http://www.arxiv.org/abs/gr-qc/0212096 Lubos Motl (at Harvard's Jefferson Phys. Lab.) this paper is pure gold for what it does on the side quite apart from what you might expect from the title, which sounds narrowly focused on a specialized technical issue. what Motl gives on the side is a *critical* overview of LQG that cuts thru the underbrush and distinguishes a short list of impressive results---you could say one impressive result Motl recognizes the landmark importance of Olaf Dreyer's 2002 paper, which seems to have put LQG on a new footing. Dreyer's paper is less than 4 pages long and has potentially far-reaching effects on quantum gravity, which Motl provides perspective on. Here's Dreyer's 4 page paper: http://www.arxiv.org/abs/gr-qc/0211076
One thing Motl does that seems very interesting to me at least is to use " good old-fashioned" methods to come up with a result suggesting that the quantum of area is 4 ln(3) times the conventional Planck area. By unexplained coincidence this is also what Dreyer came up with for the quantum of area---using LQG. But Motl's analysis is neither stringy nor loopy! It has a classical flavor----analysing the vibration frequencies of a vintage 1916 black hole based on the vintage 1916 Schwarzschild model of one! There is no quantum mechanics at all in the basic model. The classical GR model of hole supports vibrations, and the minimal steps in frequency which Motl finds (NOW planck's constant can come in) correspond to minimal steps in energy and therefore area. So there is a so-to-speak "classical" support for the quantum of area being 4 ln(3) planck. As Dreyer got by other (LQG) methods. Maybe it should be mentioned that Motl is analytically pinning down some results about the vibration frequency of black holes that were gotten four years earlier by (of all things!) a *computer simulation* of black hole vibrations. So this number was known to be equal to 4 ln(3) out to 5 decimal places---as far as the computer could get it---but until Motl one did not know that it was exactly 4 ln(3). The next decimal place could have been wrong I only mention this because this is not just the work of one person but a kind of convergence on the quantum of area by a computer simulation by a man named Sachar Hod and by classical analysis of Motl and by LQG of Dreyer and probably help from other people. It is no one person's thing. But Motl's account of the matter seems unusually clear-sighted to me. BTW for people like Instanton and Sauron who may already be somewhat familiar with LQG technicalities the corollary of this is that the LQG group changes to SO(3) and the Immirzi parameter becomes ln(3)/(2pi sqrt2) which is 1/8.088 or about 1/8. Motl explains the Immirzi parameter as giving the "bare" value of Newton's gravitational constant G. The bare value at planck scale is only about one eighth as big as the renormalized largerscale lower energy G that we know and love. For this interesting detail see middle of page 7 of Motl and also the explicit value of Immirzi at top of page 9. These developments may strike one as provocative and worth looking into---hope so anyway.
Too many remarks that miss the mark marcus. To explain: To enforce agreement of the LQG result for black hole entropy with the accepted one, a dimensionless multiplicative factor - the "immirzi" parameter - was introduced without further justification. Later someone observed that the rounded off value of a number cropping up in a certain GR-based black hole related computation equaled the immirzi parameter value needed in a version of LQG previously argued to be more natural than the standard one. Lubos in his paper strengthened the view that this may not be mere coincidence by showing that the rounded off value was in fact the exact value, though the calculation itself shed little light on the ultimate significance of this result (but about which some speculation is offered anyway). This result added credence to the view that LQG may have something important to tell us about QG, even if LQG is wrong. Unfortunately, it could also be seen as doing the same for the view that the latter is the case, since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based. As well, Lubos offers the following critique of LQG: "LQG has not been able to show that gravity at low energies behaves as it should and instead, it assumes some extremely unlikely conjectures about physics at high energies that we could not have tested: for example, LQG essentially claims that Einsteins equations are exact and uncorrected even at the Planck scale and the bad divergences in the Feynman diagrams only reflect our inappropriate choice of variables and the perturbative character of the calculations rather than new physics that we should learn. LQG formally agrees with Einstein in the regime where we have no reasons to believe that Einstein is correct; at the same moment, it most likely disagrees with Einstein at low energies where General Relativity has been successfully tested by many experiments. Since the LQG dynamics is pure Einstein at the Planck scale and the renormalization group flow is known to generate corrections, the physics at long distances probably does not exist. Many people believe that LQG, much like other discrete approaches to Quantum Gravity, does not contain large flat spacetime as a solution." Lubos has made it clear in his posts to sci.phys.research that he is no friend of LQG, and I think this paper reflects that to a significantly greater degree than marcus intimated above. Naturally, other immirzi parameter related ideas have been advanced since this paper. If your into LQG, take a look (even my always enthusiastic friend marcus )
>>Throughout this paper, we will neglect six or seven dimensions of >>the Universe and >>discuss four-dimensional Schwarzschild black holes Oh, what a lack of generality... Seriously, string theorist´s are bbecoming a bit crazy now adays. They expect for their theory the same respect that the standar model has. And by no means they deserve it. I could totally ignore string theory (it´s not the case) and still consider i am totally aware of high energy physics. I consider totally unbeliveable that somehting some exotic as M-theory is considered seriously and people like Myron Evans, who claims to have some experimntal evidence of new behaviours of electromagnetism -and a theory to explain the- would be totally ignored.
