Doubly special relativity

Doubly special relativity (DSR) – also called deformed special relativity or, by some, extra-special relativity – is a modified theory of special relativity in which there is not only an observer-independent maximum velocity (the speed of light), but also, an observer-independent maximum energy scale (the Planck energy) and/or a minimum length scale (the Planck length). This contrasts with other Lorentz-violating theories, such as the Standard-Model Extension, where Lorentz invariance is instead broken by the presence of a preferred frame. The main motivation for this theory is that the Planck energy should be the scale where as yet unknown quantum gravity effects become important and, due to invariance of physical laws, this scale should remain fixed in all inertial frames. First attempts to modify special relativity by introducing an observer-independent length were made by Pavlopoulos (1967), who estimated this length at about e-15metres. In the context of quantum gravity, Giovanni Amelino-Camelia (2000) introduced what is now called doubly special relativity, by proposing a specific realization of preserving invariance of the Planck length 1.6162e-35m. This was reformulated by Kowalski-Glikman (2001) in terms of an observer-independent Planck mass. A different model, inspired by that of Amelino-Camelia, was proposed in 2001 by João Magueijo and Lee Smolin, who also focused on the invariance of Planck energy. It was realized that there are, indeed, three kinds of deformation of special relativity that allow one to achieve an invariance of the Planck energy; either as a maximum energy, as a maximal momentum, or both. DSR models are possibly related to loop quantum gravity in 2+1 dimensions (two space, one time), and it has been conjectured that a relation also exists in 3+1 dimensions. The motivation to these proposals is mainly theoretical, based on the following observation: The Planck energy is expected to play a fundamental role in a theory of quantum gravity; setting the scale at which quantum gravity effects cannot be neglected and new phenomena might become important.