5 years ago you could think of CDT and AsymSafe as part of a group of approaches called "Loop and allied QG". The numbers of people were so small it seemed like a single non-string QG community. Rovelli convened a Loop-and-friends Nonperturbative QG workshop at Marseille in the spring of 2004. Some 50-60 people participated. Loll included. So CDT was part of that first conference. The next year both Loll and Martin Reuter gave invited talks at Loops 2005 Potsdam. Both CDT and AsymSafe were again represented at Loops 2007. Now CDT has grown and is appearing as a potential rival to Loop. 5 years ago CDT was only being done by Renate Loll's group at Utrecht. Now the CDT computer work is being done in at least two other places, Perimeter and UC Davis. People show up at conferences from places like Poland and Iceland to give CDT papers. Loll administers a large grant from the ESF (european science foundation) able to support postdoc contracts, meetings, workshops etc. AsymSafe is also appearing as a potential rival. Important landmarks were the talk at CERN by Steven Weinberg and the organization of the Perimeter conference to be held in November. Horava QG is another 4D approach that is getting a lot of attention. Herbert Hamber is making a strong pitch for massive computer calculations along Lattice QCD lines to implement his version of Regge QG. Carlo Rovelli is this week presenting a "new look" LQG, and the abstract stresses its analogy with Lattice QCD---and mentions renormalization. You may want to add others to the list of contenders. Any of these could become a star or premier successor to string. All can be seen as jockeying for position---scuffling for a place in the sunlight that has opened up. What physics differences do you see? What are the strong/weak points? Sometimes one cannot tell if some feature is an advantage or disadvantage, it is just a difference. These distinctive features should still be pointed out. All these approaches seem to echo the themes of renormalization, and continuity with the tried and true, the "good old" (as Weinberg put it) Quantum Field Theory. Several if not all the recent presentations refer at some point to the success of Lattice QCD.
Herbert Hamber gave a talk at Perimeter earlier this year, the video is online. He was questioned by Lee Smolin and Laurent Freidel, among others. A lot of audience reaction. It was essentially the same talk as the one he gave to the 800-some participants of Marcel 12 in Paris this summer. Except better, more slides with more detail, if I'm not mistaken. He's aggressively saying that his simple 4D approach to lattice gravity is correct and CDT is not right and Loop is not right---and there is no need to make up extra stuff like strings. He has access to a big computer and has run dedicated programs that take 2 months. He presents his approach as the natural heir to Lattice QCD. To the extent this is to be taken seriously, we definitely need to pay close attention. I'll get the link to that PIRSA talk by Hamber. Here is the link: http://pirsa.org/09050006
I hesitate to call it "successor to string" because string theory was (is?) much more ambitious than "only" quantizing gravity. None of the approaches you mentioned has the potential to unify all known interactions and to replace strings. They should be compatible with a large class of interactions, but are not predictive in the sense that they single out specific interactions. OK, string theory failed or is trapped in a multiverse of dead-ends, but originally it was heading for true unification and uniqueness. In that sense no program should be called a successor. But (!) my secret hope is that "new LQG" with braiding could do the job to derive particles = their symmetries and interactions from topological and/or pure geometrical considerations. That's why I voted for "new LQG".
Do we know for a fact there is a force unification? If nature does not unify forces at high energies, neither should our theories
Unification does not necessarily mean that it is something like the old-fashioned GUT SU(5) <= U(1) * SU(2) * SU(3). It can be something like an explanation of a specific symmetry structure based on a deeper and in in some sense simpler model. That's my expectation.
The problem of all current theories is in a self-action ansatz. I find it failed physically and mathematically. I think our theories need reformulation and it is very close to what we have now but simpler. We have just to admit that interacting particles form compound systems so what we observe is quasi-particles, not particles. Nobody argues that in a solid state the energy-momentum is distributed amongst quasi-particles. But who said, for example, that the electron, permanently coupled to the quantized electromagnetic field, is elementary? Only those who could imagine it decoupled. Then, to couple it, one introduces a self-action. At the same time we can look at photons as at quasi-particles of a compound system and understand their "decoupling" as decoupling separated variables in one compound system. Such an approach excludes the self-action from the very beginning (rather than perturbatively, as in renormalization prescription), preserves the energy-momentum conservation laws and correctly describes the physical phenomena (soft radiation, Lamb shift, etc.) I believe this physical and mathematical approach has to replace current attempts so full of problems, patches, and patches of patches. In this sense it will be a successor.
