Quantum geometry includes matter

[marcus]

A short overview of quantum geometry by Ashtekar (2002)
http://www.arxiv.org/abs/math-ph/0202008

A recent paper by Perez (2003) points out that quantum geometry, or Loop Quantum Gravity as it is often called, incorporates matter fields in a divergence-free way without the need for the usual renormalizations to remove infinities. As Thiemann discovered, the infinities do not arise essentially because volumes are quantiized.
See page 4 of Perez
http://lanl.arxiv.org/abs/gr-qc/0301113
and the reference to previous work by Thiemann (1997)
http://arxiv.org/abs/gr-qc/9705019

The incorporation of fermions by LQG, in particular, has recently proven essential. Corichi confirmed the theory's SU(2) symmetry by invoking (local) fermion number conservation consistent with the Immirzi constant being 1/8.088 See Corichi(2002)

http://lanl.arxiv.org/abs/gr-qc/0212126

Quantum Cosmology

A recent paper by Ashtekar on Loop Quantum Cosmology shows that the time-zero singularity does not arise in the LQG model of the big bang. The model incorporates matter in an essential way and shows that the extreme conditions at time-zero nevertheless remain bounded. See Astekar et al (2002)

http://www.arxiv.org/abs/gr-qc/0304074

 

[marcus]

Originally posted by marcus
...The incorporation of fermions by LQG, in particular, has recently proven essential. Corichi confirmed the theory's SU(2) symmetry by invoking (local) fermion number conservation consistent with the Immirzi constant being 1/8.088 See Corichi(2002)

http://lanl.arxiv.org/abs/gr-qc/0212126
...

The paper is titled "On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry"

I hope that Alejandro Corichi's paper (link here) may be seminal---may start a larger "thread" of research papers---and am impressed by this quote:

"The heuristic physical process of conversion of area quanta to matter quanta via the 'emission of an edge' is, of course, very rough. One would like to have a clear picture of this geometry-matter transition."

In its own way the thinking here could be radical, as was the equivalence of energy and inertia proposed in Einstein's 1905 paper. Corichi's paper---only 3 pages long---suggests that at a BH event horizon matter can convert to area and area to matter. Since we believe that the area of a BH event horizon is proportional to the BH mass, it seems not entirely unnatural to imagine an exchange of matter for area at the horizon.

I will try if I can to summarize Corichi's main argument in the next post.

 

[marcus]

derivations of the Immirzi parameter

Originally posted by marcus
The paper is titled "On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry"
...I will try if I can to summarize Corichi's main argument in the next post.

Corichi assumes the usual SU(2) symmetry for quantum geometry, rejecting the suggestion of Dreyer that the symmetry group is SO(3). Instead, Corichi says that because of the way a BH grows by absorbing material the great majority of the links puncturing its event horizon will be of spin J = 1. This is regardless of how the object originated--he allows for the possibility that it may have begun its existence with "primordial" J = 1/2 punctures. J = 1 is the lowest possible spin with the exception of J = 1/2 which is excluded during the BH's growth by local conservation of fermion number.

He also uses a standard LQG result that the contribution to the area from a puncture of spin J is 8 pi γ√(J(J + 1)). So that in this case where the vast majority of punctures have J = 1, the typical contribution to the area is 8 pi γ√2.

Approach 1: A purely classical analysis of the quasinormal vibration modes indicates that a BH gains or loses mass-energy in steps of ln 3/(8 pi M). But the area A = 4 pi (2M)² = 16 pi M². So the change in area is 32 pi M ΔM = 32 pi M (ln 3/(8 pi M)) = 4 ln 3.

We can simply set the typical area associated to one link equal to 4 ln 3 and solve for gamma. Namely,
8 pi γ√2 = 4 ln 3

γ = ln 3/(2 pi √2) = 1/8.088.

Approach 2:

Let N be the number of punctures. The entropy of the surface is approximately N ln 3. This is the logarithm of 3^N, in essence the total dimensionality of the microstates.
(The Hilbertspace of microstates of the surface corresponding to a puncture with spin label J has dimension 2J + 1, the dominant case being J = 1 and dimension 3.)

But semiclassical arguments of Bekenstein and Hawking showed the entropy equal to A/4.

Now from what was said before we have that the area is
equal to N 8piγ√2, namely the number of punctures times the contribution from a typical one.

So we can write the entropy as N (8piγ√2)/4
and also, as was just observed, as N ln 3.

Setting the two equal we can solve for gamma a second time:
N (8piγ√2)/4 = N ln 3

8piγ√2 = 4 ln 3

γ = 4 ln 3/(2 pi √2) = 1/8.088

A non-trivial prediction by the theory:

Corichi makes this point near the end of the paper.

