Generalized Lorentz invariance with an invariant energy scale

By João Magueijo, Lee Smolin. 2002

605 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/5367c1fa8e2756f25be85b433840aa757b82e6c0

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Citations in the corpus

Quantum-Spacetime Phenomenology (2008, methodology): “[58, 55, 349, 140, 386, 387, 354, 388, 352, 353, 350, 26, 200, 493, 465, 291, 314, 366] and references therein), but for the purposes of this review I shall limit my consideration of DSR ideas on phenomenology to a single one of the (many) relevant issues, which is an observation that concerns the c”
Tests of Lorentz invariance: a 2013 update (2013, background): “Also to overcome some of these conceptual problems was recently advanced what we might call a ‘spin-off’ of DSR named relative locality.”
Modern Tests of Lorentz Invariance (2005, neutral): “References 84 Modern Tests of Lorentz Invariance 5”
Probing Planck-scale physics with quantum optics (2011, background): “In fact, the concept of a generalized uncertainty principle is found in many approaches to quantum gravity, for example in string theory (3–5), in the theory of doubly special relativity (6, 7), within the principle of relative locality (8) and in studies of black holes (9–11).”
Introduction to doubly special relativity (2004, background): “For example in [30] one constructs the position space along the same lines as the energy-momentum space has been constructed in [26], [27].”
Planck-scale modified dispersion relations and Finsler geometry (2006, background): “Unfortunately while on the one hand we have precise formulations of DSR in momentum space on the other hand, the implementation of DSR in spacetime is a more subtle subject and it is a theme of intense debate at present time [21, 22, 23, 24, 25].”
An invitation to loop quantum gravity (2004, background): “e lorentz transformations arerealized non-linearly when acting on the energy and momentum eigenstates of the theory. Such theories are called modiﬁed special relativity or doubly 30 special relativity[146, 149, 150, 148]. Examples are given by some forms of noncommutative geometry, for example, κ−Mi”
Black hole information, unitarity, and nonlocality (2006, neutral): “This stands in contrast to work suggesting modified dispersion relations, maximum velocities, or preferred frames[37-40], as well as approaches based on an explicit cutoff[26].”
2+1 gravity and doubly special relativity (2003, background): “This of course cannot be the case in the real world, so it is good to know that there are implementations of DSR in 3 + 1 dimensions that do not have an upper mass limit for systems of many particles, or where the upper mass limit grows with the number of particles or the mass of the total system, i”
Generalized Uncertainty Principle: Approaches and Applications (2014, background): “The presence of an upper bound agrees with DSR [62, 108].”
Minimal Length Scale Scenarios for Quantum Gravity (2012, methodology): “For example, it has been suggested that with the addition of N particles, the Planck scale that appears in the Lorentz transformation, as well as in the modified addition law, should be rescaled to mPlN [212, 171, 210].”