Ofcourse there should be some form of unification. General Relativity and QFT are two completely different ballparks - they dont match up at all. Something has to give in.
I have to admit: no fact! One of the biggest problems we face today is that we have no direct results from experiments forcing us to develop a theory beyond the standard model + GR. No facts, "only" mathematical and aesthetical reasons.
Here is the abstract for Herbert Hamber's talk. Quantum Gravitation and the Renormalization Group Herbert Hamber "In my talk I will provide an overview of the applications of Wilson's modern renormalization group (RG) to problems in quantum gravity. I will first discuss the development of the RG for continuum gravity within the framework of Feynman's covariant path integral approach. Then I will discuss a number of issues that arise when implementing the path integral approach with an explicit lattice UV regulator, and later how non-perturbative RG flows and universal non-trivial scaling dimensions can in principle be extracted from these calculations. Towards the end I will discuss recent attempts at formulating RG flows for gravitational couplings within the framework of a set of manifestly covariant, but non-local, effective field equations suitable for quantum cosmology." May 13, 2009 - http://pirsa.org/09050006/ He comes across as somewhat arrogant and aggressive against the other competing approaches like Loop and including also Loll's CDT. I think this is all right---he is just playing hardball with his close competitors. And until recently I think his research was not so visible as either of those. Since the talk is at Perimeter and Lee Smolin and Laurent Freidel are in the audience, they are among those asking questions. The slides are much the same as the ones he used for the invited plenary talk in Paris on 14 July, in a session chaired by Ashtekar, where Laurent Freidel and Juan Maldacena also gave talks. =========================== Rovelli gave his "new look" LQG talk today at the Corfu school. It seems to me that LQG gets redefined from time to time. The current version is apt to be slightly different and we won't know in what way until these 5 one-hour talks are online. Here for reference is the abstract of the lecture series that started today: Carlo Rovelli Covariant loop quantum gravity and its low-energy limit "I present a new look on Loop Quantum Gravity, aimed at giving a better grasp on its dynamics and its low-energy limit. Following the highly succesful model of QCD, general relativity is quantized by discretizing it on a finite lattice, quantizing, and then studying the continuous limit of expectation values. The quantization can be completed, and two remarkable theorems follow. The first gives the equivalence with the kinematics of canonical Loop Quantum Gravity. This amounts to an independent re-derivation of all well known Loop Quantum gravity kinematical results. The second the equivalence of the theory with the Feynman expansion of an auxiliary field theory. Observable quantities in the discretized theory can be identifies with general relativity n-point functions in appropriate regimes. The continuous limit turns out to be subtly different than that of QCD, for reasons that can be traced to the general covariance of the theory. I discuss this limit, the scaling properties of the theory, and I pose the problem of a renormalization group analysis of its large distance behavior." http://www.physics.ntua.gr/corfu2009/qg.html http://www.physics.ntua.gr/corfu2009/Program/3rdWeekSchool.html
That's remarkable. It became clear in the past years that naive lattice discretization and quantization (spin-foams) does not yield a theoy which is equivalent to canonical LQG. The reason is that LQG (the cylindrical functions) is based on graphs instead of simplices. For every discretitzation (triangulation) one can construct a dual graph, but the opposite is not true: there are graphs for which a dual triangulation does not exist. One can understand this quite easily. Take a triangulation and construct it's dual graph: associate one point within each cell (simplex) with a vertex of a graph; this is the dual graph. Now connect two arbitrary vertices (which are not nearest neighbours according to the graph) with a new edge. It's immediately clear that this new edge cuts through several simplices prohibiting to construct a dual triangulation. In the dual triangulation one would have to associate an n-1 simplex (= a face) with the new non-local edge. This new face would cut other simplices. Spin-foams which are based on a naive triangulation seem to be not rich enough to have GR as low-energy / large-distance limit. This is remarkable as the construction of the cylindrical functions starts with a kind of epsilon-regularization which relies on "cells" as well. It is not clear to me at which point the space of cylindrical functions becomes richer than a space defined for simplices only. Smolin wrote a paper in which he tried make use of these non-local edges. According to him they cause a mismatch of micro-causality (as defined by the graph) and macro-causality (as defined by a smooth Riemann manifold emerging in an effective low-energy limit). In the latter one should see a residual effect of the non-local edges which is basically equivalent with the effects of a cosmological constant. It would be interesting if Smolin's rather generic arguments can be derived in an LQG or spin foam context. This should clarify if the cosmological constant is an input for LQG (as it used to be a couple of years ago when they studied quantum-deformations of the local Lorentz symmetry of the vierbein) or a prediction of LQG (or some generalization). I would like to speculate that turning the input into a result but keeping the framing / braiding of spin networks as an option has the power to let particles emerge as topological configurations of braids.
