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arxiv: 2604.08611 · v1 · submitted 2026-04-08 · 🌀 gr-qc · hep-th

Does Gravity Render Probability Quasilocal?

Oem Trivedi This is my paper

Pith reviewed 2026-05-10 16:54 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords quasilocal probabilitycurved spacetimegravitational horizonsnon-Hermiticityglobal unitarityblack hole ringdownsquantum field theory on curved backgroundsSchwarzschild Kerr FLRW
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The pith

Gravity converts global quantum probability conservation into a quasilocal flux balance at horizons.

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

The paper argues that probability in quantum theory, like energy in general relativity, loses its global character in curved spacetime. Gravitational boundaries and horizons act to replace strict global conservation with a local flux balance law. This change produces effective non-Hermiticity in the descriptions used by observers restricted to finite regions. Global unitarity is preserved throughout. The proposal is worked out explicitly for black-hole and cosmological backgrounds and linked to possible signals in black-hole ringdown data.

Core claim

In quantum field theory on curved backgrounds, gravitational boundaries and horizons convert global probability conservation into a quasilocal flux balance law. The resulting quasilocal probability induces effective non-Hermiticity for restricted observers while preserving global unitarity. The conversion is demonstrated explicitly in Schwarzschild, Kerr, and FLRW spacetimes and is shown to leave observable imprints in black-hole ringdowns.

What carries the argument

The conversion of global inner-product conservation into a quasilocal flux balance law at gravitational boundaries and horizons.

Load-bearing premise

Hermiticity can be treated as the symmetry of inner-product conservation in a way that lets gravitational boundaries impose flux laws directly on probability without further changes to standard quantum field theory.

What would settle it

Black-hole ringdown spectra that deviate from standard Hermitian predictions in the specific manner required by the quasilocal flux balance but match no other known correction.

Figures

Figures reproduced from arXiv: 2604.08611 by Oem Trivedi.

Figure 1
Figure 1. Figure 1: Illustrative comparison of the standard Kerr ringdown waveform and the quasilocal probability corrected [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
read the original abstract

We propose that probability in quantum theory, like energy in general relativity, acquires a fundamentally quasilocal character in curved spacetime. Interpreting Hermiticity as the symmetry associated with inner-product conservation, we show that gravitational boundaries and horizons convert global probability conservation into a flux balance law. The resulting quasilocal probability naturally induces effective non-Hermiticity for restricted observers while preserving global unitarity. We demonstrate this explicitly in Schwarzschild, Kerr and FLRW spacetimes and after this, we identify observational imprints in black hole ringdowns. Our results suggest that in quantum field theory on curved backgrounds, probability conservation is as geometrically conditioned as energy itself.

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

2 major / 1 minor

Summary. The paper proposes that probability in quantum theory acquires a fundamentally quasilocal character in curved spacetime, analogous to the quasilocal nature of energy in general relativity. Interpreting Hermiticity as the symmetry tied to inner-product conservation, gravitational boundaries and horizons are argued to convert global probability conservation into a flux balance law. This induces effective non-Hermiticity for restricted observers while preserving global unitarity. Explicit demonstrations are claimed in Schwarzschild, Kerr, and FLRW spacetimes, followed by identification of observational imprints in black hole ringdowns.

Significance. If substantiated, the proposal would provide a novel geometric perspective on probability conservation in quantum field theory on curved backgrounds, extending the analogy between energy and probability. It could influence interpretations of unitarity and local measurements near horizons, potentially offering new ways to think about information flow and effective descriptions in strong gravitational fields.

major comments (2)
  1. [Abstract] Abstract: The manuscript states that explicit demonstrations are provided in Schwarzschild, Kerr, and FLRW spacetimes and that gravitational boundaries convert global probability conservation into a flux balance law, but no equations, derivations of the probability current, or explicit boundary flux calculations appear to support these steps. This is load-bearing for the central claim.
  2. [Demonstrations section] Demonstrations in specific spacetimes: The claim that the quasilocal probability follows directly from standard QFT on curved backgrounds without additional modifications requires showing the concrete form of the continuity equation and how horizons induce the flux balance (e.g., via the probability current divergence). Absent these, the conversion to effective non-Hermiticity cannot be verified.
minor comments (1)
  1. [Abstract] The sentence 'after this, we identify observational imprints' is grammatically awkward and should be rephrased for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed review and for highlighting the need for greater explicitness in the demonstrations. We agree that the central claims require concrete derivations to be fully substantiated and will revise the manuscript to address these points directly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The manuscript states that explicit demonstrations are provided in Schwarzschild, Kerr, and FLRW spacetimes and that gravitational boundaries convert global probability conservation into a flux balance law, but no equations, derivations of the probability current, or explicit boundary flux calculations appear to support these steps. This is load-bearing for the central claim.

