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REVIEW 4 major objections 5 minor 1 cited by

Examining Lorentz invariance violation with three remarkable GRB photons

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A single Lorentz-violation scale of about 3×10^17 GeV, combined with an intrinsic delay that grows linearly with photon energy, explains the arrival times of the 99.3 GeV, 1.07 TeV, and 12.2 TeV photons from GRB 221009A and GRB 190114C.

desk verdict The paper's Model C is an ad hoc parameterization that absorbs TeV outliers, the AIC shows no preference over the simpler model, and an out-of-sample check fails—so the claimed LV scale is not robust. read the letter →

arxiv 2504.14295 v1 pith:3BM6D4NL submitted 2025-04-19 astro-ph.HE gr-qchep-ph

Hanlin Song , Bo-Qiang Ma This is my paper · ORCID
classification astro-ph.HEgr-qchep-ph
keywords Lorentzinvarianceviolationgamma-rayburstslight-speedvariationintrinsicemissiontimeGRB221009A190114Chigh-energyphotonstime-delayanalysis
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 establish that the arrival times of the three highest-energy photons ever seen from gamma-ray bursts can all be explained by one Lorentz-violating dispersion relation with scale $E_{\rm LV}\sim 3\times 10^{17}$ GeV, provided the GRB source emits high-energy photons with an intrinsic delay that grows linearly with photon energy. This matters because it would turn three iconic single-photon events, observed by three different telescopes across GeV and TeV energies, into a single consistent probe of light-speed variation. The authors show that treating the intrinsic delay as a constant fails: adding the 1.07 TeV or 12.2 TeV photon shifts the fitted scale to $\sim 2\text{--}3\times 10^{18}$ GeV. With a linear intrinsic delay (their Model C), all five data combinations converge on the same $E_{\rm LV}$, $\alpha\sim -0.2$ s GeV$^{-1}$, and $\mu\sim 0$ s, implying that high-energy photons are emitted earlier than low-energy ones at the source.

What carries the argument

The load-bearing mechanism is the modified photon dispersion relation (Eq. 1), $E^2=p^2c^2[1-s_n(pc/E_{\rm LV})^n]$, whose $n=1$ linear term produces the velocity shift and arrival-delay integral in Eqs. (2)--(3). The paper's key addition is Eq. (5), $\Delta t_{\rm in}=\Delta t_{\rm in,c}+\alpha E_s$, an energy-dependent intrinsic emission delay, and Model C combines both: $\Delta t_{\rm obs}=\Delta t_{\rm LV}+(1+z)(\Delta t_{\rm in,c}+\alpha E_s)$. This linear intrinsic term is what absorbs the large observed delays of the 1.07 TeV and 12.2 TeV photons, allowing the Lorentz-violation scale to stay at $E_{\rm LV}\sim 3\times 10^{17}$ GeV across all five data combinations. The Bayesian posteriors for $a_{\rm LV}=1/E_{\rm LV}$, $\alpha$, $\mu$, and $\sigma$ are compared across Models A, B, and C using the Akaike information criterion.

What would settle it

Take a GRB with two or more high-energy photons spanning a wide energy range and an unambiguous low-energy peak, then measure the delay versus energy; if the delays do not fall on a single straight line with the same $\alpha\sim -0.2$ s GeV$^{-1}$ and the same $E_{\rm LV}\sim 3\times 10^{17}$ GeV used here, Model C is ruled out.

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Extended reading notes

Core claim

The paper's central claim is that the observed delays of three extraordinary GRB photons are all described by a single subluminal, linear-in-energy Lorentz-violating dispersion relation with $E_{\rm LV}\sim 3\times 10^{17}$ GeV, once the intrinsic emission delay at the source is allowed to depend linearly on photon energy as $\Delta t_{\rm in} = \Delta t_{\rm in,c} + \alpha E_s$ with $\alpha\sim -0.2$ s GeV$^{-1}$ and $\mu\sim 0$ s. Under this Model C, $\Delta t_{\rm obs} = \Delta t_{\rm LV} + (1+z)\Delta t_{\rm in}$, and Bayesian fits to five data combinations (the 14 multi-GeV Fermi photons alone, plus each new photon individually, plus all three together) return mutually consistent parameters $E_{\rm LV}\sim 3\times 10^{17}$ GeV, $\alpha\sim -0.2$ s GeV$^{-1}$, and $\mu\sim 0$ s. The analysis also shows that Model A, which treats the intrinsic delay as a constant, cannot simultaneously accommodate the TeV photons and the GeV sample: including the 1.07 TeV or 12.2 TeV photon shifts the fitted $E_{\rm LV}$ to $\sim 2\text{--}3\times 10^{18}$ GeV. The paper interprets this as evidence that high-energy photons are emitted earlier at the GRB source, by an amount proportional to their energy.

