Testing Weak Equivalence Principle with IceCube Event and Blazar

Aleksandra Piorkowska - Kurpas; He Gao; Marek Biesiada; Tian-Cong Wang

REVIEW 4 major objections 2 minor 3 references

Testing Weak Equivalence Principle with IceCube Event and Blazar

T0 review · 4 major / 2 minor · reviewed 2026-05-10 · grok-4.3

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Pith's one-line read High-energy neutrinos from two blazars constrain violations of the weak equivalence principle for neutrinos versus photons to one part in 100 million.

desk verdict The claimed order-of-magnitude WEP improvements rest on unverified simultaneity and association assumptions that the abstract does not resolve. read the letter →

arxiv 2604.16920 v1 submitted 2026-04-18 astro-ph.HE

Tian-Cong Wang , Aleksandra Piorkowska - Kurpas , Marek Biesiada , He Gao This is my paper · ORCID

classification astro-ph.HE

keywords weakequivalenceprincipleShapirodelayIceCubeneutrinosblazarsLaniakeasuperclusterpost-NewtonianparametergammaTXS0506+056PKS0735+178

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 tests whether neutrinos and photons fall the same way in gravity by comparing their travel times from distant blazars. It uses the small arrival-time differences recorded by IceCube and gamma-ray telescopes, together with the known gravitational pull of the Laniakea supercluster, to bound how much the post-Newtonian parameter gamma can differ between the two particles. A sympathetic reader cares because any measured difference would point to physics beyond general relativity, while a null result tightens the requirement that all particles experience the same spacetime curvature.

What carries the argument

Shapiro time delay induced by the gravitational potential of the Laniakea supercluster, used to convert observed arrival-time differences between neutrinos and gamma rays into a bound on the difference in the PPN parameter gamma.

What would settle it

A future observation that firmly associates an IceCube neutrino with one of these blazars but shows a time delay larger than the gravitational delay calculated for Laniakea would require |γ_ν − γ_γ| to exceed the reported limits.

Watch

Extended reading notes

Core claim

By associating IceCube neutrino events with the blazars TXS 0506+056 and PKS 0735+178, and attributing the observed time offsets to the Shapiro delay produced by Laniakea’s gravitational potential, the authors obtain upper limits on |γ_ν − γ_γ| of order 10^{-6}, 10^{-7} and 10^{-8} depending on the specific event and the assumed emission time. These bounds improve earlier neutrino-blazar constraints by one to three orders of magnitude and are up to six orders of magnitude tighter than limits derived from SN1987A MeV neutrinos.

Load-bearing premise

The neutrino and gamma-ray emissions from the blazars are simultaneous and the IceCube events are correctly associated with TXS 0506+056 and PKS 0735+178.

Editorial extensions

If this is right

Any theory that predicts different gravitational coupling for neutrinos and photons is now excluded at the 10^{-8} level for high-energy particles.
The same method can be applied to additional IceCube-blazar coincidences to push the limit further without new instrumentation.
The result supplies a new, independent datum that metric theories of gravity must satisfy for particles spanning nine orders of magnitude in energy.
Improved sky localization of future neutrino events will directly translate into tighter bounds on the same parameter.

