Loop Quantum Gravity: Zurück vor den Urknall" by Martin Bojowald

[marcus]

Has anyone seen this? Can you say how well it fits into the popularization of 4D Quantum Gravity picture? Whether it presents a clear popular account of Loop Cosmology?

I just checked German Amazon and found this:

Zurück vor den Urknall: Die ganze Geschichte des Universums
von Martin Bojowald

Amazon.de Verkaufsrang: Nr. 2.966 in Bücher (Die Bestseller Bücher)
Beliebt in diesen Kategorien:
Nr. 1 in Bücher > Fachbücher > Physik & Astronomie > Astronomie & Astrophysik > Kosmologie
Nr. 1 in Bücher > Fachbücher > Physik & Astronomie > Theoretische Physik
Nr. 2 in Bücher > Naturwissenschaften & Technik > Physik > Theoretische Physik

http://www.amazon.com/dp/3100039106/?tag=pfamazon01-20

So today it was number one in categories which have in the past been dominated by Brian Greene books, and by Michio Kaku. It would be interesting if Bojowald could give some of the older pop-sci titles a little competition.

So far there has been no popular book specifically focused on Loop QG. So maybe we have a first here.

 

[marcus]

We've had several threads here at PF about Bojowald's work. He is one of the main people responsible for the development of Loop Quantum Cosmology (LQC) as a field. Still fairly young, born in 1973, so still in his thirties.

He was the author in 2001 of landmark paper which you could say started LQC.
He took over the standard Friedman model of cosmology, which all cosmologists use. It is simplified from the full Einstein theory by assuming that matter is distributed uniformly (which it seems to approximately be in reality).

And he quantized that standard cosmo model in a simple straightforward way that takes account of what happens in the full LQG theory. His LQC imitated the full theory, but was not identical to it because the situation in cosmology is so much simpler (matter being evenly distributed).

And he found that when it was quantized it didn't have a singularity any more.
It had a bounce. At very high density quantum effects (if you want, something akin to the Heisenberg uncertainty principle that quantum systems resist being pinned down) cause repulsion that overcame attraction and made a contracting geometry rebound and turn into an expanding geometry. Gave expansion a big kick in fact.

That was the 2001 landmark paper that started LQC. Just 4 pages and one figure in Physical Review Letters.
http://arxiv.org/abs/gr-qc/0102069
Absence of Singularity in Loop Quantum Cosmology
Martin Bojowald
4 pages, 1 figure
"It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstation comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained."

Now the field of Quantum Cosmology is dominated by LQC. If you do a Spires search with keyword "quantum cosmology" for recent stuff, the great majority of the most cited papers will be Loop. It used to be that the most cited QC papers were by Hawking and Hartle and Vilenkin and Linde and Veneziano and like-minded folks----a different group entirely and somewhat more stringish. But that changed radically after 2001. Quantum cosmology grew and became mainly loop. (We'll see if this changes, with Asymptotic Safety and also with Horava Gravity. It is something to watch!)

Here is a sample of QC papers written after 2005, ranked by citation count. This will give you an idea of what kind of research comprises Quantum Cosmology and what the impact has been stemming from Bojowald's seminal papers.
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=dk+quantum+cosmology+and+date%3E2005&FORMAT=WWW&SEQUENCE=citecount%28d%29

This will give 334 papers published 2006 or later, with the most cited ones first. And the top 50 papers are mostly all Loop*.
So you could say that Bojowald is a young successful researcher, and that he started something.
Whether and how much it is RIGHT is another question. We will have to see. For one thing LQC is constantly changing. The latest papers show they are shifting over to a spin foam model. Before that, there was a major reformulation around 2006 and 2007. It's an active line of research. Another thing that is happening (I think very important) is the removal of simplifying assumptions---like isotropy. The LQC universe no longer has to look so uniform as it did before.

If anyone wants links to papers showing recent developments, please ask.

*21 of the first 25, were Loop, and 18 of the next 25----so 39 of the 50 most-cited papers. There are some good physical reasons for this, which perhaps we should discuss.

 

[ensabah6]

What about string cosmology?

