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

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

2002-01-30

arxiv.org/abs/hep-th/0201245v2

Class.Quant.Grav.20:5353-5370,2003

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, LaTex. v2: Andrea Procaccini (contributing some results from hia Laurea thesis) is added to the list of authors and

Scientific paper

10.1088/0264-9381/20/24/008

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.

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