You go further with this than I can. I am frustrated by our not having the media from these talks yet. I sense from how the abstract is worded that Rovelli is going to attempt a reformulation, or a new look of sorts. He may have new results to talk about as well. But I find I simply have to wait patiently to find out about that. In the meantime, I would like us to be able to list a short list of media which make the most convincing case for the other possible entries. With Horava, I would like it if there were a video talk by Horava himself, or by Robert Brandenberger, which would make the strongest possible case. I think it is significant that Horava cosmo has a bounce. Brandenberger has a paper about this. This could be seen as an important distinction. Reuter and Loll (AsymSafe and CDT) do not have a bounce. Causal Sets (if anyone is interested in that) and Fotini's Graphity do not have a bounce. You could think of it as an asset, something that will get the attention of researchers. Or as a liability, something to eventually falsify? Of these contenders I think only Loop and Horava have the possibility of a bounce cosmo. However AsymSafe has the asset of a very natural inflation, obtained by the running couplings. Weinberg pointed that out in his CERN video. Hamber gives a strong confident, almost arrogant, pitch. Also Loll gives a terrific presentation. They both explain the advantages of their two styles of Lattice QG so clearly that I don't even want to repeat the points. My take is there is a patch of stage spotlight, or of sunlight, opening up, and these different approaches are vying for a piece of the action. As they should! Perimeter has already said Weinberg and Horava. They have two conferences in November planned: for AsymSafe and for Horava gravity. The GR19 conference in Mexico City has designated Robert Brandenberger as chair of the parallel session on Mathematical Cosmology (that says a strong Horava cosmology presence). I think all these approaches SHOULD compete for the attention of the research community, especially the young researchers. So I am going to try to assemble a few links to what I think are strong presentations of leading contenders. People can if they want watch several videos and see who they bet on taking a place in the sun (or if you like the stage limelight.)
Here is a provisional choice of one single strong advocacy of each approach (where an up-to-date presentation is available) CDT Obviously Loll at the Planck Scale conference. http://www.ift.uni.wroc.pl/~rdurka/...planckscale/video/Day1/1-4.flv&tytul=1.4 Loll Video: "Causal Dynamical Triangulations and the Quest for Quantum Gravity" AsymSafe The last 12 minutes of Weinberg's CERN talk can't be beat. http://cdsweb.cern.ch/record/1188567/ Video: "The Quantum Theory of Fields: Effective or Fundamental?" To save time jump to minute 58. Horava QG Don't have a video lecture. May not have one until November conference. new look Loop Waiting for the Corfu School talks to be posted online. Hamber Regge QG Hamber does a great job on PIRSA http://pirsa.org/09050006/ Video: "Quantum Gravitation and the Renormalization Group" Condensed matter approach: geometry emerges from graph. In my view, Fotini M. makes the most persuasive presentation. Not Wen exactly, but same general condensed matter idea. http://pirsa.org/09030018/ Video: "Quantum Graphity: a Model of the Emergence of Locality in Quantum Gravity" If anybody else can suggest other similar but better presentations of the same material, that are on line, please do. The idea is to have a minimal concentrated introduction to each one, so someone could watch all 4 or 5 talks and possibly pick one or several approaches as having more going.
Wen is my favourite - the whole Sakharov, Visser, Volovik style - even though it is very unlikely to succeed - it is hard to put chiral fermions and interactions on the lattice, because of the Nielsen-Ninomiya theorem. There are some work-arounds in lattice QCD, but Wen has said that while he has some idea of how to get chiral fermions, he doesn't know how to do chiral interactions. I love it because of its playful style and it's tower of turtles philosophy. My vote for serious modelling still goes to string theory. Wen can be seen in action at http://pirsa.org/08110003/ .
