Gravity Quantized along Thiemann lines (by Lewandowski's team)

[marcus]

"Gravity Quantized" along Thiemann lines (by Lewandowski's team)

http://arxiv.org/abs/1009.2445
Gravity quantized
Marcin Domagala, Kristina Giesel, Wojciech Kaminski, Jerzy Lewandowski
(Submitted on 13 Sep 2010)
"...'but we do not have quantum gravity.' This phrase is often used when analysis of a physical problem enters the regime in which quantum gravity effects should be taken into account. In fact, there are several models of the gravitational field coupled to (scalar) fields for which the quantization procedure can be completed using loop quantum gravity techniques. The model we present in this paper consist of the gravitational field coupled to a scalar field. The result has similar structure to the loop quantum cosmology models, except for that it involves all the local degrees of freedom because no symmetry reduction has been performed at the classical level."

I did not anticipate this paper and it shows a research current in LQG that is different from the program pursued by Rovelli, Freidel, Livine, Oriti and others. It is closer to Thomas Thiemann's program.
He has one of two or three major LQG books (Thiemann 2007 Canonical Quantum General Relativity). Also this year he started a new LQG-oriented research center at the University of Erlangen. Already he has a fair number of PhD students and postdocs who have come to Erlangen from other places.

This paper by Lewandowski et al gives a different view of LQG from what you see in Rovelli's April paper, a kind of status report and summary of results. http://arxiv.org/abs/1004.1780

I want to quote some passages and think about it. My first thought is that it probably does not represent a split, but separate advances that will merge back together further on down the road. This has happened before.

Lewandowski is one of the major figures in QG and has been a longtime co-author of many papers with Ashtekar, going back some 15 years I guess. He is a rigorous mathematician as well as physicist. Proves theorems. This is why I think I should pay close attention.

What L. is doing here is very conservative. No spinfoam. Pure Hamiltonian "canonical" approach. Conventional manifold in which the spin-networks of LQG are embedded. It's contrary to where I expected the field was going. So it proves that my perception was flawed. Lewandowski et al get, it seems to me, strong results. I will quote some of the paper later.

 

[marcus]

Here's the start of the introduction:

==quote "Gravity Quantized" page 1==

The recent advances in loop quantum gravity(LQG) [1–4], strongly suggest that the goal of constructing a candidate for quantum theory of gravity and the Standard Model is within reach.
Remarkably, that goal can be addressed within the canonical formulation of the original Einstein’s general relativity in four dimensional spacetime. A way to define 'physical' dynamics in a back-ground independent theory, where space time diffeomorphisms are treated as a gauge symmetry, is the framework of relational Dirac observables (often also called 'partial' observables[5],[6, 7], section I.2 of[2]). The main idea is, that part of the fields adopt the role of a dynamically coupled observer, with respect to which the physics of the remaining degrees of freedom in the system is formulated. In this framework the emergence of the dynamics, time and space can be explained as an effect of the relations between the fields...

==endquote==

Notice that the goal of the LQG program is not a quantum theory of pure (matterless) gravity but essentially what Rovelli said in his talk to Strings 2008 conference at Geneva---a quantum field theory without background spacetime geometry. That means a quantum theory which includes not only gravity but also the matter fields of the Standard Model, and is one which does not require some prearranged spacetime geometry.

In effect, what we call quantum gravity is just to be the (un-prearranged ) quantum geometry upon which the Standard Model fields are to be defined. QG should serve as the quantum geometry on which matter fields live.

In the paper Lewandowski et al sketch in brief how the LQG program should go. They point out that LQC (the cosmology application) has included matter and allowed numerical calculation---actually for some 10 years but especially the last 4---and they have been guided by LQC in what they are now doing, which is to introduce a massless scalar field. The idea is to make progress gradually step by step.

LQC --> LQG+scalar matter --> LQG+matter

 

[marcus]

This step-by-step plan of progress (which certainly may fail) is clearly--I would actually say boldly--laid out in the paper, including acknowledgment of an obstacle to overcome:

==quote "Gravity Quantized page 1==

Applying LQG techniques to perform the quantization step has the consequence that the quantum fields of the Standard Model have to be reintroduced within the scheme of LQG. This is due to the reason that the standard quantum field theory (QFT) defined on the Minkowski (or even ADS) background is incompatible with quantization approach used in LQG. Therefore, the resulting quantum theory of gravity cannot be just coupled to the Standard Model in it’s present form. The formulation of the full Standard Model within LQG will require some work. For this reason, we proceed step by step, increasing gradually the level of complexity...

