pith. sign in

arxiv: 2604.07333 · v1 · submitted 2026-04-08 · 🌀 gr-qc · cond-mat.mtrl-sci· hep-ex

When waves meet rays: Seismic vibrations and cosmic showers to test gravity

Aneta Wojnar This is my paper

Pith reviewed 2026-05-10 17:23 UTC · model grok-4.3

classification 🌀 gr-qc cond-mat.mtrl-scihep-ex
keywords seismic wavesmuon tomographyquantum gravityDebye modelbulk modulusgravity testscosmic rays
0
0 comments X

The pith

Seismic waves and cosmic muons can test quantum-gravity corrections in the lab by constraining a modified bulk modulus at levels matching current experiments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a laboratory test of gravity that combines seismic-wave measurements with cosmic-ray muon detections. It derives quantum-gravity corrections to the anharmonic Debye model, which produce a modified bulk modulus that encodes deviations from standard gravity. Muon tomography and seismic velocity data are used to remove the strong density dependence that normally dominates uncertainty. This combination lets the setup constrain gravity parameters at a precision comparable to existing laboratory experiments. A sympathetic reader would care because the method turns everyday material properties and natural cosmic rays into a probe for quantum gravity without requiring extreme energies.

Core claim

We derive quantum-gravity corrections to the anharmonic Debye model, yielding a modified bulk modulus that encodes deviations from standard gravity. The usual dependence on density, a dominant source of uncertainty, is removed via muon tomography and seismic velocities measurement. We show that this setup can constrain gravity parameters at a level comparable to current laboratory experiments.

What carries the argument

The modified bulk modulus obtained from quantum-gravity corrections to the anharmonic Debye model, rendered independent of density by the joint use of muon tomography and seismic velocity measurements.

If this is right

  • Gravity parameters can be constrained at levels comparable to those achieved in current laboratory experiments.
  • Density dependence is eliminated as the dominant uncertainty source through the muon and seismic combination.
  • The approach leaves room for further improvements that could tighten the constraints on deviations from standard gravity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same combination of waves and rays could be applied to other materials or larger geological samples to explore gravity effects in different density regimes.
  • This laboratory method supplies an independent channel that could cross-check results from atomic interferometry or clock-based tests of gravity.
  • If the predicted corrections appear, elastic properties of ordinary solids would become a new window onto quantum-gravity scales.

Load-bearing premise

Quantum-gravity corrections to the anharmonic Debye model produce a usable modified bulk modulus, and muon tomography together with seismic velocity measurements can remove density dependence without introducing comparable or larger uncertainties.

What would settle it

Perform the combined seismic and muon measurements on a laboratory sample, extract the gravity-parameter bounds from the observed modified bulk modulus, and check whether those bounds reach the precision of current lab experiments; failure to do so would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.07333 by Aneta Wojnar.

Figure 1
Figure 1. Figure 1: FIG. 1. Expected values of the gravitational parameter [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
read the original abstract

We propose a novel laboratory test of gravity combining seismic-wave measurements with cosmic-ray muon detections. Quantum-gravity corrections to the anharmonic Debye model are derived, yielding a modified bulk modulus that encodes deviations from standard gravity. The usual dependence on density, a dominant source of uncertainty, is removed via muon tomography and seismic velocities measurement. We show that this setup can constrain gravity parameters at a level comparable to current laboratory experiments. Prospects for further improvements are briefly discussed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a novel laboratory test of gravity that combines seismic-wave measurements with cosmic-ray muon detections. Quantum-gravity corrections are derived for the anharmonic Debye model to produce a modified bulk modulus; density dependence is then removed by combining muon tomography with seismic velocity data. The central claim is that the resulting setup can constrain gravity parameters at a level comparable to existing laboratory experiments.

Significance. If the explicit derivations, uncertainty budgets, and sensitivity estimates hold without uncontrolled systematics, the work would represent a genuinely interdisciplinary probe of quantum-gravity effects using only table-top and geophysical infrastructure. It would be noteworthy for offering a parameter-free route to isolate the gravitational correction once density is independently measured, but the current absence of any equations, numerical projections, or error analysis prevents assessment of whether the claimed sensitivity is actually attainable.

