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Status report on Doubly Special Relativity (Kowalski-Glikman)

  1. Sep 16, 2010 #1

    marcus

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    Jerzy K-G is, as far as I know, one of the world's top experts on DSR (doubly special rel). He is scheduled to give a talk on DSR this month which I expect will be available online video. The planned date is 22 September.

    http://pirsa.org/10090070

    "Doubly" just means that a second physical quantity (a length or energy) is invariant and appears the same to all observers---in the same way that in ordinary SR the speed c appears the same to all observers.

    For several years (especially 2005-2007) it was thought by some people that

    A. Some type of DSR would turn out to be a flat limit of LQG, in 4D. This was shown to happen in 3D (Freidel Livine 2005) so it was natural to guess it might be true in 4D. Jerzy K-G was one of the main people trying to extend the 3d result during 2005-2007.

    B. DSR would involve observable dispersion--the dependence of speed on photon energy. In that case the standard speed c would be the speed of the low-energy photons we experience as ordinary light, but very high energy gamma would differ very slightly, perhaps travel slightly slower.

    DSR remains interesting. The first idea ("A", connection with LQG) turned out to be difficult to prove in 4D and for a while people stopped trying. But it is always possible that some obstacle that stood in the way has been overcome. Jerzy K-G may report something new on this!

    The second idea ("B", dispersion) is controversial. There are actually versions of DSR which do not involve dispersion---and involve a curved momentum space. This has never been clear to me, although I recall seeing it discussed in a paper of K-G as far back as 2002-2003.

    So there are issues surrounding DSR that are both interesting and in need of clarification. My hope is that the 22 September talk by Jerzy K-G will clear up the picture.

    ==============
    It's possible that people will eventually be able to prove rigorously that the current version(s) of 4D LQG have some type of DSR as a flat limit. Back in 2007 this did not seem possible and those working on it appeared to give up, but they may get back to it and make a breakthrough. (There are intuitive reasons one would expect this.)

    It's also always possible that this type of DSR would exhibit first-order dispersion! and that this would then serve to falsify whatever form of LQG had it as flat limit! Or it might turn out that the type of DSR in question did not have dispersion. The questions are not resolved.

    Have to go out for a few hours. Back later.
     
    Last edited: Sep 16, 2010
  2. jcsd
  3. Sep 16, 2010 #2
    Doubly Special Relativity is a way to combine relativity with quantum mechanics right?
     
  4. Sep 16, 2010 #3

    marcus

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    I would put it a bit differently, granpa. DSR was motivated by one of the ideas or intuitive hunches that comes up in quantum gravity (QG) research. DSR does not stand for the whole field of QG!

    DSR is a small line of research intended to achieve one comparatively simple goal. It certainly is not intended to accomplish the big goal of fusing general relativity (GR) with quantum mechanics (QM).

    The overall story that we are always hearing from science writers and others is that GR and QM (the major theory accomplishments of the past century) are incompatible. They represent the geometry of spacetime differently, so it's hard to work them into the same picture. Now GR is both our theory of gravity and our theory of largescale spacetime geometry (what curves space, how it expands, how light bends and stars collapse etc. etc.)
    So in some sense GRAVITY = GEOMETRY. A theory of how gravity works must be a theory of what shapes geometry and viceversa.

    So because of that, QUANTUM GRAVITY = QUANTUM GEOMETRY. A quantum theory of gravity will necessarily also be a quantum theory of geometry (how geometry interacts with matter and behaves at small scale where the classical geometry theory breaks down.)

    And so we see a large diverse research effort under the general heading QG, which in effect stands for both quantum gravity and quantum geometry, inasmuch as they're the same thing.
    ==============

    DSR can be thought of as a small spin-off of QG, that addresses a single issue. The issue is that early on, say around 2000, some QG researchers got the idea that the model of FLAT SPACE, UNCURVED BY GRAVITY that we get from special relativity (SR) was wrong.
    In 1905 Einstein gave us the SR theory of uncurved flat space where all observers measure the same speed of light. No gravity or curvature was involved in SR.
    Then in 1915 he gave us a fuller more complicated GR theory, describing gravity and curvature effects.

    The DSR spinoff occurred when some people got the notion that the uncurved 1905 space of SR should be modified so that all observers would have TWO things they could all agree on. They would all measure the same speed of light and they would all measure the same Planck mass unit, or Planck energy unit (equivalent).

