De Sitter Relativity and its Relation to Special and General Relativity

[dswkdlk@googlemail.com]

There are a few groups of researchers currently working on
reformulating relativity as de Sitter relativity:

*R. Aldrovandi, J. P. Beltran Almeida, J. G. Pereira, http://arxiv.org/abs/0805.2584
*S. Cacciatori, V. Gorini, A. Kamenshchik, http://arxiv.org/abs/0807.3009
*Han-Ying Guo, Chao-Guang Huang, Zhan Xu, Bin Zhou, http://arxiv.org/abs/hep-th/0405137

Ignazio Licata and Leonardo Chiatti say Fantappié-Arcidiacono theory
of relativity was the same thing as the recent work on de Sitter
relativity. http://arxiv.org/abs/0808.1339

This is described in the wikipedia article:
http://en.wikipedia.org/wiki/De_Sitter_invariant_special_relativity

Can someone answer these questions from the article's talk page and
related pages:

*Is de Sitter Relativity any different from other work on Doubly
Special Relativity ?
*Is Fantappié-Arcidiacono theory of relativity the same as de Sitter
relativity ?
*Is de Sitter relativity just the same as special relativity using
different coordinates ?
*Does it contradict results in cosmology ?
*Does de Sitter general relativity make any sense ?

 

[jacques]

On 8 déc, 22:05, dswk...@googlemail.com wrote:
> There are a few groups of researchers currently working on
> reformulating relativity as de Sitter relativity:
>
> *R. Aldrovandi, J. P. Beltran Almeida, J. G. Pereira,http://arxiv.org/abs/0805.2584
> *S. Cacciatori, V. Gorini, A. Kamenshchik,http://arxiv.org/abs/0807.3009
> *Han-Ying Guo, Chao-Guang Huang, Zhan Xu, Bin Zhou,http://arxiv.org/abs/hep-th/0405137
>
> Ignazio Licata and Leonardo Chiatti say Fantappié-Arcidiacono theory
> of relativity was the same thing as the recent work on de Sitter
> relativity.http://arxiv.org/abs/0808.1339
>
> This is described in the wikipedia article:http://en.wikipedia.org/wiki/De_Sitter_invariant_special_relativity
>
> Can someone answer these questions from the article's talk page and
> related pages:
>
> *Is de Sitter Relativity any different from other work on Doubly
> Special Relativity ?
> *Is Fantappié-Arcidiacono theory of relativity the same as de Sitter
> relativity ?
> *Is de Sitter relativity just the same as special relativity using
> different coordinates ?
> *Does it contradict results in cosmology ?
> *Does de Sitter general relativity make any sense ?

The solution in fact does not involve GR (Einstein equation). It is
just geometry.
This is clearly described in "Spacetime and geometry" book by Sean M.
Caroll chapter 8. Addison Wesley

In short:

When you look for maximally symmetric 4D (t, x, y, z) pseudo-
riemannien universes [metric signature (-,+, +, +)] , i.e manifolds
invariant under space translation and rotation and time translation
you find three solutions. Just rely on the form of the Riemann tensor
for a maximally symetric n-dimensionnal manifold: R_abcd = K
( g_ac.g_bd - g_ad.g_bc), where K is a normalized measure of the Ricci
curvature: K = R/n(n-1) where R is the Rici scalar and g_ij is the
metric tensor.
All these manifolds have constant curvature. (Maximally symmetric: 10
elements group , I guess it is the Poincare group)
Depending on the sign of K, normalized to (-1, 0, +1) you have only
three types of solutions.
For K = 0 it's the Minkowski spacetime. Curvature is zero.
For K =1 it's the Sitter spacetime: Curvature is positive
K= -1 it's the anti De Sitter space time: Curvature is negative.
All these spacetime have the same symmetries. I do not know the De
Sitter SR but whether it relies on a symmetry group it should be very
similar (identical?) to the standard SR. Idem for anti De Sitter I
guess.

 

[hendriko373]

The symmetry group underlying a de Sitter SR is certainly not the same as the one underlying Minkowski SR. The symmetry group of the latter is the Poincaré group P, and the Minkowski spacetime is defined as the quotient group P/SO(1,3) such that it is transitive under ordinary translations. The symmetry group of de Sitter SR is the group SO(1,4) and the de Sitter spacetime is the quotient group SO(1,4)/SO(1,3) which is still a maximally symmetric spacetime, transitive under the de Sitter translations (which do not commute as opposed to Poincaré (ordinary) translations).

As you see, the Lorentz group SO(1,3) is still a subgroup of the symmetry group, such that Lorentz invariance is not broken - and this is a improvement with respect to other doubly special relativities

De Sitter general relativity can make sense, as this depends on the way you define it :) Take a look at http://arxiv.org/abs/0711.2274

Cheers
Hendrik