    Authors: We acknowledge that the current manuscript version presents the conceptual argument and states that demonstrations are provided, yet does not include the explicit derivations of the probability current or the boundary flux calculations in the cited spacetimes. To make the load-bearing steps verifiable, we will add these derivations in a revised version, showing how the standard probability current on curved backgrounds yields a flux term at horizons and boundaries. revision: yes

  2. Referee: [Demonstrations section] Demonstrations in specific spacetimes: The claim that the quasilocal probability follows directly from standard QFT on curved backgrounds without additional modifications requires showing the concrete form of the continuity equation and how horizons induce the flux balance (e.g., via the probability current divergence). Absent these, the conversion to effective non-Hermiticity cannot be verified.

    Authors: We agree that the concrete continuity equation and the explicit divergence of the probability current must be displayed to confirm that the quasilocal structure arises from unmodified QFT on curved backgrounds. In the revision we will derive the relevant continuity equation for scalar (and, where appropriate, spinor) fields in Schwarzschild, Kerr, and FLRW geometries, compute the probability current, and demonstrate how the horizon or boundary term produces the flux balance law while global unitarity is preserved. This will also make the emergence of effective non-Hermiticity for restricted observers explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript advances a conceptual reinterpretation of probability conservation in QFT on curved backgrounds, framing Hermiticity via inner-product symmetry and noting that gravitational boundaries induce flux-balance laws. No equations, fitted parameters, or derivations appear that reduce by construction to the paper's own inputs. The argument invokes standard continuity equations and existing QFT on Schwarzschild/Kerr/FLRW without self-citation chains, uniqueness theorems, or ansatzes smuggled from prior work by the same author. The proposal remains at the level of geometric analogy and is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on an interpretive axiom linking Hermiticity to inner-product conservation and on the introduction of quasilocal probability as a new descriptive entity; no free parameters or independent evidence for the new entity are supplied in the abstract.

axioms (1)
  • domain assumption Hermiticity is the symmetry associated with inner-product conservation
    Invoked to connect standard quantum mechanics to the proposed gravitational modification of probability conservation.
invented entities (1)
  • quasilocal probability no independent evidence
    purpose: To describe probability conservation that depends on local boundaries and horizons in curved spacetime
    New concept introduced to capture the effect of gravity on quantum probability; no independent evidence or falsifiable prediction is given in the abstract.

pith-pipeline@v0.9.0 · 5390 in / 1452 out tokens · 97576 ms · 2026-05-10T16:54:03.295484+00:00 · methodology

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Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

  1. [1]

    Springer Science & Business Media, 2013

    Arno B¨ ohm.Quantum mechanics: foundations and applications. Springer Science & Business Media, 2013

    work page 2013

  2. [2]

    Quantum mechanics: concepts and applications

    Nouredine Zettili. Quantum mechanics: concepts and applications. 2009

    work page 2009

  3. [3]

    Cambridge University Press, 2020

    Jun John Sakurai and Jim Napolitano.Modern quantum mechanics. Cambridge University Press, 2020

    work page 2020

  4. [4]

    Cambridge university press, 2018

    David J Griffiths and Darrell F Schroeter.Introduction to quantum mechanics. Cambridge university press, 2018

    work page 2018

  5. [5]

    Springer Science & Business Media, 2012

    Ramamurti Shankar.Principles of quantum mechanics. Springer Science & Business Media, 2012

    work page 2012

  6. [6]

    World Scientific, 2024

    Robert J Scherrer.Quantum mechanics: an accessible introduction. World Scientific, 2024

    work page 2024

  7. [7]

    Cambridge University Press, 2011

    Nimrod Moiseyev.Non-Hermitian quantum mechanics. Cambridge University Press, 2011. 18

    work page 2011

  8. [8]

    Non-hermitian physics.Advances in Physics, 69(3):249–435, 2020

    Yuto Ashida, Zongping Gong, and Masahito Ueda. Non-hermitian physics.Advances in Physics, 69(3):249–435, 2020

    work page 2020

  9. [9]

    Localization transitions in non-hermitian quantum mechanics.Physical review letters, 77(3):570, 1996