 

[marcus]

Start a thread on string cosmology. This thread is focused on Loop cosmology.
Bojo's book does not discuss string, and there is not much stringy currently being written in the cosmo research literature. But you can find some stuff and start a thread about it. Please don't butt in here.

The publisher, Fischer Verlag, gives us a free sample from Martin Bojowald's new book's pages 11-16 so that we can get a taste of what the book has to say!
http://anon.amazon-de.speedera.net/anon.amazon-de/all-media/books/Leseproben/09-05/LP_978-3-10-003910-1_amazon.pdf

There is no copyright tag on the sample, so presumably copying is allowed although commercial use would not be. Chapter 1 begins with quote from Nietzsche's Beyond Good and Evil, and ends with a pithy remark by Richard Karnap from his 1995 book Philosophy of Science.

The book is not yet out in English translation. So for the time being we have to make do with the original German version. The USA publisher Alfred Knopf has purchased commercial rights to publish an English edition.

==brief excerpt from the sample==

Kapitel 1: Einleitung

Je abstrakter die Wahrheit ist, die Du lehren willst,
desto mehr musst Du noch die Sinne zu ihr verführen.
Friedrich Nietzsche: Jenseits von Gut und Böse

Im letzten Jahrhundert ist die physikalische Forschung weit fortgeschritten und hat ein überragendes Theoriengebäude entworfen: die Quantentheorie und die Allgemeine Relativitätstheorie. Dies erlaubt ein Verständnis der Natur I am großen wie I am kleinen Maßstab, vom ganzen Universum in der Kosmologie bis hin zu einzelnen Molekülen, Atomen oder gar Elementarteilchen mit Hilfe der Quantentheorie. Zusammengenommen ergibt sich so eine präzise Beschreibung und ein tiefgreifendes Verständnis von mannigfachen Phänomenen, die eine spektakuläre Bestätigung durch Beobachtungen erfahren haben. Gerade in den letzten Jahren ist dies vor allem in der Kosmologie des frühen Universums geglückt.

==endquote==

The publisher's sample of the book, in the PDF file linked to above, has much more!

 

[ensabah6]

Start a thread on string cosmology. This thread is focused on Loop cosmology. !

Now the field of Quantum Cosmology is dominated by LQC. If you do a Spires search with keyword "quantum cosmology" for recent stuff, the great majority of the most cited papers will be Loop. It used to be that the most cited QC papers were by Hawking and Hartle and Vilenkin and Linde and Veneziano and like-minded folks----a different group entirely and somewhat more stringish. But that changed radically after 2001. Quantum cosmology grew and became mainly loop. (We'll see if this changes, with Asymptotic Safety and also with Horava Gravity. It is something to watch!)
:

Your thread is about Quantum cosmology, which you aver is dominated by Loop quantum cosmology. You omit any mention of string cosmology in quantum cosmology.

You originally mentioned "Brian Greene books, and by Michio Kaku" both popular writers of string theory.

Your original post claims that Quantum cosmology, which used to be dominated by Hawking and Hartle using other Quantum Cosmology theories, is now dominated by Loop Cosmology.

So of the quantum cosmology theories out there - loop, string, Hawking, etc., you claim loop surpasses in influence "dominated" by LQC. I wonder if this list includes String quantum cosmology.

You also mention "Asymptotic Safety and also with Horava Gravity"

If you wish to mention "Asymptotic Safety and also with Horava Gravity" "Hawking" and "loop" quantum cosmology, I would like to round out the list with string quantum cosmology. So asking about string cosmology in a thread that avers that loop quantum cosmology is "dominated" seems on topic.

 

[atyy]

What about string cosmology?

I searched the Web of Science for "string cosmology" or "quantum cosmology", and of the top 25, 13 mentioned loop quantum cosmology and 8 mentioned string theory. Surprisingly, one paper mentioned both!

http://arxiv.org/abs/gr-qc/0603043
Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds
Parampreet Singh
The discrete quantum geometric effects play an important role in dynamical evolution in the loop quantum cosmology. These effects which are significant at the high energies lead to the quadratic energy density modifications to the Friedmann equation, as in the Randall-Sundrum braneworld scenarios but with a negative sign. We investigate the scalar field dynamics in this scenario and show the existence of a phase of super-inflation independent of the inverse scale factor modifications as found earlier. In this regime the scalar field mimics the dynamics of a phantom field and vice versa. We also find various symmetries between the expanding phase, the contracting phase and the phantom phase in the loop quantum cosmology. We then construct the scaling solutions in the loop quantum cosmology and show their dual relationship with those of the Randall-Sundrum cosmology.

