These three appeared this year, present versions are dated April, October, and December 2003 http://arxiv.org/hep-th/0304027 http://arxiv.org/hep-th/0304101 http://arxiv.org/hep-th/0312140 Jerzy K-G and co-authors discovered this year that in DSR (which he suggest should be called "quantum special relativity") the speed of any massless particle is c---independent of energy. The Lorentz algebra doesn't change although its action on momenta does. Both results appear in the first article linked: Daszkiewicz, Imilkowska, Kowalski "Velocity of particles in Doubly Special Relativity" The next article is longer and discusses the results at greater length: Kowalski-Glikman, Nowak "Doubly Special Relativity and de Sitter space" The third is authored solo: Kowalski-Glikman "Doubly Special Relativity and quantum gravity phenomenology". ------------------------------ It would be hard to overstate the unexpectedness and importance of these results, particularly the constancy of the speed of light. Until this year it was presumed that if, instead of only one observer-independent quantity, one postulates two (the low-energy speed of light and the Planck energy) then a photon's speed would vary with energy. Very high energy gamma photons were expected to travel perceptibly faster, so that a difference in time-of-flight would appear over very large distances. Kowalski-Glikman proves otherwise and points to a flaw in the earlier reasoning. These papers distinguish between DSR (or "DSR1") which K-G and his coworkers is developing and a later version ("DSR2") which Smolin and Magueijo investigated for the first time in 2002, in their paper "Generalized Lorentz invariance with an invariant energy scale" gr-qc/0207085. The presence of different versions complicates things but K-G manages to get all the versions into a single form. The energy-independent speed of light appears to be a robust result, valid for all versions. We seem to be looking at a Lorentz-invariant theory with two quantities (a speed and an energy) instead of one, which are the same for all observers. And where massless particles, such as photons, all travel at the same speed. To me this seems shocking and unintuitive. A lot has happened in quantum gravity in 2003. At the moment this K-G result seems the hardest to comprehend. It changes the expectations about what kind of information one may get from the forthcoming GLAST data.
Reading down in the first paper you give, we find they say that the result: the the 3-velocity of massless particles = c is true in ALL DSRs, implicitly including the one studied by Smolin et al. They get this result - different from other workers, by taking special account of the phase space of any DSR theory, which they assert, based on an earlier paper, requires the poisson brackets of the time derivatioves of the space and time variables to take a particular form, from which the speed theorem follows. I am going to look up that earlier paper - it was published in 1995 but its preprint date is 1993, and see how they get the result. (Edit) the paper is http://arxiv.org/abs/hep-th/9312153 (2d Edit) Rats! The paper can't be read by PDF!
great! I just looked up the link myself, to Lukierski Ruegg and Sakrzewski Classical quantum mechanics of free kappa relativistic systems good to have company!
selfAdjoint I got the abstract but my computer could not get the PDF. I am not able to download postscript. Perhaps you can get the PS version? The connection with ref [17} which you described, for anyone listening, is on K-G page 3 "The starting point of our investigations reported here consists of two major assumptions: that velocity is defined as the Poisson bracket of position with deformed relativistic hamiltonina (see also [17], and that to compute this bracket one must take into account the nontrivial phase space structure..." We see the explicit form of the hamiltonian in their equation (8) on page 4. The poisson brackets with the hamiltonian are written out and calculated on the next page and top of page 6, equation (14). I wonder if it can be any clearer in the 1993 paper, or presented with more intuitive justification.
Ghostscript to the rescue? SelfAdjoint, marcus, Running Windows? Can't read PS files? Ghostscript may be your saviour! IIRC, there's a free viewer, just google.
Re: Ghostscript to the rescue? Nereid, all we need PS for (excusing my unstudliness) is this one harmless-looking equation on page 5 equation (10) It is a defintion of what I would like to call "Polish velocity" [x,H] = ∂H/∂p_{0}[x,p_{0}] + ∂H/∂p_{i}[x,p_{i}] put in x_{0} and x_{i} for x, in the above, or look for yourself on page 5 of http://arxiv.org/hep-th/0304027 He says "this is how we define the velocity, in accordance with the ancient Polish custom, see reference 17" And reference 17 is a 10 year old paper by Lukierski available only in PS and not in PDF. But I am right now feeling like taking his word for it instead of going and fetching and installing ghostscript which I have been time and time again told I should do. Just look at equation (10) as it stands! What could be nicer and more civilized? The reference to Lukierski may just be a courtesy to a mentor.