    DSR stands for DOUBLY special rel, because there are TWO invariant quantities instead of just one.

    It is not clear that these particular researchers were right. It has still not been shown that a QG theory must have a flat (zero gravity) limit that is DSR, rather than simply SR. The idea has intuitive support, as a hunch, but has not been proven.

    So DSR is not about unifying GR with QM. It is about developing a variant of Einstein's 1905 uncurved geometry which has an extra invariant quantity, an invariant mass as well as a speed. And people have done it! They have invented several modifications of SR which have an invariant mass (or invariant energy scale, or length scale.) But the connection with other stuff is not decided yet. We still can't say if any of these versions of DSR are right. They are well-motivated spinoffs from the main QG effort but we don't know if they are actually needed, to build a satisfactory QG.

    In some versions of DSR, but not in others, extremely energetic photons are slightly slowed down compared with the ordinary low-to-moderate energy light we are used to. That's a separate issue which Jerzy K-G may discuss in his talk.

    DSR is an interesting line of research that I haven't heard much about since around 2007 (when it appeared to stall). I'll be interested to hear Jerzy's talk and get caught up on what has been happening and what the current status is on the various issues.
     
    Last edited: Sep 16, 2010
  5. Sep 16, 2010 #4
    This is whats known as Noncommutative_geometry right?
    http://en.wikipedia.org/wiki/Noncommutative_geometry

    wow this thread already shows up in a google search for double special relativity
     
  6. Sep 16, 2010 #5

    marcus

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    Granpa, Noncommutative Geometry (NCG) is another broad area of research. It is not the same as DSR.

    Maybe this is just my personal viewpoint, but I insist on seeing DSR as a narrow single-purpose research field: just aiming to tweak SR so that it has two observer-independent quantities---making that adjustment in various different ways and investigating the consequences. When you do that, often some of the accessory algebra becomes non-commutative. That's OK. A lot of basic math is NC---like just multiplying 2 small matrices together---simple 2x2 or 3x3 matrices.

    So people doing DSR often find themselves working with quantities that don't commute--so it makes a different in which order you multiply them or combine them in some fashion. Basically NC just means the order in which you do things matters.

    But Noncommutative Geometry has a special meaning. For me it means the work of Alain Connes, Ali Chamseddine, Matilda Marcoli. Possibly also Shawn Majid. I can't get into that now, have to go. Part of this is just semantics. Maybe I mean by NCG something quite particular and different from what you mean by it.
     
    Last edited: Sep 16, 2010
  7. Sep 18, 2010 #6

    marcus

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    So Jerzy K-G, who I think knows more about DSR than anyone else (esp its possible but unconfirmed connection with QG) is going to talk 22 September:
    http://pirsa.org/10090070
    Here is the abstract.
    "In my talk I would like to discuss the present status of Doubly Special Relativity. DSR is an extension of Special Relativity aimed at describing kinematics of particles and fields in the regime where (quantum) gravity effects might become relevant. I will discuss an interplay between DSR physics and mathematics of Hopf algebras."

    And to get an idea of his current research, and what results might appear in the talk, there is a recent paper.

    http://arxiv.org/abs/1008.2962
    Kinematics of a relativistic particle with de Sitter momentum space
    Michele Arzano, Jerzy Kowalski-Glikman
    12 pages
    (Submitted on 17 Aug 2010)
    "We discuss kinematical properties of a free relativistic particle with deformed phase space in which momentum space is given by (a submanifold of) de Sitter space. We provide a detailed derivation of the action, Hamiltonian structure and equations of motion for such free particle. We study the action of deformed relativistic symmetries on the phase space and derive explicit formulas for the action of the deformed Poincare' group. Finally we provide a discussion on parametrization of the particle worldlines stressing analogies and differences with ordinary relativistic kinematics."

    My impression has been that the topic of DSR is involved with the idea of curved momentum space. And Jerzy K-G gives a historical perspective on that in this paper. We are used to the idea of simply adding momenta, because we assume the momenta constitute an ordinary flat vector space. But in the curved situation, simple addition could be replaced---and combining momenta might become a (noncommutative) group operation.