I see your point. I wasn't thinking of any of these approaches pursuing exactly the same program goals as string! I see the attention of researchers shifting in a 4D direction and these various contenders competing to some extent to "take up the slack" in research interest. Steven Weinberg described the situation in a helpful way, I thought. String might not be needed, he suggested, and gravity might be brought together with the rest essentially within the framework of "good old" quantum field theory. In his case the idea was Asymptotic Safety, but there are other ways of handling 4D gravity within something more like traditional quantum fleld theory---not so drastically inventive of new degrees of of freedom. Anyway I don't think anyone is suggesting that these new approaches are "better" in some sense than string. We don't know the ultimate value of any type of research ahead of the results. And no one is saying that those who continue doing string should stop! It's just a fact that interest has declined or is no longer so intensely focused. Former string folks are finding other areas to research. The field is no longer so much in the limelight. So there is slack, and the natural question is what other areas of theory will take up the slack.
I agree. I don't think that the idea of unification based on one physical entity (string?) is wrong. What was wrong (or at least not successful) with strings is the idea of doing everything like in old-fashioned quantum field theory w/o taking into account other lines of thought. With that I mean "fixed background", "perturbation series", ... Perhaps there's a chance to re-start with strings but from the very start incorporate these lessons learned.
These attempts are not phenomenological, i.e., they are not physical. They are some mathematical exercises. They proceed from some artificial constructions and are in fact nothing but soap operas: many watch them today and will forget tomorrow.
:rofl: the comparison with "soap opera" is funny! But I think in fact that we can't know the future. Some of these approaches may either teach us something valuable or continue into a successful development. And of course some may not. In any case for now I want to choose one single strong advocacy for each approach (wherever a current presentation is available). Here is an up-date of the earlier list: CDT Loll at the Planck Scale conference is tops--best available single lecture on the subject. http://www.ift.uni.wroc.pl/~rdurka/...planckscale/video/Day1/1-4.flv&tytul=1.4 Loll Video: "Causal Dynamical Triangulations and the Quest for Quantum Gravity" AsymSafe The last 12 minutes of Weinberg's CERN talk can't be beat. http://cdsweb.cern.ch/record/1188567/ Video: "The Quantum Theory of Fields: Effective or Fundamental?" To save time jump to minute 58. Horava QG A video lecture by Horava himself. Fixed camera though. We may get something better after the November conference. http://online.itp.ucsb.edu/online/adscmt_m09/horava/rm/flash.html Video: "Quantum Gravity with Anisotropic Scaling" new look Loop Waiting for the Corfu School talks to be posted online. For the time being here's Rovelli's talk at Strings 2008. http://cdsweb.cern.ch/record/1121957?ln=en http://indico.cern.ch/getFile.py/access?contribId=30&resId=0&materialId=slides&confId=21917 Hamber Regge QG Hamber does a great job on PIRSA http://pirsa.org/09050006/ Video: "Quantum Gravitation and the Renormalization Group" Condensed matter approach: geometry emerges from graph. In my view, Fotini M. makes the most persuasive presentation. This is not Wen exactly, but same general condensed matter idea. http://pirsa.org/09030018/ Video: "Quantum Graphity: a Model of the Emergence of Locality in Quantum Gravity" However Atyy has suggested a 2008 PIRSA video of Xiao-Gang Wen. So let me put that link up too. http://pirsa.org/08110003/ Video: "The Emergence of Photons, Electrons, and Gravitons from Quantum Qbit Systems" ============== Just a comment about the Horava presentation. We are all aware of the enormously successful 1940s theory of QED (Quantum Electrodynamics). Horava says in his speech that QED can ( "morally" I suppose ) be considered to be a part of string theory and thus, in the same spirit, his new 4D QG (the Horava-Lifgarbagez) can be viewed as a part of string theory. He is giving the talk at Santa Barbara KITP with David Gross in the audience and has some nice things to say about both David Gross and string. So one knows not to think of Horava 4D gravity as breaking away from the string program and community, in any sense. It is "really" a part of string theory just as Feynman's QED is, and Newton's gravity theory as well, one might add.