Generalized Lorentz invariance with an invariant energy scale
Open accessAbstract
The hypothesis that the Lorentz transformations may be modified at Planck scale energies is further explored. We present a general formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Several examples are discussed in which the speed of light varies with energy and elementary particles have a maximum momenta and/or energy. Energy and momentum conservation are suitably generalized and a proposal is made for how the new transformation laws apply to composite systems. We then use these results to explain the ultrahigh-energy cosmic ray anomaly and we find a form of the theory that explains the anomaly, and leads also to a maximum momentum and a speed of light that diverges with energy. We finally propose that the spatial coordinates be identified as the generators of translation in Minkowski spacetime. In some examples this leads to a commutative geometry, but with an energy dependent Planck constant.
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- Authors
- Magueijo, J., & Smolin, L.
- Affiliations
- Imperial College London (GB)
- University of Waterloo (CA)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2003-02-27
- Volume
- 67
- Issue
- 4
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2152978115
- Cited by
- 691
- References
- 38
- Citations by year
- 2026: 9 · 2025: 24 · 2024: 23 · 2023: 27 · 2022: 25 · 2021: 31 · 2020: 25 · 2019: 31 · 2018: 33 · 2017: 37 · 2016: 45 · 2015: 36 · 2014: 32 · 2013: 39 · 2012: 41
- FWCI
- 19.03
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (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 › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Keywords
- Planck scale, energy-dependent speed of light, energy conservation (physics), momentum conservation, composite systems, ultra-high-energy cosmic rays, momentum space
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