"Indeed, one could even argue for a stronger result. Namely, one could say that a consistent framework for LQG, incorporating fermions and black holes, requires that j_min = 1 and in fact predicts the QNM frequencies."

In other words Approach 2 determines what gamma must be based on fermion conservation and the known result about BH entropy. Therefore Approach 1 is not needed as a way of determining gamma and can be turned around into a prediction concerning the Quasinormal Modes of BH vibration. And this is apparently a true predicition, lending credibility to the theory, because the QNM frequencies have been calculated by purely classical means (without any quantum mechanics at all). It means in this case that quantum geometry is looking good in the classical limit.

 

[marcus]

so THAT'S what you were talking about

quote:
--------------------------------------------------------------------------------
Originally posted by marcus
The paper is titled "On Quasinormal Modes, Black Hole Entropy, and Quantum Geometry"
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I alerted you to this paper on 06-10-03 in the "the rotations, SO(3), in Loop Quantum Gravity" thread as follows:


quote:
--------------------------------------------------------------------------------
Originally posted by jeff
I found a paper yesterday published in january of 2003 in which a by now well-known but inconclusive argument is made that SU(2) can be restored without hurting lubos's result. But for some stupid reason today I can't find it. If you have any time between doing all that typing, see if you can locate it. I think it's important.
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So that's what you were referring to! It is an interesting paper
I discovered it in the references of a second Lubos Motl paper, with Andrew Neitzke----"Asymptotic black hole quasinormal frequencies."

I wish you had included mention of an author's name or part of the title---to use in a keyword search. I'll bet I would have come across the paper much earlier then!

Thanks for trying to help!




Report this post to a mentor | IP: Logged

 

[marcus]

Your question, Jeff

You asked:
It sounds like you're understanding is that the problem of how to include matter in LQG has been solved. Is this so?
---------------------------------

You should know better than that. I am a total skeptic about the current state of quantum geometry

One should not naively suppose that all the problems have been solved, despite the surprising progress in the past 2 or 3 years.

Read papers by good people like Ashtekar and Corichi. They qualify their statements and point out what remains to show.
Corichi is clear in this paper that more needs to be done on the matter problem.

 

[selfAdjoint]

Originally posted by jeff
Yep, I've read the papers, and like most people in the physics community, I have little faith in the LQG program. Still, studying LQG provides good opportunities for forum members to deepen their knowledge of physics since not only is it interesting, it's accessible, as it doesn't require the sophistication in mathematics and QFT that string theory does: LQG really is quite a simple theory, and I feel that's the basis of it's special appeal for people here. For me, LQG is very much like the decoherent histories, euclidean quantum gravity and geometrodynamical approaches to QG and/or quantum cosmology in that it frames beautifully intuitive physical ideas in elegant mathematics with striking results, but is obstructed by problems that are not merely technical or the result of intermediate understanding (as currently appears to be the case with string theory) but are fundamental in that they're a direct result of the naive assumptions upon which LQG is founded, and so are (almost certainly) insoluble. Hence, however much insight is gained from LQG, as with the previously celebrated aforementioned theories, I feel that it's just a matter of time before LQG hits the proverbial wall.

And what would those problems and assumptions be? Currently as I understand it LQG for 4d spacetime is held up by the huge number of possible states that have to be summed. This is a deep problem due to naive assumptions?

 

[Sauron]

Wich is the problem with decoherence? And what does it has to do with cosmology?. I thought it was just an alternative interpretaton of the wavefunction colapse based in an experimentally oriented aproach.


Anyway jeff, we clearly differ in the vission we have abouth physycs and mainly about string theory.

You think it is a deep theory. I think it is a very naive theory which just uses aproachs that worked in gague theory and try to go with them to realms for where they were not concived.


The math difficoulties have to do more with internal technicalities that with deeping understanding of anything.

In fact the most difficoult parts mathematically, if am not wrong, are the perturbative calculations of loops (modulli and all that) and the part related to copactifications (calaby´s orbifolds and all that, which by the way is the only part of theory i find mathematically beatifull).

What i readed about d-branes, dualities, and m-theory didn´t result me very hard in the mathemathicall level. In fact my major problem was with the few "heuristic" intepretation.


And i don´t think LQG is mathemathically easier. It requires a more solid basic in math that string theory. that is it requires a complete formation in math because it uses in every ste full "physician-mathematician" level of rigourosity instead of an "alla Feyman" way of using maths which is common in the string comunity.

And what i definitivelly don´t accept is the afirmation about the knowledge of stringy physics aobut QFT. I know a fesw people, and i am getting the impression that it´s number is fastlly increasing, that don´t know almost nothing about gauge theorys. they get a basic course in QFT, (covering lambda phi^4 and a bit of QED) and begin working directlly wiht strings. And thins such borel summability instantons, or confinement are things that read in divulgative books.