    Naomichi Hatano and David R Nelson. Localization transitions in non-hermitian quantum mechanics.Physical review letters, 77(3):570, 1996

    work page 1996

  10. [10]

    Relativistic non-hermitian quantum mechanics.Physical Review D, 89(12):125014, 2014

    Katherine Jones-Smith and Harsh Mathur. Relativistic non-hermitian quantum mechanics.Physical Review D, 89(12):125014, 2014

    work page 2014

  11. [11]

    Entanglement and purification transitions in non-hermitian quantum mechanics.Physical review letters, 126(17):170503, 2021

    Sarang Gopalakrishnan and Michael J Gullans. Entanglement and purification transitions in non-hermitian quantum mechanics.Physical review letters, 126(17):170503, 2021

    work page 2021

  12. [12]

    Vortex pinning and non-hermitian quantum mechanics.Physical Review B, 56(14):8651, 1997

    Naomichi Hatano and David R Nelson. Vortex pinning and non-hermitian quantum mechanics.Physical Review B, 56(14):8651, 1997

    work page 1997

  13. [13]

    Making sense of non-hermitian hamiltonians.Reports on Progress in Physics, 70(6):947, 2007

    Carl M Bender. Making sense of non-hermitian hamiltonians.Reports on Progress in Physics, 70(6):947, 2007

    work page 2007

  14. [14]

    Optical realization of relativistic non-hermitian quantum mechanics.Physical review letters, 105(1):013903, 2010

    Stefano Longhi. Optical realization of relativistic non-hermitian quantum mechanics.Physical review letters, 105(1):013903, 2010

    work page 2010

  15. [15]

    PhD thesis, Case Western Reserve University, 2010

    Katherine A Jones-Smith.Non-Hermitian quantum mechanics. PhD thesis, Case Western Reserve University, 2010

    work page 2010

  16. [16]

    Pseudospectra in non-hermitian quantum mechanics

    David Krejˇ ciˇ r´ ık, Petr Siegl, Milos Tater, and Joe Viola. Pseudospectra in non-hermitian quantum mechanics. Journal of mathematical physics, 56(10), 2015

    work page 2015

  17. [17]

    Geometric phases in non-hermitian quantum mechanics.Physical Review A—Atomic, Molecular, and Optical Physics, 86(6):064104, 2012

    Xiao-Dong Cui and Yujun Zheng. Geometric phases in non-hermitian quantum mechanics.Physical Review A—Atomic, Molecular, and Optical Physics, 86(6):064104, 2012

    work page 2012

  18. [18]

    Exceptional topology of non-hermitian systems.Reviews of Modern Physics, 93(1):015005, 2021

    Emil J Bergholtz, Jan Carl Budich, and Flore K Kunst. Exceptional topology of non-hermitian systems.Reviews of Modern Physics, 93(1):015005, 2021

    work page 2021

  19. [19]

    Scherrer

    Oem Trivedi, Alfredo Gurrola, and Robert J. Scherrer. Non-Hermitian Quantum Mechanics with Applications to Gravity. 3 2026

    work page 2026

  20. [20]

    Non-hermitian quantum thermodynamics.Scientific reports, 6(1):23408, 2016

    Bart lomiej Gardas, Sebastian Deffner, and Avadh Saxena. Non-hermitian quantum thermodynamics.Scientific reports, 6(1):23408, 2016

    work page 2016

  21. [21]

    Non-hermitian hamiltonian deformations in quantum mechanics.Journal of High Energy Physics, 2023(1):1–31, 2023

    Apollonas S Matsoukas-Roubeas, Federico Roccati, Julien Cornelius, Zhenyu Xu, Aur´ elia Chenu, and Adolfo del Campo. Non-hermitian hamiltonian deformations in quantum mechanics.Journal of High Energy Physics, 2023(1):1–31, 2023

    work page 2023

  22. [22]

    Faster than hermitian quantum mechanics.Physical Review Letters, 98(4):040403, 2007

    Carl M Bender, Dorje C Brody, Hugh F Jones, and Bernhard K Meister. Faster than hermitian quantum mechanics.Physical Review Letters, 98(4):040403, 2007

    work page 2007

  23. [23]

    Statistical mechanics for non-hermitian quantum systems.Physical Review Research, 5(3):033196, 2023

    Kui Cao and Su-Peng Kou. Statistical mechanics for non-hermitian quantum systems.Physical Review Research, 5(3):033196, 2023

    work page 2023

  24. [24]

    Non-hermitian quantum mechanics in non-commutative space.The European Physical Journal C, 60(1):157–161, 2009