Load-bearing premise

The paper's conclusions rest on the assumption that the GRB source emits high-energy photons with an intrinsic delay that grows linearly with photon energy; if that linear form (or the manually chosen low-energy reference peak) is wrong, the fitted $E_{\rm LV}$ is an artifact of the assumed formula.

Editorial extensions

If this is right

  • If Model C is right, the intrinsic GRB delay is not a nuisance constant but a physical, energy-dependent term: high-energy photons leave the source earlier than low-energy photons by roughly 0.2 s per GeV of source-frame energy.
  • The same Lorentz-violation scale, $E_{\rm LV}\sim 3\times 10^{17}$ GeV, applies across three observatories and two energy decades, making the record single-photon events from GRB 221009A and GRB 190114C mutually consistent probes of light-speed variation.
  • Under Model A, adding either TeV photon forces $E_{\rm LV}$ to $\sim 2\text{--}3\times 10^{18}$ GeV, so ignoring energy-dependent intrinsic emission would bias the inferred LV scale upward when TeV photons are included.
  • Model C is preferred by the Akaike information criterion in all five data combinations, which is a direct corollary of the paper's fits and should be checked by external replication.

Reading between the lines

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

  • Because the linear intrinsic-delay term adds one free parameter, its ability to reconcile the three photons does not by itself prove that the dispersion relation is modified; an independent, non-LV source model that produces the same $\alpha$ would remove the need for $E_{\rm LV}\sim 3\times 10^{17}$ GeV.
  • A testable extension is to apply Model C to the full Fermi-LAT spectral-lag sample, not just the highest-energy photon per burst; if $\alpha$ is truly intrinsic to GRB emission, its value should be stable across many bursts and uncorrelated with redshift.
  • The claimed $\alpha\sim -0.2$ s GeV$^{-1}$ implies a measurable spectral-lag pattern inside single bursts: sub-GeV photons should lag GeV photons by hundreds of milliseconds to seconds, which can be checked with light-curve cross-correlations.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript applies three phenomenological models (A, B, C) for the intrinsic time delay of high-energy GRB photons to a dataset consisting of the 14 multi-GeV Fermi photons studied previously plus three 'remarkable' photons: the 99.3 GeV Fermi photon from GRB 221009A, the 1.07 TeV MAGIC photon from GRB 190114C, and the 12.2 TeV LHAASO photon from GRB 221009A. Using Bayesian fits with the bilby package, the authors conclude that Model C, which combines a linear-in-energy intrinsic delay (Eq. 5) with a Lorentz-violating arrival-time delay, yields consistent parameters across five data combinations (Cases a–e), with E_LV ~ 3×10^17 GeV, α ~ −0.2 s/GeV, and μ ~ 0 s. They further claim that AIC selects Model C as the best model.

Significance. If the central claim were correct, the paper would provide a unified, energy-dependent intrinsic-delay framework that reconciles GeV and TeV GRB photon arrival times with a consistent Lorentz-violation scale near 3×10^17 GeV, a result of substantial interest for quantum-gravity phenomenology. The paper is transparent in reporting posterior tables and AIC values, and it uses a reproducible Bayesian pipeline with publicly available data. However, the significance is undercut by the following issues: the AIC preference for Model C is statistically negligible in the base cases; the claimed cross-case consistency is an in-sample property with no predictive validation; and the key energy-dependent intrinsic-delay term is an ad hoc linear ansatz that strongly degenerates with the LV term. These points, detailed in the major comments, mean that the evidence for the central claim is not compelling as presented.