Not to say constructive QFT (wich i must accept i don´t neither know) which i have the impression is bringing as a diferent viewpoint on QFT that the mainstrean interpretation. In particular it seems that they are finding ways to advoid renormalizaton.

And it is promeoted as an soon experimentally testable theory. If it faills to succed in these it will be left behind, but till them it is the right theory to go with in my viewpoint.


Anyway i would liike to know which area of string theory you are working. i thought you would answer my question about brane universes but you didn´t.

 

[marcus]

Originally posted by jeff
In order to be a genuine quantum theory of gravity, and not just a quantum theory based on GR - no matter how pretty - a theory must actually produce GR in the low energy limit. From this point of view, there is in fact only one known QGT at the moment, and it's not LQG. So what classical physics does LQG predict? The answer is nobody knows. There's an ambiguity in the theory that's a direct result of it's background independence that makes it impossible to say what classical is even suppose to mean.

It's as if in order to produce a theory that would coincide with certain notions of what such theories should look like, they had to burn every bridge between their ideas and the ordinary low energy classical world so that now they simply can't get back.

LQG is an interesting laboratory to study certain ideas, but at this point it's really tough to defend LQG as being anything more.

Excuse me, jeff, but this sounds like your own opinion. Please supply a link to some critique on the web.

"In order to be a genuine quantum theory of gravity, and not just a quantum theory based on GR - no matter how pretty - a theory must actually produce GR in the low energy limit."

I claim stringy models don't produce expanding space in ANY limit.
If you think they do, give a link.
String models are based on flat Minkowski space---so are unrealistic from the outset, by your own criterion (reproducing essential features of General Relativity.)
THEY do not reproduce GR, whereas background independent quantum geomety DOES reproduce essential features of GR.

You seem to be criticising the theoretical development of
Background Independent Quantum Gravity for being background independent!
Yet quantizing GR means quantizing geometry (necessitating background independence since it is the very spacetime background that is to be quantized) and this has been a focus of research since the Sixties (Geometrodynamics by JA Wheeler 1962)
Quantum geometry is a longterm mainstream development in which Ashtekar's approach is only the latest phase.

 

[Sauron]

I'm not sure what you're saying here. Is it that people are skipping QFT and going directly to strings, because if you are I can tell you that string research requires a deep understanding of QFT.

Yes, it should. But the thruth is htat the tendence is in the oposite way. For example if you read the prologue of the Polchinsky books it is clearly stated there than they are oriented to people with a weak knowledge of QFT and that they are intended to carry people as quick as possible to the frontier of research withouth requiring an intermediate curse in advanced QFT.


And certainly many people is getting these way nowadays.

String theory is pushing pure mathematical research to an extent not equalled by any other scientific theory ever.

Yes, maths. And Witten is a field medalist. But the TFT are not a rigurous math. Their results need to be confirmated by ulterior investigations using standard math. That´s why i say that string physics is doing maths "alla Feyman".


By "heuristic" interpretation do you mean you understood the math but not the physics?

Yes. Or best to say. I missunderstood it the firs time i readed. Later reading of some papers beyond the Kaku bood showed me that my naive physial understanding of the idea couldn´t be correct. i had to reread it and search another sourced to gain a best understanding.

I´ll read later today the papers you linked and i´ll comment them in the thread about brane universes. Thanks for the info.

 

[marcus]

Originally posted by jeff
In order to be a genuine quantum theory of gravity, and not just a quantum theory based on GR - no matter how pretty - a theory must actually produce GR in the low energy limit. From this point of view, there is in fact only one known QGT at the moment, and it's not LQG. So what classical physics does LQG predict? The answer is nobody knows. There's an ambiguity in the theory that's a direct result of it's background independence that makes it impossible to say what classical is even suppose to mean.

It's as if in order to produce a theory that would coincide with certain notions of what such theories should look like, they had to burn every bridge between their ideas and the ordinary low energy classical world so that now they simply can't get back.

LQG is an interesting laboratory to study certain ideas, but at this point it's really tough to defend LQG as being anything more.

The only thing I would add is that the above statements characterize the majority view.

We have no proof that you are close enough to the physics research community to have any idea of what the "majority view" is. So far you seem something of a loner, not connected with any institution, just developing your own ideas by yourself.

You should give links to corroborate your statement that your opinion is a "majority view". Something by a qualified mainstream person, reviewing the current state of quantum gravity.

There was a quantum gravity conference in June 2003, want to know the relative numbers of papers? It's one measure of how mainstream and how live a field is.

You claim that background indep. quantum gravity is inconsistent with general rel. Give a link. this is way off target. I see plenty of evidence of GR results being matched in the classical limit and refined at Planck scale. That is what it's supposed to do and it does it. Can give plenty links to current research papers if you want.

