Quantum-reduced loop gravity (first quantize, then reduce)

In summary: Thomas Thiemann University of ViennaFeb 26 Loop quantum gravity in the context of string theory Gabor Fazekas University of OxfordMar 5 Loop quantum gravity: from theory to observation Lorenzo Baldisseri University of Florence Mar 12 Gauge/gravity duality and the low-energy landscape of the universe Matteo Bertola University of PisaSo in summary, the 4th quarter MIP poll introduced a new version of LQG which could be important for cosmology. This paper confirms one's sense that the earlier (October 2012) paper was in fact significant and not just a "flash in the pan." This paper is essentially explaining this no?I'm glad the paper interested you, but AFA
  • #1
marcus
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One of the papers on the 4th quarter MIP poll is one which introduced for the first time a new version of LQG which could be important. It directly gives rise to the corresponding LQC application to cosmology. Because instead of first reducing the classical system (say to Bianchi I, a simple anisotropic setup) and THEN quantizing one does things in reverse order: start with the full LQG kinematic Hilbert space and then reduce.

So in this quantum-reduced loop gravity (QRLG ? :biggrin:) the bridge from full theory to quantum cosmology is straightforward, one is a direct application of the other. This was not the case with earlier formulations, where LHC was obtained by proceeding from classical cosmology not directly but merely in a LQG manner, so there was parallelism and similarity but no direct connection.

Happily enough, a longer "QRLG" paper has just appeared and was spotted by John86, who added it to the bibliography.

http://arxiv.org/abs/1301.2245
Quantum-Reduced Loop Gravity: Cosmology
Emanuele Alesci, Francesco Cianfrani
(Submitted on 10 Jan 2013)
We introduce a new framework for loop quantum gravity: mimicking the spinfoam quantization procedure we propose to study the symmetric sectors of the theory imposing the reduction weakly on the full kinematical Hilbert space of the canonical theory. As a first application of Quantum-Reduced Loop Gravity we study the inhomogeneous Bianchi I model. The emerging quantum cosmological model represents a simplified arena on which the complete canonical quantization program can be tested. The achievements of this analysis could elucidate the relationship between Loop Quantum Cosmology and the full theory.

This confirms one's sense that the earlier (October 2012) paper was in fact significant and not just a "flash in the pan".
 
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This paper is essentially explaining this no?

 
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  • #3
I'm glad the paper interested you, but AFAICS they are unrelated.
 
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"This approach is not expected to work only in cosmology, but it can be extended also to other symmetric sectors of the theory. This way, we define a new framework for the analysis of the implications of LQG in relevant (symmetry-reduced) physical cases (Quantum-reduced Loop Gravity)."

Will they be able to for example start calculating background-independent scattering amplitudes assuming the sector corresponding to Minkowski spacetime? How far does this take us to approximating physical observables and knowledge of the physical Hilbert space, at least for reduced situations?
 
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  • #5
Julian, I have the feeling that it's useless for me to speculate about that. One just has to wait and see how far they carry it and into what areas. It would already be great if it proves successful in cosmology.
So far they have applied it to Bianchi #1 case, which is anisotropic. (Includes the possibility of some pretty wild behavior around the bounce---you probably know more about that than I do: "Kasner", "Mixmaster"...)
Let's see if other researchers pick up on this, and confirm that it is a valid approach. And then let's see what other anisotropic and inhomogeneous models they proceed to deal with.
Win or lose, I think this one is important. But I can't guess how it is going to turn out.
 
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No Marcus, you know more about modern LQC than me and I appreciate your posts explaining it. I guess I'm looking at it from a more ambitious perspective on things, but I think it is a legit question to ask of authors making such a statement...
 
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julian said:
... I think it is a legit question to ask of authors making such a statement...
Certainly! It would be an excellent question to ask of either Alesci or of Cianfrani. And I expect they would have fairly specific answers---relating to planned or projected work.

But it might also be interesting to hear Thomas Thiemann's perspective on it. Alesci has been a postdoc in Thiemann's group at Erlangen for several years and is now moving on to take a postdoc at Warsaw in Lewandowski's group. The people with the most comprehensive 3rd person perspective on this would be those senior faculty. Also Alesci has been using Thiemann's canonical analysis, his type of "master constraint" hamiltonian in this work. Thiemann has to have a detailed idea of whether and how promising this approach is.

It would be a good sign if Thiemann discusses the work when he lectures at the Zakopane school:
http://th-www.if.uj.edu.pl/school/2013/speakers.html
the first week of July
or mentions it in the plenary talk he will give at the GR20 conference
http://gr20-amaldi10.edu.pl/index.php?id=17
one week later.

