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Triply Special Relativity is the Max

  1. Jul 12, 2004 #1


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    the flat limit of Quantum Gravity will probably not be Minkowski space
    but the space of an extended special relativity like
    the Triply Special Relativity that Lee Smolin and Jerzy K-G just posted a paper about

    "Triply Special Relativity"

    The idea is analogous to what happend circa 1900 with Singly Special.
    They took old galilean framework and said "how can we bend this slightly so the speed of light will be the same for all observers?"
    the coordinate change transformations---the symmetries----are nearly the same as euclidean/galilean except at very high speeds.

    then you can say what if TWO quantities are the same for all observers. The speed c and also a very small length, like the Planck length?
    And you can bend Singly Special a little bit to make that happen and you get Doubly special.

    Now Jerzy K-G and Smolin have addressed the problem of what if you want to have 3 absolute quantities---speed of light, and Planck length AND the cosmological constant.

    And they bend things just a wee bit more and they get that. It seems like a good candidate for the flat limit of Quantum Gravity doesnt it?

    And that leaves the question that any mathematician would immediately ask which is "can you go any higher?" Could you futher deform or extend the K-G and S triple relativity so that it becomes quadruple?

    Well Chryssomalakos and Okun have proven that you cant


    Triple Relativity is max.

    From their abstract:
    "...As a corollary we assure that, within the Lie algebra framework, there is no Quadruply Special Relativity."
    Last edited: Jul 12, 2004
  2. jcsd
  3. Jul 12, 2004 #2
    The reason I am putting this here is the paper you and Nereid offered sometime past.

    If you go to the conclusion in this paper on page 8

    In quantum mechanics, the vacuum of space is not a vacuum; rather, it is a field with virtual particles, such as the graviton. Light passing through this field of virtual particles is refracted just as it is passing through water or any medium


    I was looking for some method that would help me discern the nature of this quantum geometry, yet it has revealled a non communitive geometry for thinking, so this begins a new road.

    It must be recognized tha LQG does not recognize the graviton, yt strings do. So looking to SR I see where LQG is basing its bets?

    I hope this falls in line with your post.
  4. Jul 13, 2004 #3


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    Hi sol,

    you have some evocative analogies (at least one anyway) here but I want to back up and emphasize something that I think is understood and implicit.

    There are currently several Quantum Gravity approaches that seem to be close relatives----Loop is one, then there is Simplex Gravity (ambjorn-loll style) and there Stephen Hawking's "Path Integral" approach, and also Spin Foams (worked on by john baez in particular, and others). there is also a kind of Pre-1986 Wheeler-DeWitt quantum gravity that is still alive expecially in cosmology. A new result in one of these can often be carried over. Advances in one approach encourage parallel attempts in related ones.

    Meteor recently hazarded a guess that quantum gravity would remove the BH singularity within 5 years----by 2009. It is a good bet because
    the BB singularity was removed in 2001 using Loop cosmology. (and this has been duplicated using different but related approaches, even the pre-loop Wheeler-DeWitt cosmology!) So it is a good bet that the BH singularity will be quantized away using SOME quantum gravity approach.

    But it does not make sense to bet on which. Why would one want to, unless one craves for a sense of belonging and wants a team to root for.
    I prefer to observe the progress being made by these allied approaches and not favor one or the other. (they are all background independent, not stringy, and basically rather similar)

    All these approaches require something different from Minkowski space for a flat limit. IMHO.
    the flat limit for quantum gravity will probably turn out to be some slight deformation or bending of minkow. space that keeps the Planck length, and maybe also the cosmological constant, invariant.

    At the moment the only theory left out of this, I guess, is string---which is built on Minkowski space (or on other set geometries with Mink. space for flat limit). This is believed to be a virtue by string theorists, I understand. But maybe they will get busy and create yet another version of their theories that gets off of minkowski space and onto something like Smolin's triply special relativity extension of it. I really can't guess.

    Oh, here is a related paper
    Girelli Livine Oriti
    "Deformed Special Relativity as an effective flat limit of quantum gravity"
    http://arxiv.org/gr-qc/0406100 [Broken]

    they talk about Triple Relativity too, but under a different name, and
    sketch out possible relations between it and the MOND alternative explanation of dark matter and energy. The connection seems very tenuous to me, but potentially exciting.

    this Triple Relativity thing is so new that everybody has a different name for it.
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  5. Jul 13, 2004 #4

    I appreciate the summary, because if you step back and to look at the overall picture this helps to align ones thinking from those different perspectives. Its a lot to take in sometimes. Also finding the fundamental beginnings of all these approaches in terms of a discription of quantum gravity, asks how one would ever have ventured a means for descrbining something at plancklength. So I needed to understand the limits current measures are bringing forth and from which perspective.

