Physics of deformed special relativity: relativity principle revisited

Abstract

In many different ways, Deformed Special Relativity (DSR) has been argued to provide an effective limit of quantum gravity in almost-flat regime. 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 Poincaré group to the Poincaré-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 κ. 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.

Five dimensional formulation of a deformed special relativity

“…(15) does not allow us to consider the whole left-hand side as a norm. Using the same trick used in the previous section, we argue that χ α = −χ α while χ 4 = χ 4 , so 6 Eq. (15) can now be written as…”

“…As has already been underlined, in Refs. [6] and [7], the authors pointed out that this problem can be solved in their five-dimensional approach to the DSR, since the deformation scale is not the same for elementary particles and composite bodies. Nonetheless, a solution has recently been given in the Relative Locality approach too; see, for example, Ref.…”

“…The other possibility is x 0 = −x 0 and x i = x i which would lead also to a change of sign of the right hand sign of Eq. (6).…”

Macroscopic systems, dual gravity lensing and other emerging topics in quantum-gravity phenomenology

“…An emerging line of study within quantum-gravity phenomenology concerns the effects of quantum gravity on macroscopic bodies [2][3][4][5][6][7][8][9][10] . One of the most promising approaches for providing guidance to these studies is aimed at formulating manifestations of the Planck scale on momentum space [11][12][13][14] .…”

Blackbody radiation inκ-Minkowski spacetime

“…(46) which originates from the non-trivial form of the Casimir invariant Eq. (25). The presence of the complex mode is not of the usual form of the canonical field theory and may raise the unitarity problem.…”