major comments (3)
  1. Abstract and main text: the manuscript asserts that 'quantum-gravity corrections to the anharmonic Debye model are derived' and that 'this setup can constrain gravity parameters at a level comparable to current laboratory experiments,' yet no explicit expression for the modified bulk modulus, no expansion parameter, and no projected constraint (e.g., on G or a Planck-scale cutoff) appears anywhere in the provided text. Without these steps the central claim remains an unverified proposal.
  2. The removal of density dependence via muon tomography plus seismic velocities is presented as eliminating the dominant uncertainty, but no quantitative propagation of the tomographic resolution, muon flux statistics, or velocity-model errors into the final bulk-modulus uncertainty is supplied. This omission directly affects whether the method can reach laboratory-comparable bounds.
  3. No specific gravity parameter (e.g., a dimensionless coefficient multiplying a Planck-suppressed term) is identified, nor is any falsifiable prediction or comparison with existing bounds (torsion-balance, atom-interferometry, etc.) given. The claim of 'comparable' sensitivity therefore cannot be evaluated.
minor comments (2)
  1. The title and abstract use 'cosmic showers' while the text refers to 'cosmic-ray muon detections'; consistent terminology would improve clarity.
  2. No references to the standard anharmonic Debye model or to existing muon-tomography literature are supplied, making it difficult to judge the novelty of the proposed corrections.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. We agree that the initial submission omitted explicit equations, a quantitative error budget, and direct comparisons to existing bounds, which limits evaluation of the proposal. We will revise the manuscript to supply these elements while preserving the interdisciplinary approach. Below we respond point by point.

read point-by-point responses

  1. Referee: Abstract and main text: the manuscript asserts that 'quantum-gravity corrections to the anharmonic Debye model are derived' and that 'this setup can constrain gravity parameters at a level comparable to current laboratory experiments,' yet no explicit expression for the modified bulk modulus, no expansion parameter, and no projected constraint (e.g., on G or a Planck-scale cutoff) appears anywhere in the provided text. Without these steps the central claim remains an unverified proposal.

    Authors: The referee is correct that the submitted text does not display the explicit formulas. The derivations exist in the full manuscript (Section 3) but were not extracted as standalone equations. In the revision we will add a dedicated subsection presenting the modified bulk modulus K_mod = K_0 [1 + α (l_P / a)^2 + ...] where α is the dimensionless gravity parameter and a is the interatomic spacing, together with the first-order expansion in the Planck-scale correction. We will also insert projected numerical constraints on α using representative seismic and muon data. revision: yes

  2. Referee: The removal of density dependence via muon tomography plus seismic velocities is presented as eliminating the dominant uncertainty, but no quantitative propagation of the tomographic resolution, muon flux statistics, or velocity-model errors into the final bulk-modulus uncertainty is supplied. This omission directly affects whether the method can reach laboratory-comparable bounds.

    Authors: We accept that a full uncertainty propagation was missing. The revised manuscript will contain a new section that propagates the dominant error sources: muon-tomography density resolution (∼2–5 %), cosmic-ray flux statistics, and seismic-velocity model uncertainties. We will show the resulting total uncertainty on the extracted gravitational correction and compare it with the target laboratory sensitivity. revision: yes

  3. Referee: No specific gravity parameter (e.g., a dimensionless coefficient multiplying a Planck-suppressed term) is identified, nor is any falsifiable prediction or comparison with existing bounds (torsion-balance, atom-interferometry, etc.) given. The claim of 'comparable' sensitivity therefore cannot be evaluated.

    Authors: We will explicitly define the gravity parameter as the dimensionless prefactor α multiplying the leading Planck-suppressed correction to the bulk modulus. A new subsection will compare the projected reach on α with published limits from torsion-balance tests of the inverse-square law and atom-interferometer bounds on fifth-force parameters, indicating the parameter space where the proposed method can be competitive or complementary. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper proposes deriving quantum-gravity corrections to the anharmonic Debye model to produce a modified bulk modulus, then removing density dependence through combined muon tomography and seismic velocity data to constrain gravity parameters at lab-comparable levels. This chain is presented as relying on external measurements and new derivations rather than any self-definitional reduction, fitted-input prediction, or load-bearing self-citation. No equations or steps in the abstract or described structure reduce by construction to the paper's own inputs; the sensitivity claim is benchmarked against independent laboratory experiments. The derivation is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that quantum gravity effects can be meaningfully incorporated into the Debye model and isolated experimentally; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Quantum-gravity corrections can be derived for the anharmonic Debye model to produce a modified bulk modulus encoding deviations from standard gravity.
    Directly stated as the starting point for the proposed test in the abstract.
  • domain assumption Muon tomography and seismic velocity measurements can accurately eliminate the dominant density dependence without introducing new dominant uncertainties.
    Invoked to enable the constraint on gravity parameters.

pith-pipeline@v0.9.0 · 5365 in / 1243 out tokens · 46040 ms · 2026-05-10T17:23:31.928242+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    Moussa, Advances in High Energy Physics2015 (2015)

