arxiv: 2510.18670 · v1 · submitted 2025-10-21 · 🌀 gr-qc · hep-th· quant-ph

Decay of uniformly rotating particles

Luciano Petruzziello , Martin B. Plenio This is my paper

Pith reviewed 2026-05-18 04:55 UTC · model grok-4.3

classification 🌀 gr-qc hep-thquant-ph

keywords circular Unruh effectparticle decaygeneral covariancenegative energy quantarotating observersparticle stabilitynon-inertial frames

0 comments p. Extension

The pith

Uniformly rotating particles cannot be stable as they emit negative-energy quanta due to lacking a global vacuum state.

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

This paper applies general covariance to the decay properties of non-inertial particles to reinterpret the circular Unruh effect. It shows that the tree-level decay rate of an inverse-beta process with scalar fields remains a scalar under coordinate transformations without needing any thermal or non-thermal bath in the comoving frame. The decay is instead understood as the emission of negative-energy quanta. The existence of such quanta is motivated by the fact that uniformly rotating observers have no global vacuum state. This leads directly to the claim that no uniformly rotating particle can be regarded as stable.

Core claim

By applying the principle of general covariance to the decay properties of non-inertial particles, the tree-level decay rate of an inverse-β process involving scalar fields does not require the introduction of a thermal (or non-thermal) bath in the comoving frame to be a scalar under general coordinate transformations. Instead, any decay process is interpreted as an emission of negative-energy quanta, whose existence is motivated by the absence of a global vacuum state for uniformly rotating observers. This implies that, in principle, no uniformly rotating particle can be regarded as stable.

What carries the argument

Absence of a global vacuum state for uniformly rotating observers, which motivates emission of negative-energy quanta to keep decay rates covariant.

Load-bearing premise

Uniformly rotating observers lack a global vacuum state, which permits the existence and emission of negative-energy quanta in decay processes.

What would settle it

An experiment that measures whether an isolated uniformly rotating particle decays or remains stable in its comoving frame, without external fields or baths, would confirm or refute the instability claim.

read the original abstract

In this paper, we revisit the interpretation of the circular Unruh effect. To this aim, we rely on the principle of general covariance applied to the decay properties of non-inertial particles. Specifically, we show how the tree-level decay rate of an inverse-$\beta$ process involving scalar fields does not require the introduction of a thermal (or non-thermal) bath in the comoving frame to be a scalar under general coordinate transformations. Instead, we interpret any decay process as an emission of negative-energy quanta, whose existence is motivated by the absence of a global vacuum state for uniformly rotating observers. This implies that, in principle, no uniformly rotating particle can be regarded as stable.

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.

Desk Editor's Note private letter to a colleague

The paper claims rotating particles must decay via negative-energy emission to preserve covariance, but this rests on reinterpreting the lack of a global vacuum rather than a demonstrated non-zero amplitude.

read the letter

The central point is that uniformly rotating particles cannot stay stable because any decay, like an inverse-beta process, has to involve negative-energy quanta once you apply general covariance and note there is no single global vacuum for rotating observers. The authors avoid introducing a thermal bath by showing the tree-level rate remains a scalar under coordinate changes and then read the decay as emission of those negative quanta. That move is the main novelty here. It gives a direct, bath-free way to think about the circular Unruh effect and ties the instability claim straight to the absence of a Fock space annihilated by all positive-frequency modes with respect to rotating time. If the calculation holds, it sharpens the picture for non-inertial observers without extra assumptions about heat baths. The approach is clean on the covariance step and stays within standard QFT on rotating backgrounds. The soft spot is that the abstract and available summary give no explicit mode expansion, interaction Hamiltonian, or check that the rotating-frame energy actually drops. The stress-test note is fair: lacking a global vacuum does not by itself prove the interaction couples to negative-energy modes with a non-zero on-shell amplitude or produces net energy loss. Without those details the instability conclusion looks more like an interpretation layered on the rate than a derived result. The paper is aimed at people who already work on the Unruh effect and rotating frames in QFT. A reader who wants to see how covariance arguments play out in decay processes could get something from it, but only after the technical steps are verified. I would send it to peer review so the mode analysis and energy accounting can be checked directly.

Referee Report

2 major / 2 minor

Summary. The manuscript revisits the circular Unruh effect by applying general covariance to the tree-level decay rate of an inverse-β process involving scalar fields for non-inertial particles. It shows that this rate remains a scalar under coordinate transformations without requiring a thermal or non-thermal bath in the comoving frame. The authors reinterpret any decay as emission of negative-energy quanta, motivated by the absence of a global vacuum state for uniformly rotating observers, and conclude that no uniformly rotating particle can be regarded as stable.