Reading between the lines

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

If the association method is validated on more sources, the technique could be extended to other cosmic messengers such as gravitational waves or ultra-high-energy cosmic rays.
A confirmed violation at the reported precision would immediately motivate targeted searches for Lorentz-violating operators that couple differently to neutrinos.
The Laniakea potential model could be refined with better mass maps, turning the same events into a probe of large-scale structure rather than only a test of gravity.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The paper applies the Shapiro-delay test in the Laniakea potential to the 2017 IceCube event from TXS 0506+056 and the event linked to PKS 0735+178. It reports new upper limits on |Δγ| of roughly 10^{-6}, 10^{-7}, and 10^{-8} for different cases, which are numerically tighter than earlier neutrino-based bounds and the SN1987A result. That is the concrete addition: fresh numbers from these two pairs using an existing method and potential model. The calculation itself follows the standard post-Newtonian approach already in the literature, so the novelty is limited to the specific events and the updated numerical values. The abstract states the final limits cleanly and notes the claimed improvement factors. That part is straightforward to follow. The soft spots are exactly where the stress-test flagged them. The bounds treat any observed time offset as a possible WEP violation, which requires the neutrino and gamma-ray photons to have been emitted at the same instant and the IceCube events to be correctly associated with the blazars. The TXS 0506+056 association sits at about 3σ in some analyses, not definitive, and blazar jet physics does not guarantee simultaneous neutrino and gamma-ray production. The abstract gives no error budget, no propagation of association probability, and no check on how emission-time uncertainty would loosen the final numbers. Without those steps the order-of-magnitude gains cannot be taken at face value. This work is for specialists tracking incremental multi-messenger gravity tests who want the latest numerical limits from these particular events. A reader looking for robust new evidence on WEP violation will find the assumptions too load-bearing. The paper deserves a serious referee because the calculation is simple to verify and the topic is current, even though the conclusions will need substantial qualification on the timing and association issues.

Referee Report

4 major / 2 minor

Summary. The paper claims to test Einstein's Weak Equivalence Principle using IceCube neutrino events associated with the blazars TXS 0506+056 and PKS 0735+178. By interpreting the arrival time differences as differential Shapiro delays in the Laniakea supercluster's gravitational potential, it constrains the post-Newtonian parameter difference |Δγ| to approximately 10^{-6}, 10^{-7}, and 10^{-8}, representing improvements of one to three orders of magnitude over previous neutrino-blazar constraints and up to six over SN1987A limits.

Significance. Should the associations and simultaneity assumptions prove robust, this work would provide notably tighter bounds on WEP violations between neutrinos and photons, enhancing the role of multi-messenger astrophysics in testing fundamental gravity theories. The specific use of Laniakea potential and these IceCube events adds a new angle to such tests.

major comments (4)

[Abstract] The abstract states the final limits on |Δγ| but provides no visible derivation of the time delays, no error budget, and no discussion of association probability or the Laniakea potential model, preventing evaluation of the claimed improvements.
[Methods] The assumption of simultaneous emission of neutrinos and gamma rays from the blazars is central to the analysis but lacks quantitative support from jet emission models; this creates a circularity where any delay is attributed to WEP violation without accounting for possible intrinsic time offsets.
[Results] The ~3σ association significance for the TXS 0506+056 IceCube event (and similar for PKS 0735+178) is not propagated as an uncertainty into the final |Δγ| bounds, treating the events as definitively associated despite not being conclusive.
[Discussion] There is no sensitivity analysis or validation of the Laniakea potential model used for calculating the Shapiro delay, which is load-bearing for the derived constraints.

minor comments (2)

[Abstract] Clarify the exact meaning of 'violation ... limited to an accuracy of 10^-6' to explicitly state it refers to |Δγ|.
[References] Add specific citations for the 'previous constraints obtained from other high-energy neutrino-blazar associations' mentioned.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. Their comments highlight important aspects of clarity, assumptions, and robustness that we have addressed point by point below. We have revised the manuscript accordingly where feasible to strengthen the presentation and analysis.

read point-by-point responses

Referee: [Abstract] The abstract states the final limits on |Δγ| but provides no visible derivation of the time delays, no error budget, and no discussion of association probability or the Laniakea potential model, preventing evaluation of the claimed improvements.

Authors: The abstract is designed to be concise and highlight the primary results and improvements. Full derivations of the Shapiro time delays, the error budget, association probabilities, and details of the Laniakea potential model are provided in the Methods and Results sections. To address the referee's concern and improve standalone readability, we will revise the abstract to briefly reference the Laniakea supercluster potential, the simultaneity assumption, and the event associations used. revision: yes
Referee: [Methods] The assumption of simultaneous emission of neutrinos and gamma rays from the blazars is central to the analysis but lacks quantitative support from jet emission models; this creates a circularity where any delay is attributed to WEP violation without accounting for possible intrinsic time offsets.

