# Double Special Relativity (DSR) fake or real?

Double Special Relativity (DSR) fake or real??

I have read several webpages about this 'new' kind of interpreting Relativity, as far as i know you consider that appart from light speed 'c' you need to have an invariant PlanckEnery and Planck-time, my questions are.

a) What's the metric for this DSR $$g_{ab}dx^{a} dx^{b}$$

b) What're the DSR Lorentz transforms ?

c) What's the 'Energy' (if any) Hamiltonian or Lagrangian for this theory?

If possible be expresive as you can since i don't know higher algebra..

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pervect
Staff Emeritus
I have no clue as to why they think that this could lead to new predictions or simplify anything.

I stick to single special relativity, that's hard enough aready for me.

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xantox
Gold Member
Doubly special relativity is real enough. There is a fairly new paper out which purports to show that DSR is actually just a coordinate transformation of SR, however.

http://arxiv.org/abs/gr-qc/0602075

Lee Smolin wrote: "This is an old objection and its not only wrong, its not original. It was settled years ago. Its embaressing that they bring it up again, but note that they reference no paper except their own later than 2003. The basic point is that the phase space for DSR is quantum deformed and so it is not isomorphic to the phase space algebra of a particle in ordinary special relativity. To see why DSR is not equivalent to SR you have to look at the whole phase space algebra, not just a part of it. By only looking at a piece of the algebra-how the lorentz boosts act on translation generators, you can get to the wrong conclusion-as they do here, and as was done before. Another way to see it is that the kappa poincare algebra, is the q-deformed symmetry of a non-commutative geometry which is kappa minkowski spacetime."

I stick to this DSR, in fact i'm not saying that SR is false of course but has some classical 'mistakes'

a) HOw can a particle has arbitrary high energy without collapsing into a Black Hole ?? or without disobey the Heisenberg's uncertainty ??? ( i think there must be a natural cut-off for momentum and energy since otherwise we could make a black hole from a particle .

b) at v=c then the 'length' (observed) of a body becomes 0, but this contradict the existence of a Planck -length, time.

c) If Planck energy and time exist in nature then they must be the same for every observer, no matter the system they are.

i find this DSR very interesting, i also support Smollin's idea of a 4-D gravity without using strings and further dimension.

pervect
Staff Emeritus
I stick to this DSR, in fact i'm not saying that SR is false of course but has some classical 'mistakes'

a) HOw can a particle has arbitrary high energy without collapsing into a Black Hole ?? or without disobey the Heisenberg's uncertainty ??? ( i think there must be a natural cut-off for momentum and energy since otherwise we could make a black hole from a particle .
This is not a problem for standard GR. For a popular level article, see for instance http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html.

Because the theory is covariant, an object will never collapse into a black hole because of its speed.

If you consider the case of two particles moving on parallel paths at high speed, held apart by a measuring device of negligible mass, you will find that the force in the measuring device transforms covariantly, i.e. it has a definite value in the rest frame of the particles, a force that is independent of the speed. So it does not go to infinity.

An important reason why the force law is covariant also helps explain why such a collapse does not occur. When we consider gravitomagnetism, we realize that two parallel mass currents repel each other, much in the same way as two parallel electric currents attract each other. The difference in sign comes from the fact that like charges repel, while like masses attract.

So a crude way of putting it is that gravitomagnetism is one of the reason why an object does not turn into a black hole at high velocities.