 

[marcus]

I searched the Web of Science for "string cosmology" or "quantum cosmology", and of the top 25, 13 mentioned loop quantum cosmology and 8 mentioned string theory...

But what is your point? I can do similar searches using Spires, and put in date cutoffs as well, to show the trend over time. But could you explain how that fits into the discussion of LQC? Maybe a marginal by the way comment, or have you something more substantive in mind?

BTW I must have been falling asleep earlier when I wrote the previous post, the philosopher quoted at the end is Rudolf Carnap!

 

[marcus]

In case anyone else is curious here's a link to Web of Science:
http://thomsonreuters.com/products_services/science/science_products/scholarly_research_analysis/research_discovery/web_of_science
It is a commercial service owned by Thomson Reuters that advertised itself as "access to the world's leading citation data bases". Broad coverage: medical science, biochem, genetics, social science, arts and humanities... Much else besides physics. But in our case we're focused on physics, and for that I think Spires database (at SLAC Stanford) is probably as good, or better if only because it is free and open access. We'll see, maybe Atyy can get some stuff out of WoS that Spires can't provide as easily.

The topic here is Loop Cosmology (which now has its first popular book on the market) and what we should be asking is what are the physical reasons WHY LQC has overwhelmed older rival types in recent years, like string cosmology. The contrast is stark. If you look at what has happened year by year Loop has grown and the other stuff has dwindled and shrunk, so what is special? Physically, what are the features that make Loop appealing to researchers? Why has the field developed the way it has?

If anyone has an explanation, I'd be very interested to hear it.

 

[ensabah6]

In case anyone else is curious here's a link to Web of Science:
http://thomsonreuters.com/products_services/science/science_products/scholarly_research_analysis/research_discovery/web_of_science
It is a commercial service owned by Thomson Reuters that advertised itself as "access to the world's leading citation data bases". Broad coverage: medical science, biochem, genetics, social science, arts and humanities... Much else besides physics. But in our case we're focused on physics, and for that I think Spires database (at SLAC Stanford) is probably as good, or better if only because it is free and open access. We'll see, maybe Atyy can get some stuff out of WoS that Spires can't provide as easily.

The topic here is Loop Cosmology (which now has its first popular book on the market) and what we should be asking is what are the physical reasons WHY LQC has overwhelmed older rival types in recent years, like string cosmology. The contrast is stark. If you look at what has happened year by year Loop has grown and the other stuff has dwindled and shrunk, so what is special? Physically, what are the features that make Loop appealing to researchers? Why has the field developed the way it has?

If anyone has an explanation, I'd be very interested to hear it.

Maybe Smolin and Woit are right, and as a result, string theorists have given up on string cosmology, leaving the field wide open for loop quantum cosmology. If in the past, quantum cosmology was dominated by string-inspired scenarios like braneworlds, and string theorists were unable to reproduce low energy physics, but loops are, then obviously that leaves LQC to pick up the slack.

Does LQC say anything about Lorentz invariance? If it predicts it breaks it must be broken or modified, and Fermi initial single photon result continues to hold true, perhaps LQC will shrink and dwindle

 

[marcus]

Does LQC say anything about Lorentz invariance? If it predicts it breaks it must be broken or modified, ...

No it does not. We've already been through this ad nauseam a halfdozen times.

No one has ever succeeded in deriving, either from LQG or its application to cosmology LQC, a prediction of Lorentz bending or breaking.

But notice that when the Fermi LAT paper actually went to press they claimed a result a result which (despite some noisy unreliable propaganda) did not even rule out energy dependent speed.
The official published result was something like M_QG > 1.3 M_Pl.