==endquote==

So now they have a QG model with massless scalar field, and they reach the physical Hamiltonian (equation 4.41 on page 15).

This is just a model, and it could fail to live up to the expectations gleaned from previous work (LQC bounce cosmology, QFT on curved spacetimes, singularity resolution...). What they propose to do now is try out the model and see how it does.

There is something straight-forward, open, and common-sense about this program that I like. I suppose if this model fails they go back and restructure and revise the Hamiltonian and try again. But if this gradual step forward succeeds, then they go on to build more matter on it, this time more complicated than a massless scalar field.

==quote page 17==

4. Application of this model

Our model can be used to verify the properties of quantum space-time we expect after learning the lessons from LQC and QFT in curved spacetime.

In the LQC models of the homogeneous massless scalar field coupled to gravity, Big Bang turns out to be replaced by Big Bounce, as the result of the quantum gravity effects. Now, with our model, we can consider the same system of fields from the point of view of the full theory, without the symmetry reduction. Similarly, we can also consider the quantum gravitational collapse, quantum black holes, theory entropy. All those cases are manageable within our model, and the only difficulty is of technical nature.

Also the Hawking radiation and black hole evaporation process expected from the theory of quantum fields on the classical black hole background are in the range of our model.

The next step to obtain progress in this direction is the construction of semiclassical states for full LQG, which are preserved under quantum dynamics generated by the physical Hamiltonian on appropriate time scales.

In conclusion, our paper opens the door to understanding the properties of quantum spacetime from the point of view of the full quantum gravity.

==endquote==

 

[sheaf]

Notice that the goal of the LQG program is not a quantum theory of pure (matterless) gravity but essentially what Rovelli said in his talk to Strings 2008 conference at Geneva---a quantum field theory without background spacetime geometry. That means a quantum theory which includes not only gravity but also the matter fields of the Standard Model, and is one which does not require some prearranged spacetime geometry.

In effect, what we call quantum gravity is just to be the (un-prearranged ) quantum geometry upon which the Standard Model fields are to be defined. QG should serve as the quantum geometry on which matter fields live.

But surely it makes the picture more complicated when you bring other fields in. Is the implication that there is, for some reason, less value in persuing a "pure" i.e. gravity-only treatment ? I would have thought that the way to go would be gravity first then gravity plus interacting fields. As far as I can tell, the model of gravity-only is still far from complete.

 

[marcus]

But surely it makes the picture more complicated when you bring other fields in. Is the implication that there is, for some reason, less value in persuing a "pure" i.e. gravity-only treatment ? ...

I don't think it makes the picture more complicated to bring in the simplest kind of matter.
If it does not actually make things simpler, at least it radically changes the kind of obstacles.

We see this in quantum cosmology, where LQC has experienced rapid growth. In cosmology they (Bojowald, Ashtekar, Lewandowski...) never did a *pure* version.
AFAIK they started from the beginning with massless scalar matter.
This allowed time: they could treat time relationally. So then they had a hamiltonian and time evolution they could calculate. Then they could conveniently do numerical *simulations* of the universe. The field took off around 2006. As far as I can look back, it was never "pure".

However LQC has always been "symmetry-reduced". Instead of all the degrees of freedom one only had one or two---like the standard model used in cosmology (Friedmann equations) which assumes matter is uniform, geometry is uniform, and one only studies the evolution of the size, or "scale factor".

Jerzy Lewandowski's idea here, I think a smart one, is to repeat LQC development, at the outset, but with all the LQG degrees of freedom. Geometry should not be symmetry reduced.

Anyway that is how I interpret what they are doing.

You might want to have a look at the Spires search with keyword "quantum cosmology" and date > 2005, ranked by citation count.
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=dk+quantum+cosmology+and+date%3E2005&FORMAT=WWW&SEQUENCE=citecount%28d%29
Jerzy probably wants to know if the full LQG theory (with scalar field) will duplicate the results of the reduced LQC (with scalar field). It would not prove something about Nature, but it would definitely be interesting.

 

[sheaf]

Thanks Marcus - sounds reasonable. I haven't read up on the LQC programs at all (just getting my head round the basics of LQG at the moment) - maybe now is a good time to do this.

