Lorentz invariance with an invariant energy scale.

By João Magueijo, Lee Smolin. Physical Review Letters, 2001

998 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9278533e3e1c4e48cac97e9d1f321cc5c99b5e27

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Citations in the corpus

Principle of relative locality (2011, background): “A second formulation of DSR expressed the same idea as an energy dependence of spacetime [32].”
Deformed special relativity as an effective flat limit of quantum gravity (2004, methodology): “From the Magueijo-Smolin algebraic point of view [3], the generalized DSR theories should be obtained by applying a unitary transformation to the Poincaré generators, J, p → UJU, UpU, and we would be studying the dynamics of this unitary transformation U .”
The Cosmological Constant and Dark Energy (2002, background): “Magueijo and Smolin (2002) mention a related issue: In which reference frame is the Planck momentum of a virtual particle at the threshold for new phenomena?”
Analogue Gravity (2005, background): “The formulation of effective gravitational theories that incorporate some sort of MDR at high energies is currently under investigation (see for example [247, 2]); these exciting developments are however beyond the scope of this review.”
The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field (2011, background): “Moreover, in doubly special relativity theories, in order to preserve velocity of light and the Planck energy as two invariant quantities, the existence of a maximal momentum is essentially required [17, 18, 19].”
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].”
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.”
2+1 gravity and doubly special relativity (2003, background): “The doubly or deformed special relativity proposal (DSR)(1) is that quantum gravity effects may lead in the limit of weak fields to modifications in the kinematics of elementary particles characterized by [5] – [9]”
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].”
Reconcile Planck scale discreteness and the Lorentz-Fitzgerald contraction (2002, background): “[2] J Magueijo, L Smolin, Lorentz invariance with an invariant energy scale, Phys Rev Lett 88 (2002) 190403.”