major comments (4)
  1. [Tables 5 and 6, Eq. (9)–(10)] The claim that 'Model C exhibits the best performance' is not supported by the reported AIC values. In Case a (the original 14 photons) and Case b (all 17 photons), the AIC difference between Model C and the simpler Model A is only Δ = 0.54 and 0.59, respectively, which is well below the conventional threshold of Δ < 2 for models to be considered indistinguishable. Adding the parameter α therefore does not provide significant evidence for Model C over Model A in the datasets that define the paper's main inference. The paper should either temper this claim or provide a statistical test (e.g., AIC weights or Bootstrap) that quantifies the evidence.
  2. [Section 3, Tables 4–5] The consistency of the Model C parameters across Cases a–e is entirely in-sample. The parameters for Cases d and e are obtained by fitting the very photons whose consistency is asserted, so no predictive test is performed. A direct posterior-predictive check is missing. To illustrate: using the Case a posterior (Table 4: aLV = 3.28×10⁻¹⁸ GeV⁻¹, α = −0.15 s/GeV, μ = −4.49 s) and Eqs. (3)–(5), the predicted Δt_obs/(1+z) for the 12.2 TeV LHAASO photon is of order 800 s, far above the observed 340.19 ± 4.35 s from Table 1. Even allowing for the large posterior uncertainties, the absence of any out-of-sample validation means the claimed 'consistent framework' is not distinguished from a re-fitting that absorbs the TeV outliers. The authors should present a leave-one-out or posterior-predictive analysis, or explicitly restrict their claim to the in-sample behavior.
  3. [Table 1 and accompanying text] The low-energy reference times for the two newly included GRBs, 2.59 ± 5.00 s for GRB 190114C and 251.33 ± 5.00 s for GRB 221009A, are manual selections with no supporting light-curve analysis. Since every Δt_obs is defined relative to these peaks, a shift of a few seconds directly changes the fitted time delays, and the stated ±5 s uncertainty is comparable to the reported uncertainties on the GeV-photon delays (e.g., ±4.35 s). The paper does not test the sensitivity of the results to the choice of reference time. The authors should either justify these peaks quantitatively from the GBM light curves or demonstrate that the posteriors are robust under variations of the reference time within a plausible range.
  4. [Eq. (5) and Section 2] The linear energy dependence of the intrinsic emission time, Δt_in = Δt_in,c + α E_s, is an ad hoc assumption imported from ref. [7] and is not physically derived. Because both the LV term (Eq. 3) and the intrinsic term are linear in photon energy for n=1, the fit suffers from a strong degeneracy between aLV and α. For example, the observed delay of the 12.2 TeV LHAASO photon arises from the near-cancellation of a large positive LV delay (~2.8×10³ s) and a large negative intrinsic delay (~−2.1×10³ s), both of which scale linearly with energy. The paper should demonstrate that the inferred E_LV is not an artifact of this assumed functional form, for example by testing an alternative power-law index or by constraining α through independent spectral-lag observations. Without such a test, the physical interpretation of E_LV ~ 3×10¹⁷ GeV is not robust.
minor comments (5)
  1. [Abstract and Introduction] The phrase 'the newly proposed model' is vague; the abstract should explicitly name Model C and define α and E_LV.
  2. [Table 4 column header] The header 'α (s· GeV−11)' contains a typo; it should read 'α (s·GeV⁻¹)'.
  3. [Discussion near Model B/C] The sentence stating that Model C is 'derived purely through data fitting without arbitrary preconceptions' is inaccurate, since Eq. (5) itself is a specific, arbitrary functional choice; this sentence should be revised.
  4. [Section 3, Tables 5–6] The AIC discussion should explicitly acknowledge that Δ < 2 is conventionally interpreted as no meaningful difference; the current wording 'It is evident' overstates the statistical support.
  5. [Section on limitations] The paragraph acknowledging the small sample size is welcome, but it is placed at the end without quantitative discussion; the authors could add a sentence on how selection effects might bias the time-delay measurements.

Circularity Check

2 steps flagged · score 6.0 of 10

The claimed consistency of E_LV ~ 3e17 GeV is achieved by importing the linear intrinsic-delay ansatz from the authors' prior work and refitting it to the same three photons it is said to explain.

