I just got back from the Marseille conference on loop quantum gravity and spin foams: http://w3.lpm.univ-montp2.fr/~philippe/quantumgravitywebsite/ It was really great, so I devoted "week206" of my column This Week's Finds entirely to this conference: http://math.ucr.edu/home/baez/week206.html In particular, I spend a lot of time giving a very simple nontechnical introduction to the recent work of Ambjorn, Jurkiewicz and Loll in which they seem to get a 4d spacetime to emerge from a discrete quantum model - something that nobody had succeeded in doing before! http://www.arXiv.org/abs/hep-th/0404156 I hope this lays to rest certain rumors here that I'd burnt out on quantum gravity.
Thank you professor Baez! So two threads come together here. Marcus posted about the AJL paper yesterday and several questions have been raised. We need to read your essay! (Added in edit) Mike2 on the other thread raised the question of whether the quantum gravity model assumed by AJL had been rigorously developed. Just to clear the air on this I would like to ask this: Has any quantized fully relativistic (1,3)-dimensional theory of any kind been rigorously based? I know of rigorous (1,1)-dimensional theories and maybe some (1,2)-dimensional ones, but I don't know of any fully (1,3) relativistic quantized ones.
While we are on possibly important papers (of which e.g. AJL's) does anyone have any guidance or comment about Marni Dee Sheppeard's recent http://arxiv.org/gr-qc/0404121 unless for some reason it is tactless of me to ask. also I wish we could hear more about the Marseille conference since Week 206 merely whetted my appetite [edit: BTW Livine's talk at the conference was called "Instantons in Gauge Field Theory and the continuum limit" here is a definition of instanton http://en.wikipedia.org/wiki/Instanton in case anyone's curious.]
Thanks for the credit. A further question that comes to mind is whether this 4D spacetime is flat or curved. Would it explain the uncurling of space-time from the singularity at the start to the entire universe of today?
I read in a recent Sci Am article that there need not be 10 dimension for a consistent string theory if the curvature of space was large enough. Did I read that right? If so, then perhaps the 4D of the article of this thread may be fundamental and not just an effective theory.
recalling the main topic Baez reported in "Week 206" on the May 2004 Marseille conference and the main focus of his report was what Renate Loll had to say about this http://www.arXiv.org/abs/hep-th/0404156 recent paper by Ambjorn Jurkiewicz and her. This looks like a landmark paper, judging from remarks on SPR by Baez and Larsson and other reaction, and there are some previous papers by AJL which foreshadow the current one and illuminate what is going on. I think John Baez gave these links to lead-ups. http://arxiv.org./hep-th/0002050 http://arxiv.org/hep-th/0105267 As far as I can tell the ideas that bear fruit in the recent paper (and generate an extended 4D world) are already three years old. I can't find anything conceptual that wasnt already suggested in the paper dated 27 May 2001: "A Nonperturbative Lorentzian Path Integral for Gravity" so right now I'm trying to understand the lead-up papers BTW Mike2 you mentioned curvature. What they found does not seem to require a high degree of curvature. It does call for a positive cosmological constant, however, which is kind of nice because, as everyone realizes, a positive CC has been deduced from the much celebrated recent supernova observations
Was this paper an attempt to justify or perhaps even derive the very overall topology of space-time? I wonder if causality is the key to the topology of space-time. For from the simplest logic, causality is one event producing another event. Those events would have to be represented by some region. Even if the events were a single point, one "event" producing another, would require one point to produce another. I suppose that at such a differential state as one or two points that the properties between points or small regions would not change between points, since the changes in these properties cannot be instantaneous at such a differential scale. This causality, one point producing another, would mean that the number of points (or regions) would all increase at the same rate. This would give an expansion of the universe proportional to its size, or an exponential expansion as is predicted in an inflationary universe. I wonder if the number of dimensions and the metric can be determined from this topology. Since the closes points (or regions) would be responsible for the next point produced, and since all these points in conjunction implies that all are the cause of the others and the next, it would figure that the universe at this scale would be tightly curled up, not elongated into a line for example. This would seem to indicate a tightly curved metric for space-time. The first point would produce a second, and you would have a 1D line, these two, or one of them, would produce a 3 point, and since that next point would have to be about equally close to the other 2, you would have a 2D plane. These three would produce a forth, and since it would have to be about equally as close to the other 3 points, it would be in a 3D volume, etc. Where does this process lead? I suppose this would conflict with the idea of a specific amount of space-time dispersing as it expands with time. I wonder if the two views can be reconciled
