclidean and Lorentzian actions in Eqs. (1) and (2). No measurement fixes their separate values; they are later set equal by assumption (6).

assumptions (4)

domain assumption The holographic principle and the AdS3/CFT2 correspondence can be modelled as a qubit tensor network (MERA).
The paper takes this framework as its starting point without proof, citing Refs. [1-12].
ad hoc to paper A superselection rule with the Pauli Z operator exists in the ground state, classicalizing the tensor network.
This is the paper's stated 'novelty' but it is assumed, not derived. It is essential for defining the actions (1) and (2).
ad hoc to paper The action of the classicalized tensor network is -hbar times the Shannon entropy, with separate constants hbar_E and hbar_L.
Equations (1) and (2) are definitions imported from the author's previous work, not derived here.
standard math Wick rotation connects the Euclidean and Lorentzian actions.
Equation (3) and the continuation (5) are standard analytic continuation, though their application with two different hbar constants is nonstandard.

invented entities (1)

Classicalized disentangler (pixel)
purpose: A unit of the classicalized tensor network that carries one negative degree of freedom and action -hbar_E or -hbar_L.
Introduced in the author's prior papers [15,19]; no falsifiable prediction is given in this preprint.

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Cite this review

Pith. "Pith review of The weak equivalence principle and the Dirac constant: A result from the holographic principle." pith.science (2026). https://pith.science/paper/WMNYNBMN

@misc{pith2026250107594,
  author       = {Pith},
  title        = {Pith review of: The weak equivalence principle and the Dirac constant: A result from the holographic principle},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WMNYNBMN}},
  note         = {Machine review of arXiv:2501.07594}
}

read the original abstract

In this article, based on a recent formularization of the holographic principle proposed and investigated by the present author, we show that the weak equivalence principle in general relativity is equivalent to the equivalence between two forms of the Dirac constant, that is, the action of the spin degree of freedom in the two-dimensional Hilbert space and the lower bound in the quantum mechanical uncertainty relations. This result follows from an equation between the Euclidean and Lorentzian world-line actions of a massive particle divided by the Dirac constant, via the Wick rotation, by using the Euclidean and Lorentzian actions of a holographic tensor network, whose quantum state is classicalized by introducing the superselection rule.

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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