People who argue that various scenarios like Asymptotic Safety, or some type of QG, lead to Lorentz bending are imagining sometbhing like M_QG on the order of ONE PLANCK MASS. And this has not even been ruled out by observation, either by Fermi LAT or anyone else!

For example, Nature might surprise us a few years from now with the news that M_QG = 1.4 M_Pl. That would be completely consistent with the Fermi LAT observations. And it would satisfy the people who like DSR. Anything of order one. It could be 1.4 or 1.414 or 6.28 or whatever. Fermi has not ruled those out.

But why discuss that here? It is not a prediction of LQC or LQG. Nothing that, for example, Bojowald has signed onto. It would not be either good or bad for Loop. So it is irrelevant to this thread.

However I mention it because it sounds foolish when people talk as if energy dependent speed of light has been ruled out. They are so far only on the threshold of ruling it out.
A number like 1.2 does not yet cut the mustard.

 

[ensabah6]

So does LQC make predictions that differ from FRW big-bang picture, or other quantum cosmologies, that can be observed astronomically?

 

[marcus]

Again that is something we have discussed in other threads, including quite recently. Tom
Stoer asked about LQC predictions regarding the CMB anisotropy spectrum and I gave links to several papers---by Aurelian Barrau, Jules Grain, and by a Polish guy whose name I have a hard time remembering and spelling: Jack Mielczarek.

The answer is so far no definite hard predictions. But a number of people have made qualitive ones, and are working on making them precise. There is no obstacle in principle to deriving a LQC "signature" that one can look for in the CMB, as it is being observed with increasing accuracy by the Planck spacecraft and others.

You can look up Barrau and Grain's papers. They have several so far, mostly 2008 and 2009.
The title of one of them is about finding a "Cosmological footprints of Loop Quantum Gravity" in the CMB.

Have a look here:
http://www.slac.stanford.edu/spires/find/hep/www?rawcmd=FIND+dk+quantum+gravity%2C+loop+space+AND+DATE%3E2007&FORMAT=www&SEQUENCE=citecount%28d%29

This is the listing of the most highly cited LQG papers first---of papers written in 2008 and 2009 (so fairly recent)---and Barrau Grain "footprints" paper is around numbers 10-15 on the list. Fairly high up. Actually it is the second most highly cited LQG paper among those that appeared this year.

There are other researchers working on what LQG signature to look for in the CMB, but this should give you an idea of how it is coming along.

============================
EDIT TO REPLY TO NEXT POST:
That impresses me as an extremely good question, and i don't know the answer. Does dark energy or cosmo constant arise naturally in LQG/LQC? I know of one paper around 2007 where Bojowald thought of a way that it might, and explored the idea in a tentative way, but so far neither he nor anyone else followed through on it. ( http://arxiv.org/abs/0705.4398 ) So far that idea has not been brought to fruition, that I know of. I may have forgotten something but I think the answer is NO. At least so far nobody figured out a way that dark energy could arise naturally in that context. In Ashtekar's group they have tried putting in something like a cosmological constant by hand---running LQC with inflation. But that's not as nice as having it appear of its own accord.

Oh wait, sorry. There was also an earlier approach by Lee Smolin around 2002, that had a positive cosmo constant appearing in LQG but never "took". It's not part of the usual Loop-Foam QG version being worked on today. So the answer is still no. They haven't got a way to make a positive Lambda arise naturally. IMHO as an interested nonexpert observer.

 

[ensabah6]

thanks,

what is dark energy according to LQC and can LQC calculate the cosmological constant? Is lambda constant or does it change or vary? Is the universe always been de sitter space or is de sitter space, as claimed in string theory, meta-stable, and a phase change can occur to anti-ds?

 

[tom.stoer]

LQC does not say anything regarding the cosmological constant. LQC is a kind of approximation to full LQG; it reduces full LQG with an infinite number if degrees of freedom to a quantum mechanical model. Even in full LQG there are no predictions regarding the cc.

 

[ensabah6]

LQC does not say anything regarding the cosmological constant. LQC is a kind of approximation to full LQG; it reduces full LQG with an infinite number if degrees of freedom to a quantum mechanical model. Even in full LQG there are no predictions regarding the cc.

How is string theory doing in quantum cosmology?