BTW, a clarification about my knowledge of LQG, ii hve readed basicaly two intros, the Rovelli´s one in living reports and a a Thieman intro in pDF format of around 90 pages. I clarify it because i know there is another Thieman intro of 300+ pages wich i am begining to read now. Also i readed the Gambini-pullini book on the subjecto of gauge fields, knot theory and gravity. I have notices that Gambini has writen a more recent one, these time in collaboration wiith jonh Baez, but i am not sure aobut it.
No, he hasn´t. But i colaborate from time to time with a friend in developing (extending into other areas, for example Yang-Mills) a theory of electromagnetic knots. And Myron Evans has sometimes cited these theory as favourable to his own work. Even, throught one of his collaborators hasmade to my friend the oportunity to publish the developments of the electromagnetics knot theory in his new incoming book.
Hey Sauron, Motl is kind of outrageous in places----like at the end in the Unsolved Questions section he raises the question "could it be that LQG does not allow for the existence of fermions?" And his comic side comment you cited "thoughout this paper we neglect 6 or 7 dimensions!!!" But I still like his paper. He acknowledges a real advance in LQG even though he has often attacked LQG in the past. particularly around the issue of the Immirzi parameter. Now, while he talks critically about LQG, he has actually contributed a significant supporting result.
Sauron, did you notice that steinitz said: " since it was already known that this alternative arguably more natural version of LQG is inconsistent with the existence of matter. " It is not what Motl said, either in his footnote (which speculates as to the original motive for using SU(2) instead of SO(3)) or in his "unanswered questions" at the end. Nobody else I know of says this either. Yet steinitz would have us think that this is "already known" .
Motl has been a staunch and vocal supporter of strings in the past and has attacked LQG. In this paper he uses a derogatory tone but makes several important contributions to LQG. It is revealing to see what has interested this one-time enemy but now partial collaborator. On page 7 he says: "The most interesting result of this controversial approach to quantization of gravity is the following area quantization law that results driectly from [the two basic defining equations] Area = 8piG_{newton} x Immirzi x Σ spin network terms ...Immirzi parameter, a pure number that can be interpreted as the finite renormalization of 8piG_{newton} between the Planck scale and low energies..." I cannot easily write this out. It is simple and elegant and I can understand Motl being intrigued by it. The minimal spin network term dominates the sum and is equal to the sqrt 2. The sum is over network links intersecting the surface whose area is to be measured. The newtonian gravitational constant occurs as 8piG in the main equation of GR, the Einstein equation. People have often taken 8piG_{newton} as the "real" gravitational constant. Motl (usually a foe of LQG) is telling us in effect that the constant in front of the sum of sqrt 2 terms (one for each crossing of the surface) is the *real, bare* gravitational constant. Motl is helping in this paper to establish the value of the Immirzi number as about 1/8.088 and in effect establish that the true gravitational constant (at Planck scale) is about 1/8 of our usual largescale low energy 8piG_{newton} And yes he certainly does his share of grudging quarreling and nit-picking while he is doing this!!! But Motl is making a substantial contribution and meanwhile recognizing (for all his critical-sounding talk) an impressive development. Wish I could write out the Σ sum of spin label terms as he has it in the paper. Very elegant formula for area. So this area formula is what impresses one of the most vocal critics of this new approach to modeling gravity. Its always important to notice what impresses the enemies of a theory and even temporarily brings them over to the other camp.
Yep, I think you're right for bringing this up because looking at it again I clearly was cavalier, so thanks (and yes I really do mean that). But it's not that I was attributing that particular statement to motl or his paper. That statement was purely my own. Like any high energy theorist coming across this, I, and obviously the proponents of SO(3) LQG - of which I'm not one, as you know - immediately understood why - despite it's advantages purely in the context of the LQG program - coupling it to matter was impossible. What was wrong of me to do was make the unqualified remark that "In fact this inconsistency directly reflects the very naturality argument that "there is no reason why a man-made theory like LQG that is meant to reinterpret old physics should know about our desire to incorporate fermions" on which advocacy for this version of LQG was based." Btw, just in case there's any confusion - and I'm not suggesting there is - all matter is fermionic. Anyway, I appologize for this (sorry marcus). Btw, my name is jeff ("steinitz" is a reference to wilhelm steinitz, the father of modern chess)
No problemo steinitz, BTW since you indicate that you are a "professional researcher" (in high energy particle theory one infers from context, or some related area) I would very much like to look over some of your published research. Please post some references so I can look them up----I have ready access to a large academic library of journals and it would be no trouble for me to find pretty much anything you have in print if it is peer-reviewed hard-copy.
