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 an observer-independent maximum energy scale and minimum length scale (the Planck energy and Planck length).
First attempts to modify special relativity by introducing an observer-independent length were made by Pavlopoulos (1967), who estimated this length at about 10−15 metres. In the context of quantum gravity, Giovanni Amelino-Camelia (2000) introduced what now is called doubly special relativity, by proposing a specific realization of preserving invariance of the Planck length 16.162×10−36 m. 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. If special relativity is to hold up exactly to this scale, different observers would observe quantum gravity effects at different scales, due to the Lorentz–FitzGerald contraction, in contradiction to the principle that all inertial observers should be able to describe phenomena by the same physical laws. This motivation has been criticized on the grounds that the result of a Lorentz transformation does not itself constitute an observable phenomenon. DSR also suffers from several inconsistencies in formulation that have yet to be resolved. Most notably it is difficult to recover the standard transformation behavior for macroscopic bodies, known as the soccer-ball-problem. The other conceptual difficulty is that DSR is a priori formulated in momentum space. There is as yet no consistent formulation of the model in position space.
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