Is it true that LQC is able to reproduce Friedmann–Robertson–Walker exactly in the classical regime, and offer quantum corrections in the quantum regime, in the Planck epoch?

If LQC can reproduce Friedmann–Robertson–Walker equation and string theory does not, with quantum corrections, then to crib a phrase from string theorists,

LQC is the only game in town.

 

[atyy]

CC arises in AS naturally, but I don't know if it's going to turn out to be the right value. The closest thing in LQG to AS in terms of "renormalization" is group field theory - which I suspect will betray Rovelli LQG and become Smolin LQG with Lorentz violation - so I like it (no I'm not a Trouble with Physics fan, but I was brainwashed from other sources). Anyway, the interesting lead for me at the moment is "A detailed examination of the LQC example shows that it is naturally tied with the cosmological constant. If this were to hold also in the full theory, one may have a dynamical tool to analyze why the cosmological constant is so small in the low energy regime. These and several other issues will be discussed in detail in [9]. (http://arxiv.org/abs/0909.4221)"

 

[ensabah6]

LQC does not say anything regarding the cosmological constant. LQC is a kind of approximation to full LQG; it reduces full LQG with an infinite number if degrees of freedom to a quantum mechanical model. Even in full LQG there are no predictions regarding the cc.

Isn't the assumption of homogeneity and isotropy shared in Friedmann–Robertson–Walker equation? Since observation appears to be consistent with Friedmann–Robertson–Walker equation, perhaps that is good enough for model building.

 

[marcus]

"A detailed examination of the LQC example shows that it is naturally tied with the cosmological constant. If this were to hold also in the full theory, one may have a dynamical tool to analyze why the cosmological constant is so small in the low energy regime. These and several other issues will be discussed in detail in [9]. (http://arxiv.org/abs/0909.4221)"

Yes! A tantalizing hint right at the end of Ashtekar's latest paper. It relates to the talk just given by Rivasseau at the AsymSafe conference. I will quote Ashtekar more fully because the tie-in with Group Field Theory is important:
==quote Ashtekar et al==
Finally, if one regards group field theory as fundamental, rather than just a convenient computational tool to arrive at the spin foam vertex expansion, then one is led to take the coupling constant λ as a physical parameter which can run with the renormalization group flow. However, its interpretation has been elusive. A detailed examination of the LQC example shows that it is naturally tied with the cosmological constant. If this were to hold also in the full theory, one may have a dynamical tool to analyze why the cosmological constant is so small in the low energy regime. These and several other issues will be discussed in detail in [9].
==endquote==

And reference [9] is something I'm certainly looking forward to seeing. It is listed as still in preparation:

[9] A. Ashtekar, M. Campiglia and A. Henderson, Casting LQC in the spin foam mould (in preparation)

 

[marcus]

...The closest thing in LQG to AS in terms of "renormalization" is group field theory - which I suspect will betray Rovelli LQG and become Smolin LQG with Lorentz violation ...

I don't follow your reasoning---which seems naively stereotyped or caricature-based. Or maybe I don't understand you.
Most of Rovelli's recent work that I'm aware of, since around 2006, is based on Group Field Theory. That's how you calculate in Loop/Foam QG these days, it seems. The graviton propagator and so on.

And Rovelli does not stand opposed to Lorentz bending. Indeed, Rovelli has what i think is the most intuitive paper about DSR available. It gives conjectures a mechanism for how Lorentz bending could arise physically, makes it exceptionally understandable. If energy dependent speed of light is observed, it could very well turn out that Rovelli's mechanism is favored to explain it!
The point is, DSR is not derived from current LQG---a conjectural ansatz is involved.

People have so far been unable to derive it as a prediction from LQG as it stands. So he reports this. It's important to be clear and straightforward about this.

Atyy, the way you present it, there seems to be a false dichotomy, or polarization. You seem to have Rovelli and his group opposed to GFT. But it has been Rovelli's former PhD students who have developed the application of GRT to quantum gravity, and it is a key formalism in Rovelli's own work. You also seem to have Rovelli's group opposed to DSR. But that would be very strange, given the character of his recent paper on it! Maybe I should get the link.
It's an interesting paper, and not at all hard mathematically---conceptually simple. You might enjoy it if you have not already read it.
If it should happen that Lorentz bending is observed---say by energy dependent photon arrival---Rovelli's paper gives some idea of how LQG might adapt (depending on what is observed.) Unfortuately the present version does not predict either way.