    Again there has to be some central point that consensus gathers around for a symbol of answering the nature of quantum gravity, that such a model as the blackhole garners and holds these perspective too, to describe this process. A meausre of the progresses as you have pointed out about Loop. Strings has already been there and answered it?

    I was looking for some geometrical consistancy that would have satisfied this basis and the continuing look here is continually reforming my persepctive on the nature of all these discriptions that are materializing. But one thing indeed that made sense to me is the question of "pull" as a basis of matter distinctions in the cosmo must have some implicit design relevance to hyperbolic or spherical continuations from the einstein perspective into the areas of quantum mechanics. We know Einstein with Grossman's help choose one route specufically and why I mention Reinmann and the constant reference to Gauss.

    I recognize this flat line in the abscence of gravitational wave production and SR eucldiean discription in absolute space. So indeed some presence in this absolute space causes the refractive capabilties, and methods that I thought would help determine the nature of this geometry. It was close(glast), but on further inspection and demands of the sci string physics board I continue to look and found where the non-communitive geometry, all of a sudden brings the perspective closer for consideration on the issue sof quantum geometry.

    I continue to watch the quantum computatin end and developement at the PI institute because of the organizational aspect developing there under the leadership( Slyboy did show the other venues in regards to the computation end as well, so we must give credit to all contiued efforts here).

    If I could find Smolins early summation of the different perspectives, as you have done here at the beginning of this post, you can see where distilliation thoughts mount. I looked hard to find a underlying principal as smolin had done as mentioned in previous posts about the way in which we produce new mathematical perspectives undertanding the limitations current thought have held to certain class distinction describing that quantum gravity.

    Belonging? :smile: Some shoud be so bold not in arrogance, but truly hold high the spiritual aspect in developement recogniztion of some truth, and not succumb to the demand of such belonging. This seems a throw back to some deeper evolutionary course that has been hidden under different jackets in the mental realm? On the other end, so afraid to disturb the minds of excellence that we leave them alone to develope mind and leave all other things fall apart around them?

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  6. Jul 13, 2004 #5


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    Hi Sol,
    before I even try to respond I should be quick to say something I left out last night. Suppose gammaray observatories like GLAST find no hint of any deviation from pure and simple Lorentz invariance. I cant speak with certainty but I think that would be a discouraging result for all the non-string approaches to quantum gravity.
    This is still controversial (quoting John Baez)---but if it is true it agrees with what you suggested.

    Namely that the background independent approaches to QG do seem to favor some (call it what you want, extension, deformation, modification) bending of Lorentz symmetry.

    What Chrysso and Okon call "3-scale special relativity"

    they all seem to want some other quantity or quantities besides the speed of light to look the same to all observers.

    BTW I like the name Chryssomalakos----I think the major stress is on the "la" syllable. And at least for now I like their terminology.
    Also they cite a 1994 paper I did not know
    R. Vilela Mendes "Deformation, Stable Theories and Fundamental Constants".
    Also they point out that even in Single Relativity (with supposedly only the speed of light invariant) there is another fundamental constant that is invariant, namely hbar, but people dont count that. So if you count hbar then in what Smolin calls Triple relativity there are really 4 invariant quantities. this gets confusing, so it is better to stick with the convention and not count hbar.
    the idea that nature should have constants and that they look the same to all observers is very beautiful------they are like nature's proportions, the outlines of her face or what have you.
  7. Jul 13, 2004 #6
    High energy recognitions here make it somewhat difficult if we consider the ideas in Glast. But along the way in my research the entanglement issue comes to the forefront here in what is being done in terms of Quantum computation. Such a Axiom of sphercial considerations, that would immediately turn a certain way, while from across the cosmos, this sphere is being dictated?

    This reduces the thinking to the way in whcih such measures photonically in comparison might have revealled dynamics underlying the events arcoss the wide expansiveness of the cosmos.

    But now there would be ths problem we are being faced with if there is only a non communitive discription to discribing this geometry?

    You must be patient with me here :smile:
  8. Aug 5, 2009 #7


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    Just to tell Triply Special relativity is the last talk session of Loop's 09. Any advances in that?

    BTW, Marcus you should reread your old posts, lol.
  9. Aug 5, 2009 #8


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    Heh heh, how time flies! This paper is already 5 years old, that is the subject of the thread.
    I think the result here is mathematical in nature---it is a no-go theorem, proving that you cannot keep on adding quantities that a Lorentz-like group of transformations is required to hold constant.

    You can make a speed c be the same in all frames---then you get Lorentz
    You can instead make both a speed c and a mass M be the same to all observers and then you get double-special (DSR)

    You can even go one step farther and require that THREE quantities be the same in all frames, according to these people, and then you have triple-special (TSR).