again on the subject of the May 2004 Marseille quantum gravity conference, I wonder if anything can be learned from the list of talks. Rovelli was probably the main organizer, so the lineup would reflect somewhat how he sees the field: -------------------------- Monday, May 3rd: Loop quantum gravity am Opening remarks A. Ashtekar (Quantum geometry) T. Thiemann (Dynamics and low energy) L. Smolin (Overall results) T. Jacobson, as devil's advocate (Some questions to loop quantum gravity) pm L. Doplicher (Propagation kernel techniques for loop quantum gravity) W . Fairbairn (Separable Hilbert space in loop quantum gravity) J. Lewandowski (Quantum group deformations of the holonomy-flux algebra) B. Dittrich (Master constraint program for loop quantum gravity) J. Pullin (Consistent discretization) S. Alexandrov (Lorentz covariant loop quantum gravity) H. Salhmann (Uniqueness of the Ashtekar-Isham-Lewandowski representation) ------------------------------ Tuesday, May 4th: Spinfoam formalism am J. Baez (Spinfoams) L. Freidel (Group field theory and sum over 2-complexes) J. Barrett (BC models) R. Loll (Dynamical triangulations) pm A. Perez (Spin-foam representation of the physical scalar product in 2+1 gravity) R. Oeckl (Boundary formulation of quantum mechanics and application to spin foams) A. Starodubtsev (Definition of particles in 4d quantum gravity) F. Markopoulou (Quantum information theory and particles in spinfoam) E. Livine (Instantons in GFT and continuum limit) H. Pfeiffer (Quantum gravity smooth manifold and triangulation) 18:30 Campus Colloquium (open to external participation) A Ashtekar (Space and Time: From Antiquity to Einstein and Beyond) 20:00: Lunar eclipses --------------------------------------- Wednesday, May 5th: Miscellaneous am T. Jacobson (Mode creation: quantum field theory on a growing lattice) L. Bombelli (Statistical framework for the continuum approximation to quantum gravity) R. Gambini (Relational time in consistent discrete quantum gravity) G. Mena Marugan (Perturbative and nonperturbative cylindrical gravity) O. Winkler (Singularity avoidance or how compact is the world?) J. Swain (Spin-Networks and Approximations of Diffeomorphism Groups) E. Buffenoir (Quantum radar time in 2+1 dimensions) ---------------------- Thursday, May 6th: Applications of loop quantum gravity, cosmology, black holes and quasinormal modes am M. Bojowald (Loop cosmology) D. Sudarsky (Phenomenology) A. Corichi (Black holes) K. Krasnov (Quasi normal modes of black holes) pm O. Dreyer (Quasinormal modes) P. Forgacs (Quasi normal modes of the t'Hooft-Polyakov monopole) K. Noui (Hamiltonian analysis in Plebansky theory) S. Parampreet (Some applications of loop cosmology) K. Vandersloot (A path integral representation of loop quantum cosmology) S. Major (Observations on a lorentzian model) P. Majumdar (Universal canonical black hole entropy) ------------------ Friday, May 7th am: Related approaches M. Niedermaier (Asymptotic safety) R. Percacci (Is Newton's constant essential?) J. Klauder (Affine Quantum Gravity: An All-Scale Theory) D. Minic (Modification of quantum mechanics and quantum gravity) J. Kowalski Gliksman : (DSR as a possible limit of quantum gravity) F. Girelli (Special Relativity as a non commutative geometry: Lessons) pm Panel and general discussion Conclusion
In the thread started earlier about the AJL paper "Emergence of a 4D World" two people (arivero and Mike2) asked about what model of quantum gravity are they using. I found what I think is a good link. It turns out that it is one John Baez already recommended in "Week 206" when he was talking about the same paper. It is a pedagogical lecture by Renate Loll, with a lot of pictures. Dated 13 January 2003. I printed it out. It seemed worth keeping and studying. and to have easy parts. "A discrete history of the Lorentzian path integral" http://www.arxiv.org/hep-th/0212340 38 pages Notice that R. Loll's quantum gravity is not the same as Ashtekar's or Rovelli's or Smolin's, at least on the surface. Here is a brief exerpt from the beginning of the paper: ----exerpt--- In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach solves the problems of (i) having a welldefined Wick rotation, (ii) possessing a coordinate-invariant cutoff, and (iii) leading to convergent sums over geometries. Although little is known as yet about the existence and nature of an underlying continuum theory of quantum gravity in four dimensions, there are already a number of beautiful results in d = 2 and d = 3 where continuum limits have been found. They include an explicit example of the inequivalence of the Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the cancellation of the conformal factor, and the discovery that causality can act as an effective regulator of quantum geometry. 1 Introduction The desire to understand the quantum physics of the gravitational interactions lies at the root of many recent developments in theoretical high-energy physics. By quantum gravity I will mean a consistent fundamental quantum description of space-time geometry whose classical limit is General Relativity... --------end quote---- what seems to have just changed is that the results for d = 2 and d = 3 begin to extend to d = 4
The question becomes how fast do new points appear. I suppose that as long as the rate was not infinite, it would all be just a matter of scale. And since there is nothing else to compare with, it would all seem the same to us. So can someone tell me how such a scenario would modify the usual point set topology studies?
