Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2004-12-01
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
24 pages, Revtex4
Scientific paper
In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. Some experiments will soon be able to test some low energy effects of quantum gravity, and DSR is a very promising candidate to describe these latter. Unfortunately DSR is up to now plagued by many conceptual problems (in particular how it describes macroscopic objects) which forbids a definitive physical interpretation and clear predictions. Here we propose a consistent framework to interpret DSR. We extend the principle of relativity: the same way that Special Relativity showed us that the definition of a reference frame requires to specify its speed, we show that DSR implies that we must also take into account its mass. We further advocate a 5-dimensional point of view on DSR physics and the extension of the kinematical symmetry from the Poincare group to the Poincare-de Sitter group (ISO(4,1)). This leads us to introduce the concept of a pentamomentum and to take into account the renormalization of the DSR deformation parameter kappa. This allows the resolution of the "soccer ball problem" (definition of many-particle-states) and provides a physical interpretation of the non-commutativity and non-associativity of the addition the relativistic quadrimomentum. In particular, the coproduct of the kappa-Poincare algebra is interpreted as defining the law of change of reference frames and not the law of scattering. This point of view places DSR as a theory, half-way between Special Relativity and General Relativity, effectively implementing the Schwarzschild mass bound in a flat relativistic context.
Girelli Florian
Livine Etera R.
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