Lorentz Invariance with an Invariant Energy Scale
Open accessAbstract
We propose a modification of special relativity in which a physical energy, which may be the Planck energy, joins the speed of light as an invariant, in spite of a complete relativity of inertial frames and agreement with Einstein's theory at low energies. This is accomplished by a nonlinear modification of the action of the Lorentz group on momentum space, generated by adding a dilatation to each boost in such a way that the Planck energy remains invariant. The associated algebra has unmodified structure constants. We also discuss the resulting modifications of field theory and suggest a modification of the equivalence principle which determines how the new theory is embedded in general relativity.
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Martin Bojowald, A., Morales-Técotl, H. A., & Sahlmann, H. (2005) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.71.084012 · Cited by 92 · see citing works
Constraining the Energy-Momentum Dispersion Relation with Planck-Scale Sensitivity Using Cold Atoms
Giovanni Amelino-camelia, A., Lämmerzahl, C., Mercati, F., & Tino, G. M. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.171302 · Cited by 92 · see citing works
Planck scale effects on some low energy quantum phenomena
Das, S., & Mann, R. B. (2011) · Physics Letters B · doi:10.1016/j.physletb.2011.09.056 · Cited by 92 · see citing works
Taming Nonlocality in Theories with Planck-Scale Deformed Lorentz Symmetry
Giovanni Amelino-camelia, A., Matassa, M., Mercati, F., & Rosati, G. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.071301 · Cited by 89 · see citing works
Modified dispersion relations and black hole physics
Ling, Y., Hu, B., & Li, X. (2006) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.73.087702 · Cited by 91 · see citing works
Charged BTZ black holes in the context of massive gravity’s rainbow
Hendi, S. H., Panahiyan, S., Upadhyay, S., & Panah, B. E. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.95.084036 · Cited by 90 · see citing works
Black holes in Gauss-Bonnet gravity’s rainbow
Hendi, S. H., & Faizal, M. (2015) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.92.044027 · Cited by 89 · see citing works
GEODESIC STRUCTURE OF THE SCHWARZSCHILD BLACK HOLE IN RAINBOW GRAVITY
LEIVA, C., SAAVEDRA, J., & VILLANUEVA, J. (2009) · Modern Physics Letters A · doi:10.1142/s0217732309029983 · Cited by 87 · see citing works
Petruzziello, L., & Illuminati, F. (2021) · RePEc: Research Papers in Economics · Cited by 86 · see citing works
Classical and quantum mechanics of the nonrelativistic Snyder model in curved space
Mignemi, S. (2012) · Classical and Quantum Gravity · doi:10.1088/0264-9381/29/21/215019 · Cited by 87 · see citing works
- Authors
- Magueijo, J., & Smolin, L.
- Affiliations
- Imperial College London (GB)
- University of Waterloo (CA)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-04-26
- Volume
- 88
- Issue
- 19
- Pages
- 190403-190403
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2087945706
- Cited by
- 1,226
- References
- 22
- Citations by year
- 2026: 40 · 2025: 67 · 2024: 59 · 2023: 56 · 2022: 52 · 2021: 69 · 2020: 53 · 2019: 55 · 2018: 52 · 2017: 57 · 2016: 61 · 2015: 50 · 2014: 55 · 2013: 64 · 2012: 60
- FWCI
- 28.36
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- Lorentz violation, modified special relativity, Planck energy, dilation, structure constants, equivalence principle, general relativity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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