• DOI:10.1103/PhysRevD.67.044017
• Corpus ID: 16998340

Generalized Lorentz invariance with an invariant energy scale

@article{Magueijo2002GeneralizedLI,
  title={Generalized Lorentz invariance with an invariant energy scale},
  author={Jo{\~a}o Magueijo and Lee Smolin},
  journal={Physical Review D},
  year={2002},
  volume={67},
  pages={044017}
}

• J. Magueijo, L. Smolin
• Published 22 July 2002
• Physics
• Physical Review D

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 non-linear 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 ultra high 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.