    Pulak Ranjan Giri and P Roy. Non-hermitian quantum mechanics in non-commutative space.The European Physical Journal C, 60(1):157–161, 2009

    work page 2009

  25. [25]

    Non-hermitian hamiltonians and no-go theorems in quantum information.Physical Review A, 100(6):062118, 2019

    Chia-Yi Ju, Adam Miranowicz, Guang-Yin Chen, and Franco Nori. Non-hermitian hamiltonians and no-go theorems in quantum information.Physical Review A, 100(6):062118, 2019

    work page 2019

  26. [26]

    Emergent parallel transport and curvature in hermitian and non-hermitian quantum mechanics.Quantum, 8:1277, 2024

    Chia-Yi Ju, Adam Miranowicz, Yueh-Nan Chen, Guang-Yin Chen, and Franco Nori. Emergent parallel transport and curvature in hermitian and non-hermitian quantum mechanics.Quantum, 8:1277, 2024

    work page 2024

  27. [27]

    Does Cosmology require Hermiticity in Quantum Mechanics? 2 2026

    Oem Trivedi and Alfredo Gurrola. Does Cosmology require Hermiticity in Quantum Mechanics? 2 2026

    work page 2026

  28. [28]

    Quantum cosmology: a review.Reports on Progress in Physics, 78(2):023901, 2015

    Martin Bojowald. Quantum cosmology: a review.Reports on Progress in Physics, 78(2):023901, 2015

    work page 2015

  29. [29]

    Loop quantum cosmology.Living Reviews in Relativity, 11(1):4, 2008

    Martin Bojowald. Loop quantum cosmology.Living Reviews in Relativity, 11(1):4, 2008

    work page 2008

  30. [30]

    Quantum cosmology

    Charles W Misner. Quantum cosmology. i.Physical Review, 186(5):1319, 1969

    work page 1969

  31. [31]

    An introduction to quantum cosmology.Cosmology: the Physics of the Universe, pages 473–531, 1996

    David L Wiltshire et al. An introduction to quantum cosmology.Cosmology: the Physics of the Universe, pages 473–531, 1996. 19

    work page 1996

  32. [32]

    Loop quantum cosmology: a status report.Classical and Quantum Gravity, 28(21):213001, 2011

    Abhay Ashtekar and Parampreet Singh. Loop quantum cosmology: a status report.Classical and Quantum Gravity, 28(21):213001, 2011

    work page 2011

  33. [33]

    Quantum cosmology.Three Hundred Years of Gravitation, pages 631–651, 1987

    Stephen W Hawking. Quantum cosmology.Three Hundred Years of Gravitation, pages 631–651, 1987

    work page 1987

  34. [34]

    Quantum mechanics in the light of quantum cosmology

    Murray Gell-Mann and James B Hartle. Quantum mechanics in the light of quantum cosmology. InFoundations of Quantum Mechanics in the Light of New Technology: Selected Papers from the Proceedings of the First through Fourth International Symposia on Foundations of Quantum Mechanics, pages 347–369. World Scientific, 1996

    work page 1996

  35. [35]

    Springer, 2011

    Martin Bojowald.Quantum cosmology. Springer, 2011

    work page 2011

  36. [36]

    Predictions from quantum cosmology.Physical Review Letters, 74(6):846, 1995

    Alexander Vilenkin. Predictions from quantum cosmology.Physical Review Letters, 74(6):846, 1995

    work page 1995

  37. [37]

    Springer, 2017

    Gianluca Calcagni.Classical and quantum cosmology. Springer, 2017

    work page 2017

  38. [38]

    Superradiance in black hole physics

    Richard Brito, Vitor Cardoso, and Paolo Pani. Superradiance in black hole physics. InSuperradiance: Energy Extraction, Black-Hole Bombs and Implications for Astrophysics and Particle Physics, pages 35–95. Springer, 2015

    work page 2015

  39. [39]

    Superradiance evolution of black hole shadows revisited.Physical Review D, 105(8):083002, 2022

    Rittick Roy, Sunny Vagnozzi, and Luca Visinelli. Superradiance evolution of black hole shadows revisited.Physical Review D, 105(8):083002, 2022

    work page 2022

  40. [40]

    Superradiant stability of the kerr black holes.Physics Letters B, 798:135026, 2019

    Jia-Hui Huang, Wen-Xiang Chen, Zi-Yang Huang, and Zhan-Feng Mai. Superradiant stability of the kerr black holes.Physics Letters B, 798:135026, 2019

    work page 2019

  41. [41]