Great stuff! I have to place the original link to the Smolin Maguejo paper of Dec 2001 :http://arxiv.org/abs/hep-th/0112090 This paper caused me to have some deep and dare I say it, intuitive thinking sessions over the xmas hols of that year. I went off onto the superstringtheory.com forum boards like a 'bat outa hell' . There is a deep understanding to be made for the transformation of Energies within the microscopic domain of Energy=Lengths. The authors of the above paper rightly state that the doppler shift formula(they express this on page 3 equation 17) should show up in certain astronomical activities. But..and its quite an important but, they also make this statement at the bottom of the page 3owever the superposition principle no longer holds. It is also the case that for massive fields there no longer is an exact plane wave solution. Now the interpretation I got from this reading at the time was there was a definate 'something-missing'? Once I got reading the rest of the paper I began to equate a number of factors that seemed to be relevant, although the authors touched upon a number of differing factors, especially the 'Lorentz Group Transformations'. The missing factor I believe is what happens to the Photon(hv) at the scales of Planck. One can formulate a number of interesting questions as I did after reading the said paper, such asow can an energy of certain quantity(hv), that appears to have no dimensional size whatsoever, exist in a frame of reference that must be between two other relative quantities of a space and a time? The reduction of (hv) from a 3+1 enviroment to one that is 2+1 or even 1+1 involves the alteration of the photon itself, although work of the paper was the production of non-linear transformations, I see it in a slightly different way, and I maintain that the photon and thus the energy changes from one dimensional frame to another. The Weak Gravitational Field can be thought of as a Vacuum of 'minumum-hv'. This has the interesting property of when a Photon is placed within a field of very little light energy, then the photon can be at equilibrium with the vacuum itself. And thus there is certain 'boosts'that are comparable to 'Vacuum Lengths'. This area is where the important conceptual breakthroughs will come, my own interpretation of the early work of Smolin and Maguejo, is to introduce a fundemantal Vacuum Length. This alters the whole picture into a much broader and precise arena for study, for instance the Smolin and Maguejo paramiter weaving around the Planck Length and Planck Energy can be equivilent to a Vacuum Length that is above a certain level, or below a certain level. One can conclude that a 'Positive-Vacuum Length'is one that is Expanding such <--> and has a minumum(positive) energy. And the Vacuum length where the gravitational field is plenty? ie for 3 Dimensional analytic fields, then the Vacuum frame is Contracting>--<. The Vacuum whereby the lp + Ep(forgive my representations of the planckian quantities), equals the zero gravity field, by fact that the photon is at rest!
Re: Re: Three papers by Kowalski-Glikman Link for some resolutions? One can conclude that a 'Positive-Vacuum Length'is one that is Expanding such <--> and has a minumum(positive) energy. http://uk.arxiv.org/PS_cache/gr-qc/pdf/0312/0312094.pdf
Re: Re: Re: Three papers by Kowalski-Glikman This is the link to the Viqar Husain/Oliver Winkler paper "On singularity resolution in quantum gravity" you found and posted. I am glad you found that and called our attention to it! I read it just now, and commented in the thread you started about this paper. It seems possible to entertain the idea that the BB singularity goes away. One cant be sure but we keep getting confirmation of Bojowald's basic result from different directions. It is beginning to look like a general result that does not depend on the method, or on who does the calculation. Will the Black Hole singularity also go away, with Loop (and other) quantization? Will quantizing GR make all the major singularities (essentially just BB and BH) of the theory go away? I must confess to feeling a bit giddy at this prospect. And also to not having anything useful to say about it, at least for now. It is, after all, what one expects. When a classical theory is quantized one expects (or at least hopes) that some of the trouble spots will get resolved, some sharp spikes and infinities get smoothed out, and so on. How nice if this is actually happening to GR as we watch!