Lollistics: what do you call it? She and her co-workers have been calling their QG approach various names and have not quite settled on one. Recently it is "Causal Quantum Gravity" (causal denotes Lorentzian rather than Euclidean") Earlier on it was "Dynamical Triangulations" and "Lorentzian Q.G." or the "Lorentzian Path Integral" approach to Q.G. Back in 1992 when Ambjorn and Jurkiewicz were doing it they called it "Simplicial Quantum Gravity" as in their 1992 article in Phys Lett B. It is a commonsense notion and maybe goes back to Regge in the 1950s (?) or further----you let spacetime build itself out of regular blocks (simplices) and get the dynamics out of a "partition function" of sorts that tells you how likely some transition is to happen by counting the number of ways it can happen. A rudimentary combinatorics of space. The new thing is that AJL got it to work and 4D spacetimes started emerging from it somehow Loll began collaborating with Ambjorn maybe around 1998, then in 2001 she moved from AEI (MPI-Potsdam) over to Utrecht, and they must have decided at some point that the Euclidean approach to Simplicial QG wasnt working (despite at least 10 years of trying) and they would try the Lorentzian approach, where you distinguish time-like legs of the simplex from space-like legs, so there is a past and future idea and the possibility of cause and effect. Strictly speaking this approach to QG is one of the newest since the "Lorentzian" or "Causal" simplicial QG papers seem mainly post-2000 I may be wrong about these details---still trying to sort this business out. Loll is probably the best historian of this approach to QG. She has an invited LivingReviews article on it which gives the history going back to 1976 and citing some 200 papers. http://arxiv.org/gr-qc/9805049 I have been trying to understand Loll's background and looked in spires, where I saw a large number of papers published since 1988 from a series of places: 1988 Imperial College London (postdoc working with Isham?) 1990 Bonn University 1992 Syracuse 1993 Penn State 1995 Florence (and MPI Potsdam) 1996 MPI Potsdam ... ... 2001 move from MPI Potsdam to Utrecht Baez Week 69 (1995) describes his meeting Loll in 1991 in Seattle and also meeting Isham and Ashtekar at the same conference----Baez introduction to LQG. Week 69 has thumbnails of the first three LQG researchers Baez encountered http://math.ucr.edu/home/baez/week69.html as a wild guess if she was a postdoc in 1988 she could have been born roughly around 1962. that could be way off of course. here's a snapshot: http://www1.phys.uu.nl/wwwitf/fotopagina's/Medewerkers/Renate.htm the URL needs to be copy/pasted in
Lecture of spring 1999. Lost of graphics. http://cgpg.gravity.psu.edu/online/Html/Seminars/Spring1999/Loll/Slides/s01.html
I think that both dynamical triangulations and Regge calculus are different approaches both encompassed by a wider theory called simplicial quantum gravity. While dynamical triangulations keep the edges of the sinplices fixed and varies the triangulations, Regge calculus do the opposite, varies the edges of the simplices and maintain fixed the triangulation. Baez 122 explains a bit about all this stuff http://math.ucr.edu/home/baez/twf.ascii/week122 I've found this review of Regge calculus by Giorgio Immirzi, curiously the same person that the famous/infamous Immirzi parameter takes name from http://arxiv.org/abs/gr-qc/9701052 "Quantum gravity and Regge calculus"
Yes there are a lot of sketches, and it helps. I hadnt seen these lecture slides and am glad you pointed to them. Meteor thanks! I will look at Week 122---hopefully it will sort simplicial QG out into its various types and I will understand it better Baez posted again on SPR yesterday about the new simplicial QG work https://www.physicsforums.com/showthread.php?p=210452#post210452
BTW happy 15 May, Kepler Day! As an aside, by his own account Kepler discovered the third law on 15 May 1618 a few days later he finished writing "Harmonice Mundi"---the book was published that year his finding those three laws set a 400 year agenda of figuring out why gravity acts like that. why do the planets go in ellipes with sun at focus, sweeping out constant area per unit time, and why does the period-squared vary as the distance-cubed? or why, as he put it, is a planet's period the "sesquipotence" ( 3/2 power) of its average distance from the sun?