Significance. If the central interpretation is placed on firmer footing, the result would bear on the stability of accelerated or rotating particles in QFT and extend discussions of the circular Unruh effect. The approach of using general covariance to sidestep bath assumptions is a clear strength and could lead to falsifiable predictions once explicit mode calculations are supplied. The manuscript does not contain machine-checked proofs or open code, but the theoretical claim is in principle testable against prior rotating-observer calculations.

major comments (2)

[section following the covariance argument] The covariance argument establishes that the tree-level decay rate is a coordinate scalar, yet the manuscript does not supply an explicit computation of the interaction Hamiltonian or matrix element with respect to the rotating Killing vector (or proper-time Hamiltonian) to demonstrate that the process couples to negative-energy modes and produces net energy loss for the rotating particle.
[interpretation of decay as negative-energy quanta] The step that converts the covariant rate into the instability claim rests on the assertion that absence of a global vacuum implies emission of negative-energy quanta in the inverse-β process. No mode decomposition or on-shell amplitude calculation in the rotating frame is provided to show that this emission actually occurs and lowers the rotating-frame energy.

minor comments (2)

The abstract mentions scalar fields but does not specify the precise field content or interaction Lagrangian; adding this detail would improve clarity.
Notation for the rotating time coordinate and the associated positive/negative frequency modes should be defined explicitly at first use to avoid ambiguity for readers familiar with the standard circular Unruh literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We respond to each major comment below, clarifying our use of general covariance and the logical basis for the negative-energy interpretation while indicating revisions to the text.

read point-by-point responses

Referee: The covariance argument establishes that the tree-level decay rate is a coordinate scalar, yet the manuscript does not supply an explicit computation of the interaction Hamiltonian or matrix element with respect to the rotating Killing vector (or proper-time Hamiltonian) to demonstrate that the process couples to negative-energy modes and produces net energy loss for the rotating particle.

Authors: We agree that an explicit evaluation of the matrix element with respect to the rotating Killing vector would make the coupling to negative-energy modes more concrete. Our argument, however, proceeds from the fact that the tree-level rate is computed in inertial coordinates (where the process involves ordinary positive-energy emission) and is shown to be a coordinate scalar. General covariance then requires that the same non-zero rate holds when the same process is described in rotating coordinates. Given the established absence of a global vacuum for uniformly rotating observers, this scalar rate must be carried by modes whose energy is negative with respect to the rotating Killing vector; otherwise covariance would be violated. We have added a clarifying paragraph immediately after the covariance argument to spell out this chain of reasoning without performing a new mode expansion. revision: yes
Referee: The step that converts the covariant rate into the instability claim rests on the assertion that absence of a global vacuum implies emission of negative-energy quanta in the inverse-β process. No mode decomposition or on-shell amplitude calculation in the rotating frame is provided to show that this emission actually occurs and lowers the rotating-frame energy.

Authors: The lack of a global vacuum for uniformly rotating observers is a standard result (cited in the manuscript) that precludes a positive-definite energy spectrum with respect to the rotating Killing vector. Consequently, any non-vanishing scalar decay rate must involve quanta whose energy is negative in that frame; this is the only way the process can be consistent across coordinate systems. While a full on-shell amplitude calculation in the rotating frame would be a valuable extension, it lies outside the scope of the present work, which focuses on demonstrating that the instability follows from covariance alone. We have revised the relevant section to state this implication more explicitly and to note that the rotating-frame energy loss is a direct corollary of the scalar character of the rate. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper applies the principle of general covariance to establish that the tree-level decay rate for the inverse-β process is a coordinate scalar without invoking a bath in the comoving frame. It separately motivates the interpretation of any observed decay as negative-energy emission by citing the known absence of a global vacuum for uniformly rotating observers. This interpretive step does not reduce the explicit rate calculation to the vacuum property by construction, nor does it rely on self-citation chains, fitted parameters renamed as predictions, or ansatzes smuggled from prior work. The central claim of instability follows from combining an independent covariant computation with an external fact about rotating observers, leaving the derivation non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on the principle of general covariance applied to decay and on the known absence of a global vacuum for rotating observers; negative-energy quanta are introduced as an explanatory device without independent evidence supplied in the abstract.

axioms (2)

domain assumption Principle of general covariance must hold for decay rates of non-inertial particles
Invoked to require that the tree-level decay rate remains a scalar under coordinate transformations.
domain assumption Absence of a global vacuum state for uniformly rotating observers
Used to motivate the existence of negative-energy quanta.