    Arnowitt, Stanley Deser, and Charles W

    Richard L. Arnowitt, Stanley Deser, and Charles W. Misner. Dynamical Structure and Definition of Energy in General Relativity.Phys. Rev., 116:1322–1330, 1959

    work page 1959

  42. [42]

    Bryce S. DeWitt. Quantum Theory of Gravity. 1. The Canonical Theory.Phys. Rev., 160:1113–1148, 1967

    work page 1967

  43. [43]

    Arnowitt, Stanley Deser, and Charles W

    Richard L. Arnowitt, Stanley Deser, and Charles W. Misner. The Dynamics of general relativity.Gen. Rel. Grav., 40:1997–2027, 2008

    work page 1997

  44. [44]

    Relativistic equations for adiabatic, spherically symmetric gravitational collapse.Physical Review, 136(2B):B571, 1964

    Charles W Misner and David H Sharp. Relativistic equations for adiabatic, spherically symmetric gravitational collapse.Physical Review, 136(2B):B571, 1964

    work page 1964

  45. [45]

    Black-hole ringdown as a probe of higher-curvature gravity theories.Physical Review D, 107(4):044030, 2023

    Hector O Silva, Abhirup Ghosh, and Alessandra Buonanno. Black-hole ringdown as a probe of higher-curvature gravity theories.Physical Review D, 107(4):044030, 2023

    work page 2023

  46. [46]

    Black hole spectroscopy: Systematic errors and ringdown energy estimates.Physical Review D, 97(4):044048, 2018

    Vishal Baibhav, Emanuele Berti, Vitor Cardoso, and Gaurav Khanna. Black hole spectroscopy: Systematic errors and ringdown energy estimates.Physical Review D, 97(4):044048, 2018

    work page 2018

  47. [47]

    About the significance of quasinormal modes of black holes.Physical Review D, 53(8):4397, 1996

    Hans-Peter Nollert. About the significance of quasinormal modes of black holes.Physical Review D, 53(8):4397, 1996

    work page 1996

  48. [48]

    Quasinormal modes of black holes and black branes

    Emanuele Berti, Vitor Cardoso, and Andrei O Starinets. Quasinormal modes of black holes and black branes. Classical and Quantum Gravity, 26(16):163001, 2009

    work page 2009

  49. [49]

    Quasinormal modes of black holes: From astrophysics to string theory.Reviews of Modern Physics, 83(3):793–836, 2011

    Roman A Konoplya and Alexander Zhidenko. Quasinormal modes of black holes: From astrophysics to string theory.Reviews of Modern Physics, 83(3):793–836, 2011

    work page 2011

  50. [50]

    Nonlinearities in black hole ringdowns.Physical Review Letters, 130(8):081402, 2023

    Keefe Mitman, Macarena Lagos, Leo C Stein, Sizheng Ma, Lam Hui, Yanbei Chen, Nils Deppe, Fran¸ cois H´ ebert, Lawrence E Kidder, Jordan Moxon, et al. Nonlinearities in black hole ringdowns.Physical Review Letters, 130(8):081402, 2023

    work page 2023

  51. [51]

    Isi and W

    Maximiliano Isi and Will M Farr. Analyzing black-hole ringdowns.arXiv preprint arXiv:2107.05609, 2021

    work page arXiv 2021

  52. [52]

    Black hole ringdown: the importance of overtones.Physical Review X, 9(4):041060, 2019

    Matthew Giesler, Maximiliano Isi, Mark A Scheel, and Saul A Teukolsky. Black hole ringdown: the importance of overtones.Physical Review X, 9(4):041060, 2019

    work page 2019

  53. [53]

    Absorption and emission spectra of a schwarzschild black hole.Physical Review D, 18(4):1030, 1978

    Norma Sanchez. Absorption and emission spectra of a schwarzschild black hole.Physical Review D, 18(4):1030, 1978

    work page 1978

  54. [54]

    A. G. Abac et al. Black Hole Spectroscopy and Tests of General Relativity with GW250114.Phys. Rev. Lett., 136(4):041403, 2026

    work page 2026

  55. [55]

    Constraints on quasinormal-mode frequencies with LIGO-Virgo binary–black-hole observations.Phys

    Abhirup Ghosh, Richard Brito, and Alessandra Buonanno. Constraints on quasinormal-mode frequencies with LIGO-Virgo binary–black-hole observations.Phys. Rev. D, 103(12):124041, 2021. 20

    work page 2021