I think that revealing identities in online public forums is not necessarily the smartest move people can make. Sorry.
For a contrast to your manner, check out this interesting website: http://www.geocities.com/jefferywinkler and the many posts by "Jeffery" on Usenet's sci.physics.research the guarded reserve of this Jeff (steinitz) sharply contrasts with the self-revelatory openness shown by Usenet's Mr. Winkler--a multifaceted and widely informed individual if there ever was one! No reflection on you but I think I may prefer the Jeff on Usenet.
Jeff Winkler's online (mostly science) resource Good gracious! http://www.geocities.com/jefferywinkler/Aristotles_Lyceum_in_Cyberspace.html Index page for Winkler's online (mostly) Science resource. All these things are links including the "idea for a Shakespearean comedy". A great many science essays on diverse topics. I will quote the page to show the remarkable and wideranging breadth. Some posters may wish to refer to some of these essays as tutorials or whatnot. At your own risk however, I cannot vouch for them. -------------------------------------------------------------------------------- Greetings Lifeform. Welcome to my humble page. I'm Jeffery Winkler. I live in Hanford, CA. Here are some things that I've written. Physics The Big Bang Quantum Physics Physics and Mathematics Tensors Lagrangian The Standard Model Beyond The Standard Model Particle Physics Brane World Cosmology Special Relativity Black Holes Superconductivity Historical and Current Cosmology Mach's Principle Alternative Histories UFO's Religion Cults Early British History Stonehenge Art Halloween Christmas Computers IBM and the first computers Political Terminology Earth's Core Reproduction NVFRAM's CGI Human Cloning Martial Arts Environmentalism Egyptian Hieroglyphics Greek Myth Triplets The Soviet Union Humor The Millennium Wine Sports I maintain a Physics Website. You can also read my posts on a Vietnam board. I wrote a chart of the ups and downs of Bill Clinton. Read my article explaining why Clinton should have been impeached. Read my interactive novel. I wrote a screenplay. Here is a short story I wrote. Here you can read my idea for a Shakespearean comedy. I wrote haiku and a sonnet. Please visit my other homepage. Here I have yet another homepage. I draw fantasy art. Finally, here you can look at various other stuff. ------------------------------------------------------------------------
marcus - and I do feel this is a fair question - do you not see the basis for this remark and why lubos ended the paper with it?
I don´t know where the claim aobut LQG unability to incorprate fermionic matter comes from. In fact it surprises me. In the Thieman paper i readed he has no problem to talk about matter. I guess that if fermionic matter is not allowed he would clarify it. Also i readed Smollin paper comparing Strings and LQG and his claim is htat LQG can include the standard model without any problem. And at first glance i don´t see areason for it. The Asthekar forumulation is based in the vielvein wich allows the introduction of fermions in gravity, is is in fact the way to include fermions. I was not criticizing the contribution these article means for LQG at all. It is just that recently i am getting the impression that string theoriests try to convince people his theory is as good as standar model physics althought it has no experimental support. And aalso that they are THE WAY to do things. And i find that a bit stupid. I recognize the erits of string theory, and also i like some of their achievemnts.But to be honest i don´t find it as elegant as some people say. The days in which the use of XX century maths (topology mainly) could givve shine to a theory by themselves are gne. Electormagnetic knots is a reformulation of classical e-m first created by Antonio Rañeda, and developed by a friend in his doctoral thesis. Ateending a sugestion by Michael Berry they applied it to ball rays (hope the back traslation from spanish to english would be right). It has no relatiion with LQG, nor even with the application of LQG thecniques to classical e-m. It is based in a change of variables of the electromagnetic field. Instead of E an dB you use a fields wich are related to them by a nonliear relation. These fields permit the use of topological thecniques to find solutions of the Maxwell equations. The can be interpreted as maps from S^3^->S^2 (I use the ^ to indicate supraindice). These solutions can be classified according the hopf index of the map that the fields represnt. These index is conserved by time evolution. And it can be related to a classical quantities, the electric and magnetic helicities. A more extensive description of these theory would lead us far from the topic i guess.