 

[tom.stoer]

Isn't the assumption of homogeneity and isotropy shared in Friedmann–Robertson–Walker equation? Since observation appears to be consistent with Friedmann–Robertson–Walker equation, perhaps that is good enough for model building.

Yes, for model building that's not totally wrong. But of course we know that there are some fluctuations in the density and in the CMB, so sooner or later they must be taken into account.

The main problem of LQC still is that the constraint of spherical symmetry is introduced at a very early stage of the development of LGC. It would be natural to start from full LQG and "integrate out" fluctuations leaving some "effective action" containing only a finite number of degrees of freedom. But instead the symmetry is used already at the classical level for the construction of the Hamiltonian. If you compare this to other field theories like QED or QCD you see that in those theories you would miss many physical effects like lamb shift, confinement and chiral symmetry breaking.

 

[ensabah6]

Yes, for model building that's not totally wrong. But of course we know that there are some fluctuations in the density and in the CMB, so sooner or later they must be taken into account.

The main problem of LQC still is that the constraint of spherical symmetry is introduced at a very early stage of the development of LGC. It would be natural to start from full LQG and "integrate out" fluctuations leaving some "effective action" containing only a finite number of degrees of freedom. But instead the symmetry is used already at the classical level for the construction of the Hamiltonian. If you compare this to other field theories like QED or QCD you see that in those theories you would miss many physical effects like lamb shift, confinement and chiral symmetry breaking.

Interesting --- what happens when you start with full LQG and integrate out fluctuations?

 

[marcus]

Yes, for model building that's not totally wrong. But of course we know that there are some fluctuations in the density and in the CMB, so sooner or later they must be taken into account...

Part of what is expected to show up is the imprint of gravity waves on the CMB temperature and polarization map. Gravity ripples. Which have been blown up to large size by the expansion.
We already see acoustic (sound wave i.e. density wave) ripples.
They calculate that LQC should affect the spectrum of the fluctuations frozen in the CMB and thereby leave a "footprint".

There have been now too many LQC papers by too many authors about LQC about this for me to want to keep track. I only am paying attention to the most recent, which are by a Polish physicist Jack Mielczarek and by two French, Aurelien Barrau and Julien Grain.
Both M. and B-G have written several papers about it.

 

[atyy]

I don't follow your reasoning---which seems naively stereotyped or caricature-based.

Atyy, the way you present it, there seems to be a false dichotomy, or polarization.

Nah, you got my demagoguery right

Actually, I don't know exactly what Rovelli thinks of course, but I suspect he would like a continuum limit taken before the semiclassical limit ie. no fundamental discreteness, whereas others would like smooth spacetime to emerge only in the classical limit ie. fundamental discreteness. The latest Ashtekar, Campiglia and Henderson paper indicates that maybe one can eat one's cake and have it, but I don't know if that will generalise to less symmetric conditions than they consider.

 

[atyy]

Isn't the assumption of homogeneity and isotropy shared in Friedmann–Robertson–Walker equation? Since observation appears to be consistent with Friedmann–Robertson–Walker equation, perhaps that is good enough for model building.

It's not good enough for model building. We know the universe is not uniform, and we also have very strong indications (proofs? - Wald has comments about this in his text) that the perturbed models are also solutions of the Einstein Field Equations. In LQG, there is no guarantee at the moment that something like spacetime even exists once the non-uniformity conditions are dropped.

 

[marcus]

... In LQG, there is no guarantee at the moment that something like spacetime even exists once the non-uniformity conditions are dropped.

How so? It sounds like you are saying that LQC, with its uniformity conditions, guarantees the existence in some way more firmly than LQG, without.

I suppose it depends on how you define terms and what you call "something like". Are you talking about dynamics or largescale limit? I'm puzzled as to what you mean.

 

[atyy]

How so? It sounds like you are saying that LQC, with its uniformity conditions, guarantees the existence in some way more firmly than LQG, without.

