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Observer-independent quanta of mass and length

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Jerzy Kowalski-Glikman

High Energy Physics - Theory · Submitted 16 Feb 2001 · 13 references

Pith's verdict: A short, honest DSR letter whose central one-line fixed-point check needs a typo corrected before a reader can reproduce it.

T0 · AI review

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arXiv IDhep-th/0102098 (version 2)
Pith IDBXLQGCOQ, Pith's permanent record of this paper and its review
CitationJerzy Kowalski-Glikman. "Observer-independent quanta of mass and length." arXiv:hep-th/0102098 (2001). https://pith.science/paper/BXLQGCOQ
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The paper

The paper claims

Using the κ-Poincaré dispersion relation, the paper constructs a modified special relativity in which the Planck mass is observer-independent and the speed of light diverges at a finite momentum.

The reading

Special relativity says the speed of light is the same for every inertial observer, but it also says lengths and masses change when you switch frames. That makes a fixed Planck length or Planck mass look impossible: boost to a fast frame and the Planck scale should shift. Amelino-Camelia had recently proposed modifying relativity so that a minimal length stays fixed. This letter makes the analogous proposal for mass. The author states three postulates: the relativity principle, a speed of light that equals c at long wavelengths but grows with energy, and a fundamental mass M_P that every inertial observer measures identically. He then borrows the dispersion relation of the κ-Poincaré algebra, a deformed Poincaré symmetry studied since the early 1990s. In that relation, momentum approaches a finite ceiling M_P c as energy goes to infinity, so the group velocity dE/dp diverges there. A short calculation shows that the boost action vanishes at p = M_P c, which is the technical sense in which M_P is observer-independent. The paper then argues that a minimal length L_P follows from the same relation, and that because the speed of light is infinite at the Planck scale, the theory becomes Galilean there. Both steps are sketched rather than proved: the minimal-length argument is dimensional analysis, and the author defers the full phase-space treatment and the four-dimensional extension to separate papers. The core kinematic check is clean; the broader interpretation is a proposal.
Extended reading notes

Core claim

The central claim is that a modified special relativity built on the κ-Poincaré dispersion relation M_P²c⁴(1 - e^{-E/M_P c²})² - c²p² = 0 makes the Planck mass M_P the same for all inertial observers, because the boost action vanishes at p = M_P c, and that the same relation implies a minimal length L_P. If correct, this supplies an existence proof that an observer-independent mass scale can be embedded in a deformed relativity, and it suggests that the Planck-scale regime is Galilean rather than Lorentzian.

Load-bearing premise

The load-bearing premise is that the κ-Poincaré bicrossproduct boost action (Eq. 4) and its dispersion relation (Eq. 6) are the right deformation to impose. The observer-independence of M_P is then a fixed-point property of that specific algebra, not a consequence of the three postulates alone. As printed, Eq. 4 has a p² term with coefficient (1/2)M_P c, which is dimensionally inconsistent; the displayed check δp = 0 at p = M_P c only works with the standard 1/(2M_P c) coefficient. So the result rests on an algebra imported from Majid-Ruegg and Lukierski et al., with a typo in the printed boost that a reader must correct to reproduce the conclusion.

Original abstract

It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. In this letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed e.g., in the framework of the quantum $\kappa$-Poincar\'e symmetry. It follows that at the Planck scale the world may be non-relativistic.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,331 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.30 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.55 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. In this letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer. It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed e.g., in the framework of the quantum $\kappa$-Poincar\'e symmetry. It follows that at the Planck scale the world may be non-relativistic.

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 It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. background 1.00 0.03 0.03 asserted 0.87
s1 As a remedy he postulated to modify special relativity by introducing an observer-independent length scale. background 1.00 0.04 0.05 asserted 0.97
s2 In this letter we set forward a proposal how one should modify the principles of special relativity, so as to assure that the values of mass and length scales are the same for any inertial observer. contribution 1.00 0.74 0.25 hedged possibility 0.36
s3 It turns out that one can achieve this by taking dispersion relations such that the speed of light goes to infinity for finite momentum (but infinite energy), proposed e.g., in the framework of the quantum $\kappa$-Poincar\'e symmetry. method 0.68 0.48 0.23 asserted 0.76
s4 It follows that at the Planck scale the world may be non-relativistic. interpretation 0.96 0.72 0.43 hedged possibility 0.99

What kind of paper the classifier reports this is: theoretical result 0.49 · evidence from argument 0.63.

What was examined, and what was not

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  • references and citing sentences
  • relations to other papers
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not run
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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

References
How the literature uses it

49 arXiv papers cite this in 63 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 · 21 sentences without a confident label

Compares with it 1 paper
Cites it as support 1 paper
Cites it as background 36 papers
  • Deformations of special relativity (DSR) [ref] allegedly make it possible to introduce an energy-dependent speed of light in position space while still preserving observer-independence.

    Comment on arXiv:1007.0718 by Lee Smolin · Introduction · 0.98

  • For this purpose we return here to the simple perspective and formalization of the first studies [ref] which noticed that some known deformations of relativistic symmetries, some of the ones studied within the “doubly-special relativity" research programme (see, e.g., Refs. [ref] ), could result in the property that coincidences of events established by nearby observers might not appear as coincidences of events in the coordinatization of spacetime by distant observers.

    Modeling transverse relative locality · Introduction · 0.80

  • The alternative possibility is a “deformation" of relativistic symmetries, in the sense of the “Doubly-Special Relativity" [ref] (DSR) scenario, which insists on a relativistic formulation of laws, as required by the first postulate, and confines all revisions of relativity to revisions of the second postulate.

    Testing quantum-spacetime relativity with gamma-ray telescopes · Introduction · 0.91

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