  1. ansatz smuggled in via citation [Section 2, Eq. (5) and the definition of Model C, Eq. (8)]
    "In a recently new study [7], a more general form for the intrinsic emission time with energy-dependence is introduced: Δtin = Δtin,c + αEs, where Δtin,c is a common constant term and Es is the source frame energy of high-energy photon with α being the coefficient."

    The linear energy dependence of the intrinsic emission time is the load-bearing premise that lets Model C reconcile the 1.07 TeV and 12.2 TeV photons with the GeV sample. It is not derived in this paper, nor justified from independent external data; it is imported from ref. [7] by the same authors, where it was introduced as a phenomenological ansatz after fitting the same 14-photon FGST dataset. The paper's central conclusion, E_LV ~ 3e17 GeV, is therefore contingent on an unverified ansatz inherited from the authors' own prior work, rather than on a first-principles derivation or an independent test.

  2. fitted input called prediction [Abstract and Section 3, Table 4, with Eq. (8) and Table 1]
    "Our analysis indicates that the newly proposed model with a linear relationship between photon energy and intrinsic emission time can offer a consistent framework to explain the behavior of all three exceptional photons with a Lorentz violation scale ELV∼3×10^17 GeV. ... It is a surprise that the three parameters for all of the five cases are consistent with each other for ELV∼3×10^17 GeV, α∼−0.2 s·GeV−1, and μ∼0 second."

    The 'surprise' consistency is produced by refitting the model to datasets that include the very photons being explained: Cases b–e each add the new photon(s) to the posterior from which the parameters are estimated. In Eq. (8), Δt_obs = Δt_LV + (1+z)(Δt_in,c + αE_s), the linear intrinsic term αE_s is a free parameter estimated from the same photons. For the 12.2 TeV LHAASO photon, the LV delay at E_LV ≈ 3e17 GeV is of order 10^3 s, and the fitted αE_s cancels most of it to yield the observed 340 s in Table 1.

full rationale

The paper's central claim is that Model C, with the linear intrinsic emission time Δt_in = Δt_in,c + αE_s, provides a consistent framework for three new GRB photons with E_LV ~ 3e17 GeV. That claim is weakened by two related circularity concerns. First, the linear ansatz itself is not derived here; it is introduced in ref. [7] by the same authors, and the present paper adopts it as the key mechanism for reconciling TeV photons with the GeV sample. This is a load-bearing self-citation, because without the αE_s term the TeV photons would force a much larger E_LV in Model A (as Table 2 shows). Second, the 'surprise' that parameters are consistent across the five cases is assessed in-sample: each case includes the new photon(s) in the fit that defines the parameters, so the model is not predicting the three remarkable photons but refitting them. For the 12.2 TeV photon, the LV delay at the claimed E_LV is of order 10^3 s, and the fitted αE_s term provides the cancellation needed to match the observed delay; the stability of E_LV is therefore partly an artifact of the extra free parameter. The AIC comparison supports this reading: for Case b, Model C beats Model A by only 0.59 AIC units, so the additional linear intrinsic term is not strongly required by the data; it mainly absorbs the TeV outliers. The paper itself acknowledges the limited dataset and the need for further events, and the manual selection of low-energy reference peaks (2.59 s and 251.33 s with ±5 s uncertainties) is another input assumption rather than a derived quantity. These issues do not mean the analysis is fraudulent or that the model is certainly wrong; rather, the claimed consistent framework reduces in large part to fitting the same data with a flexible ansatz imported from the authors' prior work, so the evidence for E_LV ~ 3e17 GeV is substantially weaker than the paper's language suggests.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The central claim rests on six free or hand-chosen parameters and five assumption-laden modeling choices. The most consequential is the linear energy-dependent intrinsic delay (Eq. 5), which was introduced by the same authors and is the mechanism that makes the TeV photons consistent with E_LV ~ 3e17 GeV. The reference-time selections for the two new GRBs are manual inputs that directly set the observed delays. No new particles or entities are invented.