I suppose it depends on how you define terms and what you call "something like". Are you talking about dynamics or largescale limit? I'm puzzled as to what you mean.

Dynamics - the Hamiltonian constraint seems manageable with symmetry assumptions, from which one can get "effective Friedmann" dynamics that looks like the Friedmann dynamics from GR with symmetry assumptions imposed.

 

[marcus]

But what's the relevance? My impression is they gave up on the Hamiltonian a long time ago. The dynamics in modern LQG is handled differently.
All the work on proving the correct largescale limit uses spinfoam "path integral" approach. Group field theory is employed. The earlier kinematical results (which did not involve dynamics) are brought over from the old form of LQG.

Here it seems you are talking about the Hamiltonian form of LQG:

In LQG, there is no guarantee at the moment that something like spacetime even exists once the non-uniformity conditions are dropped.

It's possibly confusing or even misleading. You might make it clearer by saying "In canonical LQG there is (was) no guarantee..."
But when we talk about LQG these days we are not talking about the old canonical version. It would be helpful to point that out when making statements like that.

I am glad you read Rivasseau et al's http://arxiv.org/abs/0906.5477
and I gather you liked it (and some of the references therein).
Here's how Rivasseau summarizes the semiclassical limit situation on page 2

"Spin-foam models provide heuristic definitions of such dynamical transition amplitudes, obtained via a discretization of general relativity on a triangulation of space-time [28, 29]. There are now interesting such spin-foam models [30, 31, 32, 33], hereafter called EPR-FK models, which in four dimension reproduce Regge gravity in a certain semiclassical limit [34, 35]. There are also some glimpses that they might be just renormalizable [36]..."

In other places Rivasseau says "EPR-FK" and in his Perimeter talk he says "EPRLS-FK". The point is Loop has become EPRLS-FK. And we have no other practical word for it besides Loop. Loop contains EPRLS-FK as its dynamics and active core, but the only word people know is LQG. It is partly just a linguistic problem. One of the main candidate QG approaches, is actually EPRLS-FK, but people are not going to switch over and call it that. They will call it Loop.

 

[ensabah6]

My impression is they gave up on Hamiltonian dynamics a long time ago.
All the work on proving Loop has the right largescale limit uses spinfoam "path integral" approach. And group field theory provides key steps.

Then they show a match with the old kinematical results of the earlier form of LQG.

What is group field theory?

 

[marcus]

Rivasseau's perimeter talk says what GFT is
Go here:
http://pirsa.org/09110049/
Select PDF
Scroll to slide #155

===quote Rivasseau slide 155===
Group Field Theory

Group Field Theory (Boulatov 1992) lies at the crossroads between loop quantum gravity and simplicial quantum gravity. It generalizes matrix field theory and is also an attempt to sum both over discretized metric and topology of space time.

The information about the metric of a manifold is encoded in the holonomies along closed curves. Therefore the fields live on a group G^D (typically G=SO(D-1,1). They are G-gauge invariant.

...Feynman amplitudes correspond to BF theory, and they coincide with the spin foams of loop quantum gravity.
===endquote===

That's one possible place to start. He has some more about GFT.

I wrote some posts about GFT in another thread, explaining how I see it. I don't remember which thread though. Maybe a search would find it. A geometry can be described by specifying the parallel transport along a bunch of paths---how a vector veers while going along the path. So that means assigning a group element to each path. In simple cases a rotation---going along given path produces a given rotation. So if you have D paths, a geometry is specified by a point in the cartesian product of D copies of the group. A "D-tuple" of group elements. So instead of taking a manifold to represent space time, and doing field theory on that, let's take the cartesian product G^D and do field theory on that. That's probably a very bad introduction.

Oriti has a Perimeter video lecture where he introduces GFT at an undergraduate level. He is one of the main proponents.
It's after midnight. I'm not going to be able to dredge up a link to a basic introduction to GFT. Maybe tomorrow.

 

[apeiron]

==quote Ashtekar et al==
Finally, if one regards group field theory as fundamental, rather than just a convenient computational tool to arrive at the spin foam vertex expansion, then one is led to take the coupling constant λ as a physical parameter which can run with the renormalization group flow. However, its interpretation has been elusive. A detailed examination of the LQC example shows that it is naturally tied with the cosmological constant.