    ==quote introduction==
    Field theories with curved momentum space have a long history which dates back to the early 60s when they were studied as possible examples of divergence free theories[1]. The idea of curving momentum space had been actually already introduced by Snyder in his classic paper on non-commutative space[2].

    In the past decade the topic has received a boost of new interest for different reasons. On one side certain classes of non-commutative field theories
    covariant under deformed relativistic symmetries have been shown to posses Fourier transformed counterparts which are functions of group-valued momenta. On the other hand “groupfieldtheories”, in the path integral approach,have been studied as powerful tools to generate amplitudes in the spinfoam approach to quantum gravity.

    Interestingly enough group-valued momenta emerge even in more “canonical” settings namely when analyzing the behaviour of a relativistic particle coupled to gravity. Indeed it is well known that the phase space of a standard relativistic particle is geometrically described by the cotangent bundle of Minkowski spacetime. In this case the cotangent bundle is just a product of Minkowski spacetime, the position space, and the dual of its tangentspace, the momentumspace, which is again isomorphic to R4.

    In the case when gravity is present this simple picture becomes more complex. First, gravity usually curves space, resulting in the fact that elements of momentum space become non-commutative ,with degree of non-commutativity provided by spacetime curvature.

    It turns out however that even in the case when local degrees of freedom of gravity are not present ands pacetime is flat gravity may still influence the form of the phase space of the particle in a nontrivial way...
    ==endquote==
     
    Last edited: Sep 18, 2010
  8. Sep 20, 2010 #7
    Sounds very interesting-- what time zone is the listed "4:00 PM"? Will the video be available afterward if one misses it at broadcast time?

    I will be curious to see what he says about your (B)-- if there is a sensible way to preserve an energy-dependent speed of light in the face of the fairly straightforward "nonlocality paradoxes" (a polite way to describe predicted unphysical behavior?) pointed out by Sabine Hossenfelder and I think others, I haven't seen it...
     
  9. Sep 20, 2010 #8

    marcus

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    Coin, I think it is EST (eastern standard time) but without exception, in my experience, if they have a video camera at the talk then they always post it on PIRSA. So within a day or two after the talk, you should be able to find a link-to-video on this page:
    http://pirsa.org/10090070

    PIRSA (perim. inst. recorded seminars archive) is great. Here is the overall PIRSA search link.
    http://pirsa.org/
    ======================

    Coin, I have yet to find DSR as interesting as I do LQG. The Perimeter talk I am most looking forward to this fall is scheduled for 3 November and will be given by Eugenio Bianchi. This will almost certainly be about straight LQG---little or no connection with DSR.

    But Jerzy's talk will be helpful if it clears up some of the confusion about the subject.
     
    Last edited: Sep 20, 2010
  10. Sep 20, 2010 #9

    MTd2

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  11. Sep 20, 2010 #10

    marcus

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    Wait and see. Jerzy's talk is 22 September.
     
  12. Sep 22, 2010 #11

    marcus

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  13. Sep 22, 2010 #12

    atyy

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    Excellent talk.

    The interpretation in terms of particles is problematic.
    But DSR is mathematically consistent. Field theory seems ok too.
    So is there another physical interpretation of the mathematics that will be physically ok?

    I suppose, what are the gauge invariant observables?
     
  14. Sep 22, 2010 #13

    atyy

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    From http://arxiv.org/abs/1008.2962 linked to by Marcus above, the key conclusion is "Indeed there is no a priori reason why one should pick the particular set of κ-Minkowski coordinates as “physical” coordinates of a particle since (as discussed above) they just happen to describe a dual space to the translation sector of deformed algebra of symmetry but have no other compelling role that makes them desirable candidates to describe a particle’s wordline."
     
  15. Sep 23, 2010 #14

    MTd2

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    No mention of Bee's resolution to the problem...
     
  16. Sep 28, 2010 #15
    Question mark?
     
  17. Sep 28, 2010 #16

    marcus

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    Coin, I hear your question mark, and aren't there other big ones? I was left with the impression that the main issues around DSR are still unresolved. If someone else disagrees or got a different impression, please say. The way I see it there are different versions of DSR, they have different phenomenological implications, and there is no definite hookup with any current formulation of QG. Correct me if my impression was mistaken.

    There was a chance, since JKG was giving a talk on it, that he would settle some issues and draw some firm conclusions. I was mildly expectant. But it didn't happen this time AFAICS.
     
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