invented entities (1)

negative-energy quanta no independent evidence
purpose: To account for decay processes while preserving general covariance without a thermal bath
Postulated on the basis of the missing global vacuum; no independent falsifiable prediction is given in the abstract.

pith-pipeline@v0.9.0 · 5635 in / 1360 out tokens · 29830 ms · 2026-05-18T04:55:40.847299+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the Hamiltonian is no longer bounded from below, meaning that there is no global vacuum state that can be uniquely defined... no particle can really be regarded as stable
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the non positive-definiteness of ω-bar will become manifest in the example of the proton decay

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages · 14 internal anchors

[1]

Polchinski,String theory

J. Polchinski,String theory. V ol. 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2007)

work page 2007
[2]

Polchinski,String theory

J. Polchinski,String theory. V ol. 2: Superstring theory and be- yond, Cambridge Monographs on Mathematical Physics (Cam- bridge University Press, 2007)

work page 2007
[3]

Loop Quantum Gravity

C. Rovelli, Loop quantum gravity, Living Rev. Rel.1, 1 (1998), arXiv:gr-qc/9710008

work page internal anchor Pith review Pith/arXiv arXiv 1998
[4]

Rovelli and F

C. Rovelli and F. Vidotto,Covariant Loop Quantum Grav- ity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2014)

work page 2014
[5]

Nonperturbative Evolution Equation for Quantum Gravity

M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D57, 971 (1998), arXiv:hep-th/9605030

work page internal anchor Pith review Pith/arXiv arXiv 1998
[6]

Niedermaier and M

M. Niedermaier and M. Reuter, The Asymptotic Safety Sce- nario in Quantum Gravity, Living Rev. Rel.9, 5 (2006)

work page 2006
[7]

S. W. Hawking, Black hole explosions, Nature248, 30 (1974)

work page 1974
[8]

S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys.43, 199 (1975), [Erratum: Commun.Math.Phys. 46, 206 (1976)]

work page 1975
[9]

E. W. Kolb and A. J. Long, Cosmological gravitational par- ticle production and its implications for cosmological relics, Rev. Mod. Phys.96, 045005 (2024), arXiv:2312.09042 [astro- ph.CO]

work page arXiv 2024
[10]

N. D. Birrell and P. C. W. Davies,Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, UK, 1982)

work page 1982
[11]

W. G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14, 870 (1976)

work page 1976
[12]

Barcelo, S

C. Barcelo, S. Liberati, and M. Visser, Analogue gravity, Living Rev. Rel.8, 12 (2005), arXiv:gr-qc/0505065

work page arXiv 2005
[13]

L. C. B. Crispino, A. Higuchi, and G. E. A. Matsas, The Un- ruh effect and its applications, Rev. Mod. Phys.80, 787 (2008), arXiv:0710.5373 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[14]

J. R. Letaw and J. D. Pfautsch, The Quantized Scalar Field in Rotating Coordinates, Phys. Rev. D22, 1345 (1980)

work page 1980
[15]

P. C. W. Davies, T. Dray, and C. A. Manogue, The Rotat- ing quantum vacuum, Phys. Rev. D53, 4382 (1996), arXiv:gr- qc/9601034

work page arXiv 1996
[16]

Biermann, S

S. Biermann, S. Erne, C. Gooding, J. Louko, J. Schmiedmayer, 7 W. G. Unruh, and S. Weinfurtner, Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions, Phys. Rev. D102, 085006 (2020), arXiv:2007.09523 [gr-qc]

work page arXiv 2020
[17]

Einstein, Zur Quantentheorie der Strahlung, Phys

A. Einstein, Zur Quantentheorie der Strahlung, Phys. Z.18, 121 (1917)

work page 1917
[18]

J. S. Bell and J. M. Leinaas, Electrons as accelerated thermome- ters, Nucl. Phys. B212, 131 (1983)

work page 1983
[19]

J. S. Bell and J. M. Leinaas, The Unruh Effect and Quantum Fluctuations of Electrons in Storage Rings, Nucl. Phys. B284, 488 (1987)

work page 1987
[20]

Lochan, H

K. Lochan, H. Ulbricht, A. Vinante, and S. K. Goyal, Detecting Acceleration-Enhanced Vacuum Fluctuations with Atoms Inside a Cavity, Phys. Rev. Lett.125, 241301 (2020), arXiv:1909.09396 [gr-qc]

work page arXiv 2020
[21]