    But then the math stops and will not go any farther. You cannot force four.

    Mathematically that seems like a satisfying useful result, even if it says nothing about physics. It is nice to have logical/mathematical limits. No-go theorems are nice.

    But at this point the whole DSR issue has become observational and I would say that TSR is not interesting until we know if DSR is right or wrong. The time now is to test if there is some distortion of Lorentz invariance, which will basically be simple and straightforward to do. Just acquire enough gamma-burst data from the Fermi satelite.

    Now theorizing about DSR (and further elaborations on that) is not so interesting as simply checking to see if there is energy-dependence of photon speed. Either way, yes or no, knowing that will be helpful.
  10. Aug 5, 2009 #9
    Whats the apeal of DSR or TSR besides that its mathematical consistent and tesable? Does it some how make quantization easyer? I understand that in LQG when you quantize gravity then areas and lengths become discrete but one still has lorentz invariance. But in DSR are you assuming that DSR holds in the classical limit so then you throw away lorentz invariance?
  11. Aug 5, 2009 #10


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    Basically, Finbar, I think DSR is just something that could be observationally true, and one would want to know.
    Science is based on constantly doubting your assumptions and checking them whenever a new method or instrument makes possible a new test. We have this assumption that all photons go the same speed namely c.

    But what if they don't? It is possible that a photon whose energy is a trillionth of a percent of Planck mass, travels at a speed which is a trillionth of a percent less than c.

    Sounds bizarre but the means are now available to check it. That "Planck-suppressed" slowing would be undetectable in earthbound experiments but could be detected in gammaburst phtons that have been traveling a long time. So let's test it.

    There's probably more to say but the empirical/doubt basis is for me very strong. Deviations from simple SR should be looked out for, let's not get sleepy just because
    SR is so commonly assumed.

    The best DSR paper I know is one that Rovelli did. He is not a DSR advocate and he had some notes lying around for 10 years which just last year Smolin persuaded him to write up and post on arxiv. He doesn't say DSR is likely, but he offers an interesting reason why it might be true if it just happens to turn out to be true. You might like the paper, I don't know. So I'll fetch link for it.

    A note on DSR
    Carlo Rovelli
    6 pages, 2 figures
    (Submitted on 26 Aug 2008)
    "I study the physical meaning of Deformed, or Doubly, Special Relativity (DSR). I argue that DSR could be physically relevant in a certain large-distance limit. I consider a concrete physical effect: the gravitational slowing down of time due to the gravitational potential well of a massive-particle, and its effect on the dynamics of the particle itself. I argue that this physical effect can survive in a limit in which gravitation and quantum mechanics can be disregarded, and that taking it into account leads directy to the Girelli-Livine DSR formalism. This provides a physical interpretation to the corresponding 5d spacetime, and a concrete physical derivation of DSR."

    This might be just what you are looking for because it gives one person's idea of a possible physical motivation, if it happens to turn out. Rovelli does not include or assume DSR in his normal QG research, nor do his grad students/postdocs and other associates show much interest on the whole if i remember right.

    DSR does arise in 3D QG*, so that could be a possible teaser which could motivate investigation, but it does not arise in an analogous way in 4D QG (that was looked at a lot in 2005-2006 and didn't pan out). So there is no LQG prediction of it.

    *look up Freidel Livine 2005 on arxiv for that.
    Here, I've got it: http://arxiv.org/abs/hep-th/0512113
    Last edited: Aug 5, 2009
  12. Aug 6, 2009 #11
    Here you seem convinced that something like DSR should be true by use of the word "probably". I was thinking that a reason why loop people may be interested i might be to do with finding the classical limit of LQG that agrees with classical gravity. As I understand it LQG has some issues with finding the right classical limit?
  13. Aug 6, 2009 #12


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    Finbar, what you are quoting there is something I wrote back in 2004 :biggrin:
    LQG in fact did have serious issues about classical limit back then!

    And a lot of people thought that you might be able to derive 4D dsr from a 4D quantum gravity model. So I was reflecting what a lot of the experts thought at the time. I'm not sure there was any definite relation between this and the classical limit problem, however.

    In fact it did turn out in 2005 that in 3D you get dsr derived as a flat limit from spinfoam lqg.
    This was very interesting and suggestive, but people tried unsuccessfully to extend the result to 4D and seem to have set that aside for a while. Again, I don't see a connection with classical or semiclassical or largescale limit (there may be one but I don't see it.)

    About the limit of spinfoam LQG, you might like to check out the PDF slide set for Laurent Freidel's talk on 14 July at the Marcel Grossmann meeting in Paris. If you want a link let me know.
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