], 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).
[3] 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.
[9] 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.
[14][15] Most notably, it is difficult to recover the standard transformation behavior for macroscopic bodies, known as the soccer ball problem.
However, it is now established that standard doubly special relativity does not predict any suppression of the GZK cutoff, contrary to the models where an absolute local rest frame exists, such as effective field theories like the Standard-Model Extension.