Main Question or Discussion Point
What are the main problems in non-string QG? Who is working on them? What progress has been made in the past couple of years?
This is misleading. The accurate statement is that despite years of trying, nothing has been accomplished that unambiguously constitutes meaningful progress on the central problem with these sorts of approaches. Further, since this is the central problem, obviously it should always be an active area of research. So when was the last serious attempt made to solve this problem? How many papers have been dedicated to this problem recently? I`ve heard that very little attention is being paid to it these days.IMHO this [recovering general relativity] is still an active research area despite some progress being made---undoubtably there's lots more to do.
IMHO this [recovering general relativity] is still an active research area despite some progress being made---undoubtably there's lots more to do.
Thanks for the clear statement. What you express here is a view which I think is mistaken. Perhaps as time permits i can mention some recent papers showing signs of meaningful progress on this problem, or others may.This is misleading. The accurate statement is that despite years of trying, nothing has been accomplished that unambiguously constitutes meaningful progress on the central problem with these sorts of approaches. Further, since this is the central problem, obviously it should always be an active area of research. So when was the last serious attempt made to solve this problem? How many papers have been dedicated to this problem recently? I`ve heard that very little attention is being paid to it these days.
I agree!!But, yes, I'd add a note saying that LQG is progressing rapidly in the past few years and the contact with experiments seems more and more promissing (or not... again, it seems that one can interpret the models differently, *but* the field is changing rapidly). In that sense LQG seems more promissing, a very active field *now*. (The problems in the case of LQG are conceptually interesting and challenging and worthy of a serious investigation, in my opinion).
Hi jal, I remember you from when we were discussing some of the same issues back in January. If I remember right, you referred to commentary in your PF blog. It was in this thread:I agree!!
Small step are happening regularly.
I think Kristina Giesel will also be giving a talk at the QGQG school in March-April, that Francesca told us was happening. There is listed a talk by a student of Thiemann.The three papers he cites are
Quantum Nature of the Big Bang: Improved dynamics
Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh
Revised version to appear in Physical Review D
Phys.Rev. D74 (2006) 084003
"An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as `emergent time', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness."
Algebraic Quantum Gravity (AQG) I. Conceptual Setup
Kristina Giesel, Thomas Thiemann
"We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG):The quantum kinematics of AQG is determined by an abstract *-algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single Master Constraint operator. While AQG is inspired by Loop Quantum Gravity (LQG), it differs drastically from it because in AQG there is fundamentally no topology or differential structure. A natural Hilbert space representation acquires the structure of an infinite tensor product (ITP) whose separable strong equivalence class Hilbert subspaces (sectors) are left invariant by the quantum dynamics. The missing information about the topology and differential structure of the spacetime manifold as well as about the background metric to be approximated is supplied by coherent states. Given such data, the corresponding coherent state defines a sector in the ITP which can be identified with a usual QFT on the given manifold and background. Thus, AQG contains QFT on all curved spacetimes at once, possibly has something to say about topology change and provides the contact with the familiar low energy physics. In particular, in two companion papers we develop semiclassical perturbation theory for AQG and LQG and thereby show that the theory admits a semiclassical limit whose infinitesimal gauge symmetry agrees with that of General Relativity. In AQG everything is computable with sufficient precision and no UV divergences arise due to the background independence of the fundamental combinatorial structure. Hence, in contrast to lattice gauge theory on a background metric, no continuum limit has to be taken, there simply is no lattice regulator that must be sent to zero."
Loop quantum cosmology and inhomogeneities
25 pages, 1 figure
Gen.Rel.Grav. 38 (2006) 1771-1795
"Inhomogeneities are introduced in loop quantum cosmology using regular lattice states, with a kinematical arena similar to that in homogeneous models considered earlier. The framework is intended to encapsulate crucial features of background independent quantizations in a setting accessible to explicit calculations of perturbations on a cosmological background. It is used here only for qualitative insights but can be extended with further more detailed input. One can thus see how several parameters occuring in homogeneous models appear from an inhomogeneous point of view. Their physical roles in several cases then become much clearer, often making previously unnatural choices of values look more natural by providing alternative physical roles. This also illustrates general properties of symmetry reduction at the quantum level and the roles played by inhomogeneities. Moreover, the constructions suggest a picture for gravitons and other metric modes as collective excitations in a discrete theory, and lead to the possibility of quantum gravity corrections in large universes."
Probably the most accessible detailed presentation is that given by Thiemann at the workshop. He was the only person who got TWO hours----he was scheduled to give a one-hour talk and they asked a lot of questions, so on the spot Horowitz scheduled another one-hour slot.
Thiemann seemed to be happy at his presentation---he was talking about MasterConstraint and also especially about AQG ....
IIRC Kristina Giesel has given a talk at Perimeter about AQG. ...
What Bojowald is saying is that he sees some convergence. He says that the approaches which he (on the one hand) and Ashtekar etal (on the other hand) have found to be workable dealing with cosmo singularities are in some way similar to Thiemann AQG.
I'm sorry, but you guys sound a lot like the String bods who allegedly call String Theory The only Game in Town. All approaches to quantum gravity have serious conceptual problems.ST, on the other hand, apparently has conceptual difficulties and dead-ends (like the landscape), which seems to indicate that the field is not as healthy.**I could be completely wrong here!**
here is your chance, Kea. Explain to us about the conceptual problems of the latest incarnations of Loop :-)I'm sorry, but you guys sound a lot like the String bods who allegedly call String Theory The only Game in Town. All approaches to quantum gravity have serious conceptual problems.
Hah! I'm not going to spend any time at all working through a paper such asSo what do you think are problems with the Quantum Cosmology that, say, Ashtekar is doing? If you can identify any problems that will be more stuff for LQG researchers to work on.
OK, that's fine Kea. I will go over it. it is basically a pedagogical/overview paper so it could be useful to us.Hah! I'm not going to spend any time at all working through a paper such as
An Introduction to Loop Quantum Gravity Through Cosmology
Right!I certainly don't deny problems exist---that's what makes the game fun---and I didn't think Christine did either.
Well, that's the way you see it... Or perhaps it's a sympathetic way to see it. But evidently I'm quite far off from calling myself a category theorist. I understand that cateory theory rebuilds mathematics from the concept of processes. I would like to see the idea of Nature as an inherently (quantum mechanically) concurrent system worked out in detail.So you've become a category theorist. OK, cool.
Since we're on feelings I'll put in my feeling too, or my hunch (for what it's worth). My hunch is that the main caterpillar-tread tractor here is "applied" Quantum Geometry and that by slowly advancing it will SHOW us what the missing math ingredients are....
I have a feeling this may be a missing ingredient in non-pertubative quantum gravity dynamics. Also, quantum gravity and quantum computation may have lots of common interconnections,...
What I feel that is missing is a structured model that can handle the dynamics. (a Quantum Minimum Length Structure)
It seems that Martin Bojowald went into more details to repeat what I said.
Singularities and Quantum Gravity
I'll post the rest in the new thred that you started.