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Interpreting quantum coherence of neutrinos in asymptotically flat spacetimes via effective distances: Solution to the paradoxes of the Leggett-Garg inequality and quantum information quantities

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Shan Wu, Shu-Jun Rong

High Energy Physics - Phenomenology · Submitted 16 Sep 2026 · 64 references

Pith's verdict: A clean resolution to the measure-dependence paradox in neutrino coherence via effective distances, though the claim about metric discrimination relies on limited parameter scans.

T0 · AI review

How this review was made: An AI referee (deepseek/deepseek-v4-flash) read the paper on September 18, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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  4. T3 Formal statement The claims written out in a formal math language a computer can read.
  5. T4 Proof Those claims proved, and the proof checked by computer.

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arXiv ID2609.19198 (version 1)
Pith IDVN5MIKMG, Pith's permanent record of this paper and its review
CitationShan Wu, Shu-Jun Rong. "Interpreting quantum coherence of neutrinos in asymptotically flat spacetimes via effective distances: Solution to the paradoxes of the Leggett-Garg inequality and quantum information quantities." arXiv:2609.19198 (2026). https://pith.science/paper/VN5MIKMG
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The paper

The paper claims

By mapping neutrino oscillation phases in curved spacetimes onto flat spacetime via effective distances, the paper proves that the maximum of the Leggett-Garg parameter is universal and independent of the gravitational background.

The reading

Neutrinos oscillate between flavors because their mass states travel at slightly different speeds. In curved spacetime, gravity modifies the oscillation phases through redshift and path length changes. The authors define an effective distance that absorbs these gravitational effects into a single quantity, such that the phase evolution in any asymptotically flat spacetime becomes identical to that in flat spacetime. This means that the maximal quantum coherence, quantified by the Leggett-Garg parameter, is the same everywhere, regardless of the gravitational field. Earlier work reported apparent gravitational suppression of coherence, but those results came from measuring at uniform proper-distance intervals rather than uniform effective-distance intervals. Using the correct measurement scheme restores the flat-spacetime maximum. The authors also test whether the Leggett-Garg parameter can distinguish classical spacetimes from quantum-corrected ones. They find no consistent pattern across emission positions and quantum parameters, concluding that this method cannot serve as a reliable probe of spacetime quantum structure.
Extended reading notes

Core claim

One can always map neutrino-oscillation phases in asymptotically flat spacetimes onto the phases in flat spacetime (Eq. 10), and as a result the maximal amount of quantum coherence quantified by the Leggett-Garg parameter is independent from background spacetimes (Section III.B).

Load-bearing premise

The derivation assumes that the neutrino mass eigenstates satisfy the WKB approximation and that the propagation phase can be computed via the Hamilton-Jacobi equation using a null reference trajectory (Appendix A). This requires the relativistic limit m^2/E^2 << 1 and that the affine parameter from the null geodesic is valid for massive particles at leading order.

Original abstract

In this work, we propose a notion called effective distance to characterize the essential gravitational effects on quantum coherence of neutrinos. Employing effective distances, we prove that one can always map neutrino-oscillation phases in asymptotically flat spacetimes onto the phases in flat spacetime, which is considered as a nontrivial realization of equivalence principle. Hence, the maximal amount of quantum coherence, quantified by the Leggett-Garg (LG) parameter is independent from background spacetimes, namely, the paradox that the gravitational effects on quantum coherence of neutrinos are measure-dependent (Ettefaghi et al.[1]) does not arise. Following the same route, we preclude the gravitational amplifying or damping of amplitudes of the quantum information quantities for special masses of black holes (Wang et al. [2]). To demonstrate furthermore the independence of quantum coherence from background spacetimes, we examine the proposal using the LG parameter to identify quantum-corrected models of spacetimes. For different emission positions of neutrinos and various quantum parameters, we find no consistent patterns in oscillating LG curves to discriminate a quantum metric from the classical one.

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, 5,157 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.63 · human participants 0.02 · controlled comparison 0.31 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.92 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this work, we propose a notion called effective distance to characterize the essential gravitational effects on quantum coherence of neutrinos. Employing effective distances, we prove that one can always map neutrino-oscillation phases in asymptotically flat spacetimes onto the phases in flat spacetime, which is considered as a nontrivial realization of equivalence principle. Hence, the maximal amount of quantum coherence, quantified by the Leggett-Garg (LG) parameter is independent from background spacetimes, namely, the paradox that the gravitational effects on quantum coherence of neutrinos are measure-dependent (Ettefaghi et al.[1]) does not arise. Following the same route, we preclude the gravitational amplifying or damping of amplitudes of the quantum information quantities for special masses of black holes (Wang et al. [2]). To demonstrate furthermore the independence of quantum coherence from background spacetimes, we examine the proposal using the LG parameter to identify quantum-corrected models of spacetimes. For different emission positions of neutrinos and various quantum parameters, we find no consistent patterns in oscillating LG curves to discriminate a quantum metric from the classical one.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this work, we propose a notion called effective distance to characterize the essential gravitational effects on quantum coherence of neutrinos. contribution 0.94 0.90 0.07 asserted 0.78
s1 Employing effective distances, we prove that one can always map neutrino-oscillation phases in asymptotically flat spacetimes onto the phases in flat spacetime, which is considered as a nontrivial realization of equivalence principle. result 0.68 0.94 0.19 asserted 0.99
s2 Hence, the maximal amount of quantum coherence, quantified by the Leggett-Garg (LG) parameter is independent from background spacetimes, namely, the paradox that the gravitational effects on quantum coherence of neutrinos are measure-dependent (Ettefaghi et al.[1]) does not arise. result 0.79 0.80 0.66 asserted 1.00
s3 Following the same route, we preclude the gravitational amplifying or damping of amplitudes of the quantum information quantities for special masses of black holes (Wang et al. [2]). result 0.96 0.81 0.10 asserted 1.00
s4 To demonstrate furthermore the independence of quantum coherence from background spacetimes, we examine the proposal using the LG parameter to identify quantum-corrected models of spacetimes. contribution 0.67 0.85 0.06 asserted 0.90
s5 For different emission positions of neutrinos and various quantum parameters, we find no consistent patterns in oscillating LG curves to discriminate a quantum metric from the classical one. result 1.00 0.95 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 1.00.

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

Figures
Figure 1. FIG. 1. Variation of the LG parameter
Figure 2. FIG. 2. Variation of the effective-distance interval nonuniformity
Figure 3. In fact, this value is determined by the PMNS matrix and the mass-squared differences of neutrinos. Therefore, we can preclude the paradox that the maximum amount of quantum coherence in neutrino oscillations is damped by the gravitational field when quantified by the LG parameter, but kept invariant when quantified by l1-norm measure [1]. It is worth noting that this observation also applies to gravitational modulations on other quantum information quantities in terms of neutrino phases. Let us show this in the following section. C. The Essential Gravitational Effects on…
Figure 4. FIG. 4. The variation of
Figure 5. FIG. 5. The variation of
Figure 6. FIG. 6. Effect of the quantum-correction parameters on
Figure 7. FIG. 7. The variation of
Figure 8. FIG. 8. Effect of the rotating KS quantum-correction parameter on

Figures reproduced from arXiv:2609.19198 by the authors.

References

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