Comparison of relativity theories with observer-independent scales of both velocity and length/mass

Abstract

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as illustrative example for the original proposal (gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity, and energy-momentum-conservation rules in these theories with two relativistic invariants.

21 pages, LaTex. v2: Andrea Procaccini (contributing some results from hia Laurea thesis) is added to the list of authors and the paper provides further elements of comparison between DSR1 and DSR2, including the observation that both lead to the same formula for the dependence of momentum on rapidity

References in corpus (4)

• Lorentz invariance with an invariant energy scale
• Doubly Special Relativity
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Non-commutative space-time of Doubly Special Relativity theories

Cited by in corpus (13)

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• Relativistic kinematics beyond Special Relativity
• Hamiltonian Formalism of the de-Sitter Invariant Special Relativity
• Kappa-Deformations: Historical Developments and Recent Results
• Dispersion relations in finite-boost DSR
• Bounds on Relativistic Deformed Kinematics from the Physics of the Universe Transparency
• $\kappa$-General-Relativity I: a Non-Commutative GR Theory with the $\kappa$-Minkowski Spacetime as its Flat Limit
• Regularization of Kepler Problem in $\kappa$-spacetime
• Some Features of Scattering Problem in a $\kappa$-Deformed Minkowski Spacetime
• Massive Gauge Fields and the Planck Scale