a day for thoughts concerning the shape of the world (Kepler's mundus, he too was trying to explain its proportions) and the hope that starting from those first laws of gravity mankind may come to grasp the world's geometry. it would be curious if Ambjorn Jurkiewicz and Loll were on the right track and that the world's 4D shape including the 1915 Einstein equation actually does arise from the "causal dynamical triangulation" (referred to in their abstract) which seems merely to be the random sticking together of simplices----with sensible rules that make it possible to simulate in a computer the fascinating thing is they generate pictures of 4D geometries, and Baez applied the "a picture is worth..." adage, appropriately
Meteor gives the right perspective. Simplicial Quantum Gravity (SQG?) is the overall line of research and Dynamical Triangulations is one of two or three main approaches within SQG. Simplicial Quantum Gravity seems to have a lot in common with spinfoam research (Barrett-Crane models could be mentioned). The boundaries of these research areas seem able to shift. Maybe Dynamical Triangulations will turn out to merge with Spinfoams. At the Marseille conference there was just one DT paper and it was put with the Spinfoam bunch. In his reply to Larsson on SPR https://www.physicsforums.com/showthread.php?p=210452#post210452 Baez says he hopes to work on DT with Dan Christensen at UBC and that he talked to Fotini M. who is also planning some DT research with a grad student of hers. The impressive thing to me about DT is that you can put a million identical simplices in a computer and simulate the universe and see it happen: the whole story---beginning middle and end since there is a finite number of simplex blocks it has to be a closed universe that bangs, swells up, collapses, and then crunches but that's a detail what's nice is the prospect of a 4D spacetime---a history of the geometry of the world---that you can simulate and see Baez has already done some heavyduty spinfoam computer stuff with Dan Christensen apparently they have a large computing facility at UBC so it's a good bet that they will run MonteCarlo DT simulations and get pictures I hope they get about it soon, wd very much like to see graphic results of others besides Ambjorn Jurkiewicz Loll.
2D animations at Jan Ambjorn's homepage Animations http://www.nbi.dk/~ambjorn/lqg2/ Ambjorn's homepage http://www.nbi.dk/~ambjorn/
What Matt Visser had to say about the Ambjorn/Loll work in 2002 http://www.phys.lsu.edu/mog/mog19/node12.html this includes a bibliography (mostly on line) of what Visser says are key papers ----exerpts---- Quantum gravity: progress from an unexpected direction Over the last few of years, a new candidate theory of quantum gravity has been emerging: the so-called ``Lorentzian lattice quantum gravity'' championed by Jan Ambjorn [Niels Bohr Institute], Renate Loll [Utrecht], and co-workers [1]... ...On the one hand, "Lorentzian lattice quantum gravity" has grown out of the lattice community, itself a subset of the particle physics community. In lattice physics spacetime is approximated by a discrete lattice of points spaced a finite distance apart. This "latticization" process is a way of guaranteeing that quantum field theory can be defined in a finite and non-perturbative fashion. (Indeed currently the lattice is the only known non-perturbative regulator for flat-space quantum field theory. This technique is absolutely essential when carrying out computer simulations of quantum field theories, and in particular, computer simulations of quarks, gluons, and the like in QCD.) In addition to these particle physics notions, "Lorentzian lattice quantum gravity" has strongly adopted the geometric flavour of general relativity; it speaks of surfaces and spaces, of geometries and shapes. On the other hand, "Lorentzian lattice quantum gravity" has irritated both brane theorists and general relativists (and more than a few lattice physicists as well): It does not have, and does not seem to require, the complicated superstructure of supersymmetry and all the other technical machinery of brane theory/string theory. (A critically important feature of brane theory/ string theory which justifies the amount of time spent on the model is that in an appropriate limit it seems to approximate key aspects of general relativity; and do so without the violent mathematical infinities encountered in most other approaches. Of course, there is always the risk that there might be other less complicated theories out there that