 

[marcus]

Thanks Marcus - sounds reasonable. I haven't read up on the LQC programs at all (just getting my head round the basics of LQG at the moment) - maybe now is a good time to do this.

I know that with your background and experience you don't need advice and will do what is right for you. But this brings to mind a general idea that might be useful to others.
Ashtekar got a unique pedagogical idea of how to introduce LQG to people and wrote a paper ( http://arxiv.org/abs/gr-qc/0702030 ) called something like "introduction to LQG by way of LQC". I don't know if the paper is good as an introduction (I'd have to examine it and think about it, and it's old: 2007 ) but the IDEA is very interesting. It could be a very good idea, for several reasons.

LQC is simpler.
You can calculate both analytically (solvable equation models) and numerically (computer sims).
You can experiment with different kinds of inflation and different constants.
It is closer to observational testing using CMB (e.g. possibly with Planck mission data).
There is a LQC-CMB phenomenology literature (see papers by Barrau, Grain, Mielczarek).
LQC is different from LQG (you start right away with simple scalar matter in the picture.)

Lewandowski has always worked closely with Ashtekar (though they now have their separate Penn State and Warsaw teams and don't co-author so much). Ashtekar since 2006 has been mainly involved in LQC. If Ashtekar thinks it is interesting to present "LQG by way of LQC" then probably Jerzy also at least has this idea in mind whether or not he believes it.

In some way LQC is a more "mature" field---though both are teenagers, not at all mature in any real sense. It is possible that Jerzy wants to reformulate LQG in the footsteps of LQC, only including more degrees of freedom, and then see if similar results appear (bounce cosmology, resolution of black hole, comparatively natural inflation without fine-tuning...)
That would make the pedagogical idea that Ashtekar thought of seem appropriate. But his original (2007) paper would probably be out of date and a new "intro by way of LQC" might need to be written.

Meanwhile, Rovelli and some in his group have begun to do cosmology with spinfoam LQG. The full covariant LQG theory but limited to simple graphs (and thus to simple foams.) This is totally different from canonical Ashtekar LQC as we know it. And different from canonical Lewandowski LQG in this paper.

These are the two versions of LQG cosmology that must eventually come together and be shown equivalent:

Rovelli cosmology: http://arxiv.org/abs/1003.3483
Lewandowski cosmology: this paper and whatever follows http://arxiv.org/abs/1009.2445

Neither of them is "symmetry reduced" the way LQC originally was, basically with only the scalefactor evolving. I guess for me this is the most interesting issue right now.

 

[genneth]

Actually, I find it interesting that it seems like gravity with matter is *easier* to quantize than pure GR (new LQG). Is this actually true, or is it just that I'm missing the subtleties of this paper? It seems like introducing matter removes certain metaphysical/philosophical worries, e.g. diff. invariance.

 

[Fra]

I don't think it makes the picture more complicated to bring in the simplest kind of matter. If it does not actually make things simpler, at least it radically changes the kind of obstacles.

Not beeing LQG specific: but there are several arguments and views put forward by different people that it's even an OBSTACLE to try to first try to find a fully consistent theory of pure gravity.

The idea is that if matter and space are deeply related, then it may be resonable to think that any attempt to find a consistent isolation is bound to fail, and trying to do pure QG first and try to patch something else later may be part of the problem.

So trying to account for, or explain emergence of, matter and spacetime and gravity and other interactions as inseparable parts may make even make things easier.

Maybe we don't "quantize gravity" like we do with other fields, it could equally be that if we just to "measurement theory" properly and relationally, such a reconstruction will predict gravity.

/Fredrik

 

[Fra]

Hehe genneth pretty much said the same thing, I didn't see that until I submitted my post.

I personally think that there is a good reason WHY quantizing PURE GR, just doesn't make sense (and thus, is harder). It's simply an incorrect quest, to seek a quantization of pure gravity. At least it's my personal conviction. But other a number of other people has similar arguments.

/Fredrik

 

[Fra]

I know I said this before, but quantizing pure gravity really is like constructing a measurement theory without *physical* observers(birds views or mathematical structural realism does not help); it's just attacking the problem in a strange way. To me, matter does play the role of observing systems, and spacetime is just relations between them.

Yes, it is a chicken-egg situation, but that's what suggest an emergence in terms of evolution as the seemingly only rational way forward.

/Fredrik