# What is doubly special relativity?

1. Dec 10, 2007

### cristo

Staff Emeritus
I hope this is the correct place to post such a thread.

I remember hearing about this theory called doubly special relativity a while ago, and I stumbled upon an article in one of the popular science magazines (I can't remember which.. it was an oldish paper copy though) which I think was talking about the same theory.

My question to you kind folk is, basically, what is this theory? From what I gather, it is a theory that is based on not one, but two observer independent scales; the usual c-scale, and another small length scale. I also recall that it has something to do with the symmetry breaking of the lorentz group of special relativity.

Thanks

2. Dec 10, 2007

### BoTemp

I can't be of much help other than to say that I read about the theory in Lee Smolin's book, "The Trouble with Physics". He gives a few citations in his book, the two that seem most general are:

L. Friedel, J. Kowalski-Glikman, and L. Smolin, "2 + 1 Gravity and Doubly Special Relativity," Phys. Rev. D., 69:044001 (2004)

Florian Girell and Etera R. Livine, "Physics of Deformed Special Relativity," gr-qc/041279.

As for as I remember, one of the ideas of DSR was that in the same way that c is the maximum velocity a particle can achieve, there may be a maximum energy a single particle can achieve; the leading contender for the latter being the Planck energy. According to Smolin it works out astoundingly well in 2 spatial dimensions, but I'm not sure about 3.

3. Dec 11, 2007

### etera

Doubly special relativity was introduced by Amelino-Camelia, working on the phenomenology of quantum gravity. Check this paper:
http://arxiv.org/abs/gr-qc/0012051
The basic idea is to introduce a universal length (the Planck length for instance) seen by all observers the same way that the speed of light is. A priori, one may think that the Lorentz invariance must be broken because of the length contraction of special relativity. There is nevertheless a way out. Actually, there are two possibilities: you can make the length a quantum operator instead of a classical quantity, or you can deform the Lorentz transformation to accomodate a minimal length. What's fun is that both alternatives lead to non-commutative geometry!
The older paper i know of where one builds a Lorentz invariant theory with a minimal length is a PRL paper by Snyder in 1947. For a more recent review of these ideas, you can check out http://arxiv.org/abs/gr-qc/0405085 by Livine&Oriti.
Else these days, DSR is formalized as a theory (and QFT) based on the kappa-deformed Poincare group. Keep in mind that these is not simply a Lie group but its generalization as a Hopf algebra... this means that at some point one deforms the law of addition of momenta (i.e adding the momenta of the subsystems to get the momentum of the full system is not straightforward, it becomes a non-commutative addition). But the name DSR (doubly or deformed special relativity) also applies to various attempts of building Lorentz covariant theories with an extra universal constant such as the Planck length.
For stuff on the QFT based on DSR, check (rencent) papers by Amelino-Camelia, or Kowalski-Glikman and al (among which Freidel). Other authors in DSR are Arzano, Girelli, ...
Finally, one issue is the relation between DSR and quantum gravity, i.e can we derive DSR as an effective theory in some semi-classical regime of quantum gravity. In a 3d space-time, this works perfectly, check stuff by Freidel&Livine:
http://arxiv.org/abs/hep-th/0512113
For the real 4d space-time, there are hints but nothing sure yet... check stuff by Kowalski-Glikman, Smolin.
I hope this helps...
ciao