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De Sitter special relativity José Geraldo Pereira

  1. Feb 12, 2007 #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
     
    Last edited: Feb 12, 2007
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  3. Feb 12, 2007 #2

    marcus

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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    "In the presence of a cosmological constant, ordinary Poincaré special relativity is no longer valid and must be replaced by a de Sitter special relativity, in which Minkowski space is replaced by a de Sitter spacetime.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."

    ==================
    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."
     
    Last edited: Feb 12, 2007
  4. Feb 15, 2007 #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:

    Best,
    Christine
     
  5. Feb 25, 2007 #4

    marcus

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    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.
     
    Last edited: Feb 25, 2007
  6. Feb 25, 2007 #5

    garrett

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    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. ;)
     
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