Cosmic Ray and Neutrino Tests of Special Relativity

Sheldon L. Glashow; Sidney Coleman

RECORD

Cosmic Ray and Neutrino Tests of Special Relativity

Sidney Coleman, Sheldon L. Glashow

High Energy Physics - Phenomenology · Submitted 5 Mar 1997

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We describe other tests, independent of this motion, that are or can become even more sensitive.

how it is stated · hedged possibility 0.57 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. 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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,213 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.66 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Searches for anisotropies due to Earth's motion relative to a preferred frame -- modern versions of the Michelson-Morley experiment -- provide precise verifications of special relativity. We describe other tests, independent of this motion, that are or can become even more sensitive. The existence of high-energy cosmic rays places strong constraints on Lorentz non-invariance. Furthermore, if the maximum attainable speed of a particle depends on its identity, then neutrinos, even if massless, may exhibit flavor oscillations. Velocity differences far smaller than any previously probed can produce characteristic effects at accelerators and solar neutrino experiments.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Searches for anisotropies due to Earth's motion relative to a preferred frame -- modern versions of the Michelson-Morley experiment -- provide precise verifications of special relativity.	background 1.00	0.07	0.16	asserted 1.00
s1	We describe other tests, independent of this motion, that are or can become even more sensitive.	contribution 0.95	0.31	0.13	hedged possibility 0.57
s2	The existence of high-energy cosmic rays places strong constraints on Lorentz non-invariance.	background 0.68	0.13	0.22	asserted 1.00
s3	Furthermore, if the maximum attainable speed of a particle depends on its identity, then neutrinos, even if massless, may exhibit flavor oscillations.	interpretation 0.40	0.10	0.11	hedged possibility 1.00
s4	Velocity differences far smaller than any previously probed can produce characteristic effects at accelerators and solar neutrino experiments.	interpretation 0.60	0.12	0.13	asserted 0.64

What kind of paper the classifier reports this is: review 0.79 · evidence from argument 0.77.

What was examined, and what was not

sources read

arXiv listing abstract v3

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

The paper

Original abstract

Searches for anisotropies due to Earth's motion relative to a preferred frame -- modern versions of the Michelson-Morley experiment -- provide precise verifications of special relativity. We describe other tests, independent of this motion, that are or can become even more sensitive. The existence of high-energy cosmic rays places strong constraints on Lorentz non-invariance. Furthermore, if the maximum attainable speed of a particle depends on its identity, then neutrinos, even if massless, may exhibit flavor oscillations. Velocity differences far smaller than any previously probed can produce characteristic effects at accelerators and solar neutrino experiments.

Human review

How Pith checks papers → · Full audit of this paper →

References

Forward citations

Cited by 13 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 418 citations worldwide. Full citation record

Very Special Relativity
hep-ph 2006-01 accept novelty 8.0 of 10

Certain proper subgroups of the Lorentz group, dubbed Very Special Relativity, can serve as nature's exact spacetime symmetry while mimicking almost every prediction of special relativity.
A Material Frame: Hard Recoils from Slow Force Carriers
hep-ph 2026-07 conditional novelty 7.0 of 10

Making the photon's longitudinal mode a physical, ultra-slow particle turns gauge invariance into a smooth limit and predicts rare, hard recoils of charges against a preferred frame, bounded to c_L ≲ 10^-60 by xenon d...
Vacuum Cherenkov radiation for nonminimal dimension-5 Lorentz violation
hep-ph 2025-08 conditional novelty 6.0 of 10

Isotropic dimension-5 Lorentz violation in fermions is constrained to below 1e-18 GeV^-1 (proton, m-type) and 3e-28 GeV^-1 (proton, a-type) by the absence of vacuum Cherenkov radiation in cosmic rays.
New Constraints on Neutrino Velocities
hep-ph 2011-09 accept novelty 6.0 of 10

Superluminal neutrinos would rapidly lose energy by electron-positron pair emission, which rules out the OPERA anomaly and yields new limits on neutrino speed from Super-Kamiokande and IceCube.
Imprints of a Primordial Preferred Direction on the Microwave Background
astro-ph 2007-01 accept novelty 6.0 of 10

A small preferred direction during inflation imprints a specific, calculable pattern of off-diagonal correlations in the CMB, parameterized by one amplitude and one direction on the sky.

