De Sitter special relativity José Geraldo Pereira

In summary, Pereira and Aldrovandi have written papers recently about how to adjust Special Relativity to the fact of positive Lambda. They say Minkowski space is no good and the papers do not seem too difficult to understand.
  • #1

marcus

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Pereira and friends have written a couple of papers recently about how to adjust Special Relativity to the fact of positive Lambda.

We should get to know who Pereira is, a little. Here is his picture
http://www.ift.unesp.br/users/jpereira/biography.html
he, and his long-time co-author Ruben Aldrovandi, are at the Institute of Theoretical Physics (Sao Paolo State University) in Brazil

Pereira and Aldrovandi are frank. They say Minkowski space is no good. The papers do not seem too difficult to understand. Here are some links:

oh, I have to go to supper. links are in the links thread, back later
 
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http://arxiv.org/abs/gr-qc/0702065
Some Implications of the Cosmological Constant to Fundamental Physics
R. Aldrovandi, J. P. Beltran Almeida, J. G. Pereira
15 pages, lecture presented at the "XIIth Brazilian School of Cosmology and Gravitation", Mangaratiba, Rio de Janeiro, September 10-23, 2006

"In the presence of a cosmological constant, ordinary Poincaré special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime. In consequence, the ordinary notions of energy and momentum change, and will satisfy a different kinematic relation. Such a theory is a different kind of a doubly special relativity. Since the only difference between the Poincaré and the de Sitter groups is the replacement of translations by certain linear combinations of translations and proper conformal transformations, the net result of this change is ultimately the breakdown of ordinary translational invariance. From the experimental point of view, therefore, a de Sitter special relativity might be probed by looking for possible violations of translational invariance. If we assume the existence of a connection between the energy scale of an experiment and the local value of the cosmological constant, there would be changes in the kinematics of massive particles which could hopefully be detected in high-energy experiments. Furthermore, due to the presence of a horizon, the usual causal structure of spacetime would be significantly modified at the Planck scale."

http://arxiv.org/abs/gr-qc/0606122
de Sitter special relativity
R. Aldrovandi, J. P. Beltran Almeida, J. G. Pereira
24 pages, to be published in Classical and Quantum Gravity

"A special relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincaré group, this theory turns out to be a specific kind of deformed (or doubly) special relativity. Some experimental consequences, as well as the causal structure of spacetime--modified by the presence of the de Sitter horizon--are briefly discussed."

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Here is something funny. José Pereira and his co-author Ruben Aldrovandi go back to 1996 with the De Sitter. that is they were already interested in using De Sitter instead of Poincaré to classify particles of the standard model BEFORE DARK ENERGY WAS OBSERVED in 1998! they were proposing to look at De Sitter gauge theory already BEFORE THE COSMO CONSTANT was discovered positive. So Pereira and Aldrovandi have a longer history of thinking about this than most people---not than everybody but certainly than most.
http://arxiv.org/abs/gr-qc/9610068
The Case for a Gravitational de Sitter Gauge Theory
R. Aldrovandi, J. G. Pereira
20 pages

"With the exception of gravitation, the known fundamental interactions of Nature are mediated by gauge fields. A comparison of the candidate groups for a gauge theory possibly describing gravitation favours the Poincaré group as the obvious choice. This theory gives Einstein's equations in a particular case, and Newton's law in the static non-relativistic limit, being seemingly sound at the classical level. But it comes out that it is not quantizable. The usual procedure of adding counterterms to make it a consistent and renormalizable theory leads to two possible theories, one for each of the two de Sitter groups, SO(4,1) and SO(3,2). The consequences of changing from the Poincaré to the de Sitter group, as well as the positive aspects, perspectives and drawbacks of the resulting theory are discussed."
 
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  • #3
Hi Marcus,

Very interesting to know there is a group on gravitation and gauge theory at the Instituto de Física Teórica (IFT/Unesp). It is relatively nearby where I live (1.5 - 2 hrs from here, in a good day without traffic -- hmmmm... too much to ask from São Paulo city... :yuck: ). They have some interesting papers. I was unaware of their work. Thanks for posting this! :smile:


Christine
 
  • #4
Garrett and others who happen to be around, I'd be happy to have some help understanding the implications of this paper that I mentioned earlier:
http://arxiv.org/abs/gr-qc/0702065
Some Implications of the Cosmological Constant to Fundamental Physics
R. Aldrovandi, J. P. Beltran Almeida, J. G. Pereira

To me it seems to be a persuasive and clearly reasoned paper---basically suggesting that one should replace Poincaré by deSitter where possible and see what results.

So, for example, Derek Wise says that he has a paper with JB, LF... "to appear" which deals with representations of the POINCARÉ two-group.
And John Baez was just here and said that they are proceeding with that paper and already have the IRREPS of the Poinc two-group.
At least if I understand his comment.

So can you explain to me whether Pereira and Aldrovandi would be satisfied with that? Or would they urge JB and Derek et al to study the
"deSitter two-group"? Yeah I know these are very naive questions. So maybe you will tell me what the right questions I should be asking and respond to THOSE instead of what I ask. Which would be fine.
 
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  • #5
Well, I'm afraid I can only answer this question with a question. DSR makes sense as what we get if we do physics in De Sitter spacetime instead of Minkowski spacetime, with the effects proportional to the cosmological constant. But our universe has a pretty small cosmological constant. In order to get measurable effects from DSR, people have to assume the cosmological constant is bigger locally -- say, increasing with local energy density. But, why would that be? Isn't the cosmological constant... constant? Either I don't understand what's going on, or people are making a dubious assumption in order to write papers. Right now I'd have to put it at 50/50 which of those is true. ;)
 

1. What is De Sitter special relativity?

De Sitter special relativity, also known as De Sitter relativity or De Sitter spacetime, is a mathematical framework that extends Einstein's theory of special relativity to include the effects of a non-zero cosmological constant. It describes the behavior of objects in a universe with a constant positive curvature, such as in the case of an accelerating expansion of the universe.

2. Who developed De Sitter special relativity?

De Sitter special relativity was first developed by Dutch physicist Willem de Sitter in 1917. It was later further developed by other scientists, including Albert Einstein, who used it to incorporate the cosmological constant into his theory of general relativity.

3. What are the key principles of De Sitter special relativity?

The key principles of De Sitter special relativity include the invariance of the speed of light, the principle of relativity, and the principle of equivalence. It also assumes that the laws of physics are the same in all inertial frames of reference and that the universe is homogenous and isotropic on a large scale.

4. How does De Sitter special relativity differ from Einstein's theory of special relativity?

De Sitter special relativity differs from Einstein's theory of special relativity in that it takes into account the effects of a non-zero cosmological constant, which causes the universe to expand at an accelerating rate. It also allows for the existence of a preferred frame of reference, known as the De Sitter frame, in which the cosmic microwave background radiation appears isotropic.

5. What are the implications of De Sitter special relativity?

The implications of De Sitter special relativity include a modified concept of time dilation and length contraction, as well as a different interpretation of the twin paradox. It also has implications for the structure and evolution of the universe, as it provides a framework for studying the effects of a non-zero cosmological constant on the dynamics of the universe.

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