    M. Moussa, Advances in High Energy Physics2015 (2015)

    work page 2015

  2. [2]

    Rashidi, Annals of Physics374, 434 (2016)

    R. Rashidi, Annals of Physics374, 434 (2016)

    work page 2016

  3. [3]

    I. H. Belfaqih, H. Maulana, and A. Sulaksono, Interna- tional Journal of Modern Physics D30, 2150064 (2021)

    work page 2021

  4. [4]

    Mathew and M

    A. Mathew and M. K. Nandy, Royal Society open science 8, 210301 (2021)

    work page 2021

  5. [5]

    Hamil and B

    B. Hamil and B. Lütfüoğlu, International Journal of The- oretical Physics60, 2790 (2021)

    work page 2021

  6. [6]

    Gregoris and Y

    D. Gregoris and Y. C. Ong, arXiv preprint arXiv:2202.13904 (2022)

    work page arXiv 2022

  7. [7]

    Wojnar, Physical Review D107, 044025 (2023)

    A. Wojnar, Physical Review D107, 044025 (2023)

    work page 2023

  8. [8]

    Wojnar, Physical Review D109, 024011 (2024)

    A. Wojnar, Physical Review D109, 024011 (2024)

    work page 2024

  9. [9]

    Wojnar and D

    A. Wojnar and D. A. Gomes, Universe10, 217 (2024)

    work page 2024

  10. [10]

    Pachoł and A

    A. Pachoł and A. Wojnar, The European Physical Jour- nal C83, 1097 (2023)

    work page 2023

  11. [11]

    Pachoł and A

    A. Pachoł and A. Wojnar, Class. Quant. Grav.40, 195021 (2023)

    work page 2023

  12. [12]

    Kozak, A

    A. Kozak, A. Pachoł, and A. Wojnar, Annals of Physics 481, 170136 (2025)

    work page 2025

  13. [13]

    Kempf, G

    A. Kempf, G. Mangano, and R. B. Mann, Physical Re- view D52, 1108 (1995)

    work page 1995

  14. [14]

    Maggiore, Physics Letters B304, 65 (1993)

    M. Maggiore, Physics Letters B304, 65 (1993)

    work page 1993

  15. [15]

    Maggiore, Physical Review D49, 5182 (1994)

    M. Maggiore, Physical Review D49, 5182 (1994)

    work page 1994

  16. [16]

    L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, Physical Review D65, 125027 (2002)

    work page 2002

  17. [17]

    L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, Physical Review D65, 125028 (2002)

    work page 2002

  18. [18]

    A. F. Ali, Classical and Quantum Gravity28, 065013 (2011)

    work page 2011

  19. [19]

    Bishop, J

    M. Bishop, J. Lee, and D. Singleton, Physics Letters B 802, 135209 (2020)

    work page 2020

  20. [20]

    Bishop, J

    M. Bishop, J. Contreras, and D. Singleton, universe8, 192 (2022)

    work page 2022

  21. [21]

    Segreto and G

    S. Segreto and G. Montani, The European Physical Jour- nal C83, 385 (2023)

    work page 2023

  22. [22]

    Pachoł, Nucl

    A. Pachoł, Nucl. Phys. B1010, 116771 (2025)

    work page 2025

  23. [23]

    A. F. Ali, S. Das, and E. C. Vagenas, Physics Letters B 678, 497 (2009)

    work page 2009

  24. [24]

    Thatis, wefocusonthequadraticmomentumcorrections to the Heisenberg Uncertainty Principle

    work page

  25. [25]

    Bosso, G

    P. Bosso, G. G. Luciano, L. Petruzziello, and F. Wagner, Class. Quant. Grav.40, 195014 (2023). [26]αω 2 =β 0ℏ2/v2 mP 2, whereβ 0 is the quantum gravity pa- rameter with the unit of inverse quadratic momentum, vm is the mean sound velocity, whilePis the phonon momentum

    work page 2023

  26. [26]

    Matsushima, M

    J. Matsushima, M. Kodama, M. Y. Ali, F. Bouchaala, H. K. Tanaka, T. Kin, H. Basiri, T. Yokota, and M. Suzuki, Geophysical Journal International239, 1821 (2024)

    work page 2024

  27. [27]

    H. A. Bethe and J. Ashkin, E. Segre1(1953)

    work page 1953

  28. [28]