Show 8 more citing papers

Lorentz-Violating Vector Fields Slow the Universe Down
hep-th 2004-07 conditional novelty 6.0 of 10

A Lorentz-violating timelike vector field tracks matter with negative energy density and slows cosmic expansion, and primordial nucleosynthesis bounds its norm to below about 10^18 GeV.
Spherical photon orbits around the Kerr-like black hole in Einstein-Bumblebee gravity
gr-qc 2025-07 conditional novelty 5.0 of 10

In Einstein-Bumblebee Kerr-like spacetimes, spherical photon orbits are governed by a sixth-order polynomial whose roots and critical inclination angle depend on the Lorentz-violation parameter.
OPERA-reassessing data on the energy dependence of the speed of neutrinos
hep-ph 2011-09 conditional novelty 5.0 of 10

Combining OPERA, MINOS and 1979 Fermilab muon-neutrino speed data, a momentum-independent superluminal shift fits best, while tachyon and quadratic energy-dependence models are disfavored.
TeV-PeV Gamma-ray and Neutrino Emission in the Galactic Plane
astro-ph.HE 2026-06 unverdicted novelty 3.0 of 10

Alternative ISRF models produce only modest changes to the LHAASO diffuse gamma-ray fit; the associated pp neutrinos remain consistent with IceCube all-sky data and compatible with ANTARES/KM3NeT limits.
Tests of Lorentz invariance: a 2013 update
gr-qc 2013-04 accept novelty 3.0 of 10

Lorentz-violation constraints from particle physics and astrophysics are collected and tabulated, and applying them to Horava-Lifshitz gravity is argued to force that theory's Lorentz-breaking scale well below the Pla...
Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lema\^itre-Robertson-Walker Metric
physics.gen-ph 2025-05 reject novelty 2.0 of 10

A varying speed of light in FLRW is presented as gauge freedom via the lapse function, but the key variational derivation omits the √-g measure and the claimed Hubble-tension resolution contradicts Eq. (30).
Solar neutrinos and neutrino physics
hep-ph 2015-07 accept novelty 2.0 of 10

Solar neutrino data are consistently described by large-mixing-angle MSW conversion, with measured theta12 and Delta m^2_21 and a theta13 consistent with reactor experiments.
Modern tests of Lorentz invariance
gr-qc 2005-02 accept novelty 2.0 of 10

No experiment has found Lorentz violation, and the combined terrestrial and astrophysical bounds are tight enough to exclude a generic Planck-scale origin for the effect at mass dimension six or below.

How the literature uses it

44 arXiv papers cite this in 68 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 33 sentences without a confident label

Uses its data or values 1 paper

However, we know [ref] that $v_e=1$ to a precision of at least $10^-15$.

New Constraints on Neutrino Velocities · Introduction and Conclusions · 0.85

Compares with it 3 papers

At this moment, it may be appropriate to mention that the orders of magnitude of bounds [ref] and [ref] [the first one scaled to $M=M_proton$; see below] agree with the qualitative limits of Coleman and Glashow [ref] .

New two-sided bound on the isotropic Lorentz-violating parameter of modified Maxwell theory · New indirect bounds on the isotropic LV parameter · 0.98
This distinguishing feature sets meVSL apart from traditional VSL models, which often assume or necessitate an explicit mechanism driving the evolution of the speed of light [ref] .

Revisiting Varying Speed of Light in Cosmology: Insights from the Friedmann-Lema\^itre-Robertson-Walker Metric · Introduction · 0.83
To aid comparison, Table [ref] details previous strong limits on the decay of very-high energy photons from the HEGRA [ref] , the Tevatron [ref] , CANGAROO [ref] , Themistocle [ref] , and HESS [ref] .

Constraints on Lorentz invariance violation from HAWC observations of gamma rays above 100 TeV · Details of LIV limits · 0.96

Cites it as support 1 paper

Indeed, for renormalizable operators, where the phase space does not grow quickly enough, reactions of the type we consider here never achieve the necessary rate given current bounds on their coefficients, even for UHE neutrinos over cosmological distances [ref] .

Possible cosmogenic neutrino constraints on Planck-scale Lorentz violation · Introduction · 0.96

Cites it as background 22 papers

For positive $κ_tr$, the argument [ref] is well-known (see also the review [ref] for further discussion): from a single observed cosmic-ray event with primary energy $E_prim$, the inferred absence of vacuum Cherenkov radiation [ref] implies $E_prim<E_thresh^(a)$, which, with expression [ref], gives an upper bound on $κ_tr$.

New two-sided bound on the isotropic Lorentz-violating parameter of modified Maxwell theory · New indirect bounds on the isotropic LV parameter · 0.89
Photon decay is a photon LV phenomenon proposed by Coleman and Glashow [ref] , and there are strict constraints on the photon superluminal LV scale from the observation of high-energy photons.

Comprehensive analysis on photon-electron Lorentz-violation parameter plane · Introduction · 0.93
Well-motivated scenarios include photon mixing into low-mass bosonic states like axions [ref] and dark photons [ref] , photon decay via Lorentz invariance violation [ref] , etc.

Axion and dark photon limits from Crab Nebula high energy gamma-rays · Introduction · 0.85

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.