Another positive indication would be if Alesci were invited to fill one of the two remaining vacant timeslots in the ILQGS spring 2013 program. But that seems unlikely---there are already several cosmology-related talks scheduled:

http://relativity.phys.lsu.edu/ilqgs/schedulesp13.html
ILQGS Spring 2013 Schedule

Code:
DATE	Seminar Title	                    Speaker 	     Institution
Jan 29 [B]Entanglement in loop quantum gravity[/B] Eugenio Bianchi  Perimeter Institute
Feb 12 [B]Dynamical chaos and the volume gap [/B]  Hal Haggard	     CPT Marseille
Feb 26 [B]Gravity electroweak unification[/B]	    Stephon Alexander  Haverford College
Mar 12	 
Mar 26 [B]Bianchi I LQC[/B]	                    Brajesh Gupt     LSU
Apr  9 TBA	                            Karim Noui	     Univ Tours
Apr 23 TBA                                  Martin Bojowald  Penn State	 
May  7

BTW the 26 February talk is based on a paper Stephon did with Lee Smolin---the paper is listed in the 4th quarter MIP poll---it's about a completely unexpected (by me) idea for unifying particle theory with gravity.
 
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marcus said:
...
It would be a good sign if Thiemann discusses the work when he lectures at the Zakopane school:
http://th-www.if.uj.edu.pl/school/2013/speakers.html
the first week of July
or mentions it in the plenary talk he will give at the GR20 conference
http://gr20-amaldi10.edu.pl/index.php?id=17
one week later.

Another positive indication would be if Alesci were invited to fill one of the two remaining vacant timeslots in the ILQGS spring 2013 program...
...BTW the 26 February talk is based on a paper Stephon did with Lee Smolin---the paper is listed in the 4th quarter MIP poll---it's about a completely unexpected (by me) idea for unifying particle theory with gravity.
Good!
Alesci and Cianfrani have just been assigned the 12 March timeslot!


http://relativity.phys.lsu.edu/ilqgs/schedulesp13.html
ILQGS Spring 2013 Schedule

Code:
DATE	Seminar Title	                    Speaker 	     Institution
Jan 29 [B]Entanglement in loop quantum gravity[/B] Eugenio Bianchi  Perimeter Institute
Feb 12 [B]Dynamical chaos and the volume gap [/B]  Hal Haggard	     CPT Marseille
Feb 26 [B]Gravity electroweak unification[/B]	    Stephon Alexander  Haverford College
Mar 12 [B]Quantum reduced loop gravity[/B]	    E.Alesci/F.Cianfrani Univ. Erlangen	 
Mar 26 [B]Bianchi I LQC[/B]	                    Brajesh Gupt     LSU
Apr  9 TBA	                            Karim Noui	     Univ Tours
Apr 23 TBA                                  Martin Bojowald  Penn State	 
May  7

To me this suggests that although the work is very new and has not been presented anywhere else, there is already some community interest and acceptance of its possible importance. I was very happy to see this addition to the ILQGS schedule today.
The talk will be based on this October QRLG paper:
http://arxiv.org/abs/1210.4504
A new perspective on cosmology in Loop Quantum Gravity
Emanuele Alesci, Francesco Cianfrani
(which I am pleased to say is on our 4th quarter MIP poll) and on the VERY recent:

http://arxiv.org/abs/1301.2245
Quantum-Reduced Loop Gravity: Cosmology
Emanuele Alesci, Francesco Cianfrani
(Submitted 10 January 2013)

One of the obviously cool things about QRLG is that it bridges from the main theory LQG to the application LQC. This has been for a long time on the agenda of things to get done.

A French guy I know whose name is Emanuele goes by the nickname of "Mano". I wonder what Emanuele Alesci's friends call him? Maybe Mano.
 
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Related to Quantum-reduced loop gravity (first quantize, then reduce)

What is quantum-reduced loop gravity?

Quantum-reduced loop gravity is a theoretical framework that combines elements of quantum mechanics and loop quantum gravity to describe the behavior of space and time at a very small scale.

How does quantum-reduced loop gravity differ from traditional loop quantum gravity?

Traditional loop quantum gravity is a non-perturbative, background-independent approach to quantum gravity that operates on the gravitational field directly. Quantum-reduced loop gravity, on the other hand, first quantizes the gravitational field and then reduces it to a simpler, more tractable system.

What is the significance of first quantizing and then reducing in quantum-reduced loop gravity?

The process of first quantizing and then reducing in quantum-reduced loop gravity allows for a better understanding of the quantum nature of space and time, as well as the behavior of matter and energy at a very small scale. It also allows for the calculation of physical quantities, such as the entropy of black holes, which are difficult to obtain in traditional loop quantum gravity.

What are some potential applications of quantum-reduced loop gravity?

Quantum-reduced loop gravity has the potential to provide a more complete and unified understanding of the fundamental forces of the universe, including gravity. It may also have implications for cosmology, black hole physics, and the search for a theory of everything.

What are the major challenges in developing and testing quantum-reduced loop gravity?

One of the major challenges in developing and testing quantum-reduced loop gravity is the complex mathematical framework involved. Another challenge is the lack of experimental data at the Planck scale, where quantum effects become significant, making it difficult to test the predictions of the theory. Additionally, there is still much debate and discussion within the scientific community about the validity and potential limitations of quantum-reduced loop gravity.

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