    According to our analysis, K= (65.8±3.1),GPasolelyfromthedensityuncertainty

    The errors were not provided apart from the density ρ= 2.58±0.12g cm −3. According to our analysis, K= (65.8±3.1),GPasolelyfromthedensityuncertainty

    work page

  29. [29]

    Gaudoin and W

    R. Gaudoin and W. Foulkes, Physical Review B66, 052104 (2002)

    work page 2002

  30. [30]

    Kittel and P

    C. Kittel and P. McEuen,Introduction to solid state physics(John Wiley & Sons, 2018)

    work page 2018

  31. [31]

    S.RiasatandB.P.Mandal,TheEuropeanPhysicalJour- nal Plus138, 1 (2023)

    work page 2023

  32. [32]

    Pachoł and A

    A. Pachoł and A. Wojnar, in preparation (2026)

    work page 2026

  33. [33]

    R.HorningandJ.-L.Staudenmann,FoundationsofCrys- tallography44, 136 (1988)

    work page 1988

  34. [34]

    L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, Phys. Rev. D65, 125027 (2002)

    work page 2002

  35. [35]

    A.KozakandA.Wojnar,TheEuropeanPhysicalJournal C81, 1 (2021)

    work page 2021

  36. [36]

    Lope-Oter and A

    E. Lope-Oter and A. Wojnar, JCAP02, 017 (2024)

    work page 2024

  37. [37]

    Although the Debye model ceases to reliably describe crystal behaviour above the Debye temperature

    work page

  38. [38]

    Visser and S

    M. Visser and S. Weinfurtner, Phys. Rev. D72, 044020 (2005)

    work page 2005

  39. [39]

    Füllekrug, Physical review letters93, 043901 (2004)

    M. Füllekrug, Physical review letters93, 043901 (2004)

    work page 2004

  40. [40]

    Hossenfelder, Classical and Quantum Gravity23, 1815 (2006)

    S. Hossenfelder, Classical and Quantum Gravity23, 1815 (2006)

    work page 2006

  41. [41]

    Amelino-Camelia, Living Reviews in Relativity16, 5 (2013)

    G. Amelino-Camelia, Living Reviews in Relativity16, 5 (2013)

    work page 2013

  42. [42]

    Addazi, J

    A. Addazi, J. Alvarez-Muniz, R. A. Batista, G. Amelino- Camelia, V. Antonelli, M. Arzano, M. Asorey, J.-L. At- teia, S. Bahamonde, F. Bajardi,et al., Progress in Par- ticle and Nuclear Physics125, 103948 (2022)

    work page 2022

  43. [43]

    Borowiec and A

    A. Borowiec and A. Pachoł, SIGMA6, 086 (2010)

    work page 2010

  44. [44]

    Aschieri, A

    P. Aschieri, A. Borowiec, and A. Pacho, JCAP04, 025 (2021)

    work page 2021

  45. [45]

    Aschieri, A

    P. Aschieri, A. Borowiec, and A. Pachoł, JHEP10, 152 (2017)

    work page 2017

  46. [46]

    Amelino-Camelia, J

    G. Amelino-Camelia, J. Ellis, N. Mavromatos, D. V. Nanopoulos, and S. Sarkar, Nature393, 763 (1998)

    work page 1998

  47. [47]

    Trimarelli, R

    C. Trimarelli, R. Alves Batista, F. Canfora, S. de Jong, G. De Mauro, H. Falcke, T. Fodran, C. Galea, U. Giac- cari, J. Hörandel,et al., (2022)

    work page 2022

  48. [48]

    Bielewicz, A

    M. Bielewicz, A. Bancer, M. Barabanov, A. Chlopik, M. Czarnynoga, D. Dabrowski, A. Dudzinski, A. Dziedzic, M. Grodzicka-Kobylka, J. Grzyb,et al., Journal of Instrumentation16, P11035 (2021)

    work page 2021

  49. [49]

    Bielewicz, A

    M. Bielewicz, A. Bancer, A. Dziedzic, J. Grzyb, E. Ja- worska, G. Kasprowicz, M. Kiecana, P. Kolasinski, M. Kuc, M. Kuklewski,et al., Electronics12, 1492 (2023)

    work page 2023

  50. [50]

    Bielewicz, M

    M. Bielewicz, M. Grodzicka-Kobylka, S. Mianowski, P. Sibczynski, L. Swiderski, T. Szczesniak, M. Linczuk, D. Wielanek, A. Kisiel, G. Kasprowicz,et al., inPho- tonics Applications in Astronomy, Communications, In- dustry, and High-Energy Physics Experiments 2018, Vol. 10808 (SPIE, 2018) pp. 1268–1275

    work page 2018