might do an equally good job in this regard.) Additionally, "Lorentzian lattice quantum gravity" irritates some members of the relativity community by not including all possible 4-dimensional geometries: The key ingredient that makes this Lorentzian approach different (and successful, at least in a lower-dimensional setting) is that it to some extent enforces a separation between the notions of space and time, so that space-time is really taken as a product of "space" with "time". It then sums over the resulting restricted set of (3+1)-dimensional geometries; not over all 4-dimensional geometries (that being the traditional approach of the so-called Euclidean lattice quantum gravity). ... The result of this topological/ geometrical restriction is that the model produces reasonably large, reasonably smooth patches of spacetime that look like they are good precursors for our observable universe. ... The good news is that once reasonably large, reasonably flat, patches of spacetime exist, the arguments leading to Sakharov's notion of "induced gravity" almost guarantee the generation of a cosmological constant and an Einstein-Hilbert term in the effective action through one-loop quantum effects [3]; and this would almost automatically guarantee an inverse-square law at very low energies (large distances). The bad news is that so far the large flat regions have only been demonstrated to exist in 1+1 and 2+1 dimensions -- the (3+1)-dimensional case continues to pose considerable technical difficulties. All in all, the development of "Lorentzian lattice quantum gravity" is extremely exciting: It is non-perturbative, definitely high-energy (ultraviolet) finite, and has good prospects for an acceptable low-energy (infra-red) limit. It has taken ideas from both the quantum and the relativity camps, though it has not completely satisfied either camp. Keep an eye out for further developments. References: Key papers on Lorentzian lattice quantum gravity: J. Ambjorn, A. Dasgupta, J. Jurkiewicz and R. Loll, ``A Lorentzian cure for Euclidean troubles,'' Nucl. Phys. Proc. Suppl. 106 (2002) 977-979 arXiv:hep-th/0201104 J. Ambjorn, J. Jurkiewicz and R. Loll, ``3d Lorentzian, dynamically triangulated quantum gravity,'' Nucl. Phys. Proc. Suppl. 106 (2002) 980-982 arXiv:hep-lat/0201013. J. Ambjorn, J. Jurkiewicz, R. Loll and G. Vernizzi, ``Lorentzian 3d gravity with wormholes via matrix models,'' JHEP 0109 (2001) 022 arXiv:hep-th/0106082 J. Ambjorn, J. Jurkiewicz and R. Loll, ``Dynamically triangulating Lorentzian quantum gravity,'' Nucl. Phys. B610 (2001) 347-382 arXiv:hep-th/0105267. A. Dasgupta and R. Loll, ``A proper-time cure for the conformal sickness in quantum gravity,'' Nucl. Phys. B 606 (2001) 357-379 arXiv:hep-th/0103186. J. Ambjorn, J. Jurkiewicz and R. Loll, ``Non-perturbative 3d Lorentzian quantum gravity,'' Phys. Rev. D 64 (2001) 044011 arXiv:hep-th/0011276. R. Loll, ``Discrete Lorentzian quantum gravity,'' Nucl. Phys. Proc. Suppl. 94 (2001) 96-107 arXiv:hep-th/0011194. J. Ambjorn, J. Jurkiewicz and R. Loll, ``Computer simulations of 3d Lorentzian quantum gravity,'' Nucl. Phys. Proc. Suppl. 94 (2001) 689-692 arXiv:hep-lat/0011055. J. Ambjorn, J. Jurkiewicz and R. Loll, ``A non-perturbative Lorentzian path integral for gravity,'' Phys. Rev. Lett. 85 (2000) 924-927 arXiv:hep-th/0002050. [2] A survey of brane theory and quantum geometry: G. Horowitz, ``Quantum Gravity at the Turn of the Millennium'', MG9 -- Ninth Marcel Grossmann meeting, Rome, Jul 2000, arXiv:gr-qc/0011089. [3] Sakharov's induced gravity: A.D. Sakharov, ``Vacuum quantum fluctuations in curved space and the theory of gravitation'', Sov. Phys. Dokl. 12 (1968) 1040-1041; Dokl. Akad. Nauk Ser. Fiz. 177 (1967) 70-71. ------end quote from Visser---- this is from Jorge Pullin's newsletter "Matters of Gravity" Pullin gives this address for the author: Matt Visser, Washington University visser@wuphys.wustl.edu The point of the recent AJL paper, where they get extended normal-looking 4D regions, is crumbling of what Visser calls the bad news ("The bad news is that so far the large flat regions have only been demonstrated to exist in 1+1 and 2+1 dimensions -- the (3+1)-dimensional case continues to pose considerable technical difficulties."). This barrier has now to some extent been penetrated by AJL. This opens the way, if Matt Visser is right about this, to what he calls the good news, namely that the model "almost automatically guarantees an inverse-square law at very low energies (large distances)." obviously a breaking story, to be continued