Re: de Sitter relativity
- From: jacques <jacques.fric@xxxxxxx>
- Date: Wed, 10 Dec 2008 00:03:32 +0000 (UTC)
On 8 déc, 22:05, dswk...@xxxxxxxxxxxxxx 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.
.
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