Y . Zhou, J. Hu, and H. Yu, Significant circular Unruh ef- fect at small acceleration, Phys. Rev. D111, L041702 (2025), arXiv:2412.19454 [gr-qc]

work page arXiv 2025
[22]

J. I. Korsbakken and J. M. Leinaas, The Fulling-Unruh effect in general stationary accelerated frames, Phys. Rev. D70, 084016 (2004), arXiv:hep-th/0406080

work page internal anchor Pith review Pith/arXiv arXiv 2004
[23]

Decay of accelerated particles

R. Muller, Decay of accelerated particles, Phys. Rev. D56, 953 (1997), arXiv:hep-th/9706016

work page internal anchor Pith review Pith/arXiv arXiv 1997
[24]

D. A. T. Vanzella and G. E. A. Matsas, Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect, Phys. Rev. Lett.87, 151301 (2001), arXiv:gr-qc/0104030

work page internal anchor Pith review Pith/arXiv arXiv 2001
[25]

G. E. A. Matsas and D. A. T. Vanzella, Decay of protons and neutrons induced by acceleration, Phys. Rev. D59, 094004 (1999), arXiv:gr-qc/9901008

work page internal anchor Pith review Pith/arXiv arXiv 1999
[26]

D. A. T. Vanzella and G. E. A. Matsas, Weak decay of uni- formly accelerated protons and related processes, Phys. Rev. D 63, 014010 (2001), arXiv:hep-ph/0002010

work page internal anchor Pith review Pith/arXiv arXiv 2001
[27]

Analytic Evaluation of the Decay Rate for Accelerated Proton

H. Suzuki and K. Yamada, Analytic evaluation of the decay rate for accelerated proton, Phys. Rev. D67, 065002 (2003), arXiv:gr-qc/0211056

work page internal anchor Pith review Pith/arXiv arXiv 2003
[28]

The Unruh effect for mixing neutrinos

G. Cozzella, S. A. Fulling, A. G. S. Landulfo, G. E. A. Matsas, and D. A. T. Vanzella, Unruh effect for mixing neutrinos, Phys. Rev. D97, 105022 (2018), arXiv:1803.06400 [gr-qc]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[29]

Role of neutrino mixing in accelerated proton decay

M. Blasone, G. Lambiase, G. G. Luciano, and L. Petruzziello, Role of neutrino mixing in accelerated proton decay, Phys. Rev. D97, 105008 (2018), arXiv:1803.05695 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[30]

Blasone, G

M. Blasone, G. Lambiase, G. G. Luciano, and L. Petruzziello, Neutrino oscillations in the Unruh radiation, Phys. Lett. B800, 135083 (2020), arXiv:1903.03382 [hep-th]

work page arXiv 2020
[31]

Blasone, G

M. Blasone, G. Lambiase, G. G. Luciano, and L. Petruzziello, On theβ-decay of the accelerated proton and neutrino oscilla- tions: a three-flavor description with CP violation, Eur. Phys. J. C80, 130 (2020), arXiv:2002.03351 [hep-ph]

work page arXiv 2020
[32]

G. E. A. Matsas and D. A. T. Vanzella, Weak decay of swirling protons and other processes (2003), arXiv:hep-th/0301141

work page internal anchor Pith review Pith/arXiv arXiv 2003
[33]

Blasone, G

M. Blasone, G. Lambiase, G. G. Luciano, and L. Petruzziello, Inverseβ-decay: a twin-model with boson fields, J. Phys. Conf. Ser.1226, 012027 (2019)

work page 2019
[34]

I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products(1943)

work page 1943
[35]

B. S. DeWitt, Quantum Field Theory in Curved Space-Time, Phys. Rept.19, 295 (1975)

work page 1975
[36]

G. W. Gibbons, Vacuum Polarization and the Spontaneous Loss of Charge by Black Holes, Commun. Math. Phys.44, 245 (1975)

work page 1975
[37]

L. H. Ford, Spectrum of the Casimir Effect, Phys. Rev. D38, 528 (1988)

work page 1988
[38]

Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect

F. Scardigli, Some heuristic semiclassical derivations of the Planck length, the Hawking effect and the Unruh effect, Nuovo Cim. B110, 1029 (1995), arXiv:gr-qc/0206025

work page internal anchor Pith review Pith/arXiv arXiv 1995
[39]

P. M. Alsing and P. W. Milonni, Simplified derivation of the Hawking-Unruh temperature for an accelerated observer in vac- uum, Am. J. Phys.72, 1524 (2004), arXiv:quant-ph/0401170

work page internal anchor Pith review Pith/arXiv arXiv 2004