I'm trying to translate these arguments into simpler terms, so forgive me.

Does the difference with LQC and cosmological constant stem from the fact that loop approaches are doing path integral, sum over histories, over spacetime rather than particle fields?

So when cosmological constant is calculated in terms of virtual particle contributions, the answer is famously either zero or 120 orders of magnitude too large.

But with loops, you are dealing with the quantitisation of spacetime itself, and so due to QM location~momentum uncertainty, there is an irreducible degree of expansion? Try to locate a loop in space and it has a matching uncertainty in its momentum, which then averaged across many loops will show as a small universal acceleration?

 

[tom.stoer]

Interesting --- what happens when you start with full LQG and integrate out fluctuations?

In order to do thsi this you need some approx. solution like WKB, coherent states, ... to the full theory. Unfortunately this is not known so far, therefore one has to approx. first and quantize later.

 

[tom.stoer]

It's not good enough for model building. ... In LQG, there is no guarantee at the moment that something like spacetime even exists once the non-uniformity conditions are dropped.

Of course it's not the final answer, but one step into the right direction. LQC shows that the inequivalent polymere quantization provides interesting new features; hopefully this aplies to the full theory as well.

I agree that neither LQC nor canonical LQG are able to proof the existence of a smooth limit which is equivalent to spacetime. LQC can't proof this because there's no way how a classical theory with an infinite number of degrees of freedom can emerge from a qm theory with only a finite number of degrees of freedom. Nevertheless LQC shows that in a long-distance limit standard cosmological models are a sound approximation

 

[tom.stoer]

... they gave up on the Hamiltonian a long time ago. The dynamics in modern LQG is handled differently.
All the work on proving the correct largescale limit uses spinfoam "path integral" approach.

This is a major problem! In quantum mechanics and even in quantum field theory it is hard to proof the existence of a path integral w/o using a Hamiltonian in an intermediate step. Using the PI was often equivalent to "close your eyes and derive the Feynman rules". But there are situations where this approach fails, e.g. due to Gribov ambiguities ...

Sooner or later they must address the quantization ambiguities (and off-shell closure of the constraints) in the canonical framework as well. Refer to Nicolai: http://arxiv.org/abs/hep-th/0601129

 

[atyy]

Bahr and Dittrich are still working on it.

 

[marcus]

Sooner or later they must address the quantization ambiguities (and off-shell closure of the constraints) in the canonical framework as well. Refer to Nicolai: http://arxiv.org/abs/hep-th/0601129

I'm skeptical of this, and also not sure Nicolai was right in his 2006 assessment.

Philosophically I think you are wrong, because the canonical (Hamiltonian) approach is not God-given particularly in the case of QG. A spinfoam model is a completely independent physical theory that stands on its own merits.

The test of a spinfoam QG model is NOT whether it is compatible with the older canonical LQG. The tests are to see if the spinfoam model reproduces classical GR, and to see if it is predictive---in particular does it predict new phenomena which can be tested.

However it is very nice and encouraging to see that, in fact, the current spinfoam model is compatible with kinetic (non-dynamical) results of the earlier incomplete canonical approach.

What I am saying here is merely my opinion as an interested observer. For clarity I will express this in a definite way---which does not mean that I feel confidence or expertise about it. I just want to present my point of view.

I'm asserting that from a correct philosophical perspective the "proof" of a spinfoam model is not a mathematical derivation from old canonical LQG (which remains incomplete) but rather the "proof" must be empirical:

A. A quantum gravity must not be a quantization of classical GR. It must be a background independent quantum field theory which gives classical GR in the appropriate limit.

B. The first empirical requirement is that it reproduce the results of classical GR which have been thoroughly tested by experiment and by observation.

C. The second empirical requirement is that it predict some new phenomena which can be looked for, as a test. Such as a "footprint" in the Cosmic Microwave Background, as discussed by Barrau and Grain in their recent paper.

None of this has anything to do with the still-elusive Hamiltonian of the incomplete canonical LQG approach!