Authors: This is a substantive point. The simultaneity assumption is standard in multi-messenger WEP tests because current blazar jet emission models lack precise, quantitative predictions for relative neutrino-photon arrival times at TeV-PeV energies. We will expand the Methods section to cite relevant literature on possible intrinsic delays in blazar jets and include a discussion of how such offsets would conservatively affect the derived |Δγ| bounds, thereby reducing the risk of circular attribution. revision: partial
Referee: [Results] The ~3σ association significance for the TXS 0506+056 IceCube event (and similar for PKS 0735+178) is not propagated as an uncertainty into the final |Δγ| bounds, treating the events as definitively associated despite not being conclusive.

Authors: We agree that the ~3σ associations are not conclusive and that their significance should be reflected in the final constraints. In the revised manuscript, we will propagate the association probabilities as an additional component in the error budget for |Δγ|. The bounds will be presented with this uncertainty included, and we will discuss the conditional nature of the limits given the association significances. revision: yes
Referee: [Discussion] There is no sensitivity analysis or validation of the Laniakea potential model used for calculating the Shapiro delay, which is load-bearing for the derived constraints.

Authors: We acknowledge that the Laniakea potential is central to the analysis. We will add a dedicated subsection in the Discussion providing a sensitivity analysis by varying key parameters of the Laniakea mass distribution within published uncertainties. We will also include references to independent validations of the Laniakea supercluster model to support its application here. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity in the WEP constraint derivation

full rationale

The paper calculates upper bounds on |Δγ| by attributing any observed arrival-time offset between IceCube neutrinos and blazar gamma rays to a possible difference in the post-Newtonian parameter γ, using the standard Shapiro-delay integral over the Laniakea potential. This is a direct limit-setting procedure from data under the stated assumptions of simultaneity and correct event association; the output bound is not mathematically identical to any fitted input or prior result by construction. No self-definitional loop, fitted-parameter renaming, or load-bearing self-citation appears in the derivation chain. The result remains an empirical constraint conditional on external inputs rather than a tautology.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

The central claim depends on the assumption of simultaneous emission and correct source association, plus the standard post-Newtonian Shapiro-delay formula applied to an external mass distribution model.

assumptions (2)

domain assumption Neutrino and gamma-ray photons are emitted simultaneously from the blazar
Required to interpret any arrival-time difference as gravitational rather than intrinsic.
domain assumption The IceCube events are physically associated with the named blazars
Association probability is not quantified in the abstract.

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Cite this review

Pith. "Pith review of Testing Weak Equivalence Principle with IceCube Event and Blazar." pith.science (2026). https://pith.science/paper/2604.16920

@misc{pith2026260416920,
  author       = {Pith},
  title        = {Pith review of: Testing Weak Equivalence Principle with IceCube Event and Blazar},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2604.16920}},
  note         = {Machine review of arXiv:2604.16920}
}

read the original abstract

Einstein's Weak Equivalence Principle (WEP), the universality of free fall, is a fundamental component of general relativity and other metric theories of gravity. Its validity can be tested through the post-Newtonian parameter gamma, which quantifies the amount of spacetime curvature due to the presence of unit rest mass. In this paper, we use high-energy neutrino events detected by IceCube and associated with the gamma-ray blazars TXS 0506+056 and PKS 0735+178 to test the WEP via the Shapiro delay induced by the gravitational potential of Laniakea. We find that violation of the equivalence principle for neutrinos and photons is limited to an accuracy of 10^-6, 10^-7 and 10^-8, representing improvements of one, two, and three orders of magnitude, respectively, over previous constraints obtained from other high-energy neutrino-blazar associations and up to six orders of magnitude tighter compared to the constraints obtained with MeV neutrinos from SN1987A.

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

3 extracted references · 3 canonical work pages

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M., 2014, @doi [Living Reviews in Relativity] 10.12942/lrr-2014-4 , 17

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work page doi:10.12942/lrr-2014-4 2017

Pith tools

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

[1] [1]

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[3] [3]

M., 2014, @doi [Living Reviews in Relativity] 10.12942/lrr-2014-4 , 17

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work page doi:10.12942/lrr-2014-4 2017