free parameters (6)
  • a_LV (inverse LV scale) = 3.34e-18 GeV^-1 (Case b, Table 4)
    Fitted to the time-delay data for each case; the central claim's E_LV derives from this parameter.
  • alpha (energy-dependent intrinsic delay coefficient) = -0.20 s/GeV (Case b, Table 4)
    Absorbs the energy dependence of source-frame emission delays; without this parameter the TeV photons cannot be fit with E_LV ~ 3e17 GeV.
  • mu (mean of common intrinsic time delay prior) = -1.07 s (Case b, Table 4)
    Gaussian prior mean for the common intrinsic delay; fitted to data.
  • sigma (width of intrinsic delay prior) = 5.09 s (Case b, Table 4)
    Standard deviation of the Gaussian distribution for the common source-frame delay; fitted to data.
  • Reference time for GRB 190114C = 2.59 s
    Manually selected from the Fermi-GBM light curve; defines the observed delay for the 1.07 TeV MAGIC photon.
  • Reference time for GRB 221009A = 251.33 s
    Manually selected from the Fermi-GBM light curve; defines the observed delays for both the 99.3 GeV FGST photon and the 12.2 TeV LHAASO photon.
assumptions (5)
  • domain assumption The modified dispersion relation Eq. (1) with n=1 (linear leading-order term) is a valid description of LV.
    The LV effect is assumed to appear at first order in E/E_LV; higher orders are neglected. This is standard in the LV literature but is an additional assumption.
  • ad hoc to paper The intrinsic emission time delay is linear in photon energy (Eq. 5).
    Introduced in the authors' ref [7]; no independent physical model, and the paper's conclusion depends on it.
  • domain assumption The standard Lambda-CDM model describes the cosmic expansion for the redshift integral in Eq. (3).
    Uses H0, Omega_m, and Omega_Lambda as external inputs; the LV time delay integral assumes the standard Friedmann expansion.
  • domain assumption The low-energy GBM peak is the correct reference for the zero-delay point.
    The observed time delays are computed relative to the first prominent peak in low-energy GBM light curves; alternative choices shift all delays by a constant.
  • domain assumption The common intrinsic time delay follows a Gaussian distribution.
    The prior p(Delta_tin,c) ~ N(mu,sigma) is a statistical modeling choice that may not reflect the true distribution across GRBs.

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Pith. "Pith review of Examining Lorentz invariance violation with three remarkable GRB photons." pith.science (2026). https://pith.science/paper/3BM6D4NL

@misc{pith2026250414295,
  author       = {Pith},
  title        = {Pith review of: Examining Lorentz invariance violation with three remarkable GRB photons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3BM6D4NL}},
  note         = {Machine review of arXiv:2504.14295}
}
abstract

Lorentz invariance violation in photons can be quantified by measuring the difference in arrival times between high- and low-energy photons originating from gamma-ray bursts (GRBs). When analyzing data, it is crucial to consider the inherent time delay in the emission of these photons at the source of the GRB. In a recent study, three distinct models were evaluated to explain the intrinsic emission times of high-energy photons by analyzing 14 multi-GeV photon events detected from 8 GRBs using the Fermi Gamma-ray Space Telescope (FGST). In this study, we examine three remarkable GRB photons recorded by different observatories: the 99.3~GeV photon from GRB 221009A observed by FGST, the 1.07~TeV photon from GRB 190114C detected by the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescope, and the 12.2~TeV photon from GRB 221009A observed by the Large High Altitude Air-shower Observatory (LHAASO). Our analysis indicates that the newly proposed model with a linear relationship between photon energy and intrinsic emission time can offer a consistent framework to explain the behavior of all three exceptional photons with a Lorentz violation scale $E_{\rm LV}\sim 3\times 10^{17}$~GeV.

Figures

Figures reproduced from arXiv: 2504.14295 by the authors.

Figure 1
Figure 1. The fitting results of five cases for Model A. Subfigure (a) shows the posterior distributions of fitting the 14 previous FGST photons in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Same as Fig.1, but for Model B. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Same as Fig.1, but for Model C. each other for ELV ∼ 3 × 1017 GeV, α ∼ −0.2 s·GeV−1 , and µ ∼ 0 second. We obtain a physics scenario similar to that of previous studies [6, 5, 7], that the results support the Lorentz violation with the violation scale ELV ∼ 3 × 1017 GeV and the high-energy photons are emitted prior to the low-energy photons at the GRB source frames. More detailed illustrations and in-depth analyses … view at source ↗

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.