 

[marcus]

Originally posted by jeff
Firstly, I've yet to discuss my own ideas here.

That is not true. One of your ideas, which you are constantly airing here, is that there is no room in LQG for matter.
Here is a quote from your post in the "Quarks in LQG" thread:

Originally posted by jeff
Ideas about how to move beyond pure gravity LQG are vague. The most natural (vague) idea is problematic: LQG black hole entropy calculations appear to indicate insufficient room in LQG for any other particles.

This is unfounded speculation and, in effect, rumor-mongering.
The literature is amply supplied with LQG papers with gravity coupled with matter.

It would be very interesting if anyone would do a serious analysis showing "insufficient room".
I don't just mean innuendo, heckling questions, passing references etc. but some substantive research. Instead of that I see lots of papers with matter fields----often playing key roles.
No apparent inconsistency with matter as yet!

YOUR idea, which you like to repeat at PF, is that LQG is going to "hit the wall"----meet with some theoretical obstacle it can't cope with. I wish you would be more specific

Or if this is not your private idea, show us a link to some serious substantive mainstream critique indicating that it is encountering fatal contradictions of some kind. This would be news to a lot of people because just now the field is going gangbusters.

 

[marcus]

Here's something Jeff posted to Sauron a couple of weeks ago which he must know is misleading (given a paper by Corichi he says he has read). I quote the whole post:
******************************

quote:
--------------------------------------------------------------------------------
Originally posted by Sauron
Jeff, i understand that people eidt it´s messages, but it makes a bit confusing to follow the thread, why not just to indicate your previous mistakes in a new post?
--------------------------------------------------------------------------------

Okay, sorry about that.


quote:
--------------------------------------------------------------------------------
Originally posted by Sauron And i still see a self-contradiction in the posts. You say LQG allows particles of spin not minor than 1/2, but that means fermions are allowed, and in other places ou say LQG doesn´t couple to fermionic matter. And your argument says that the absence of SU(2) is forbiding spin 1/2, so ,why are them allowed and only spin 0 particles are not allowed?.
--------------------------------------------------------------------------------



The point was simply that lubos's result strengthened a previous result suggesting that the lowest spin particles that can be coupled to gravity in LQG are spin-1 so that the gauge group should be taken as SO(3) rather than SU(2). Since all matter is composed of spin-1/2 particles this would make LQG inconsistent with the existence of matter. If you continue to feel that I'm contradicting myself, quote the contradictory passages and I'll comment on them.

Last edited by jeff on 06-13-2003 at 05:57 AM
*********************************
It may "suggest" this to jeff (whose take on things could be unusual) but does not seem to "suggest" it to other people.
Corichi specifically included the idea that spin-1/2 links could penetrate the BH horizon but argued that because of fermion number conservation they would not be in the majority.
The whole discussion jeff refers to (including Lubos Motl's paper) concerns BH event horizon area.

jeff is blowing a few comments by Motl out of proportion. They have not effected the subsequent course of research. The issue was addressed, in any case, by Corichi who is more central to this area of research and whose opinions carry considerably more weight.

Corichi's paper was referenced in a follow-up one by Motl (that was how I found it in fact).
I went over it in some detail earlier in this thread. The arXiv number is gr-qc/0212126

 

[marcus]

What kind of link is this? this is to Perez "Spin Foam" models paper, not even to LQG proper! This is not "the most comprehensive review" of anything, contrary to what you say.

Originally posted by jeff


I'm going to provide a link, but I greatly resent the way you respond to me only when you think you can somehow insult me.

The following is the most recent comprehensive review of the subject, I know that you've seen it.

http://xxx.lanl.gov/abs/gr-qc/0301113

The following passage is on page 36:

"A basic test to any theory of quantum gravity is the existence of a well defined classical limit corresponding to general relativity. In the case of the spin foam approach this should be accomplished simultaneously with a limiting procedure that bridges the fundamental discrete theory with the smooth description of classical physics. That operation is sometimes referred to as the continuum limit but it should not be confused with the issues analyzed in the previous subsection. There is debate on how one would actually setup the definition of the ‘low energylimit’ in the background independent context. The general strategy—in fact motivated by our experience in background physics—is to setup a renormalization scheme (`a la Wilson) where microscopic degrees of freedom are summed out to obtain a coarse grained effective description. The previous strategy is to be regarded as heuristic until a clear-cut definition is found which encompasses all the issues discussed in this section. It should be emphasized that even when various spin foam models for quantum gravity have been defined, none of them has been show to reproduce gravity at ‘low energies’. This is a major open question that deserves all our efforts."

 

[marcus]

Originally posted by jeff

By "ideas" I thought you meant my own theories, but yes, this is my personal opinion, and how widely held it is should be easy enough to check by emaiing or phoning someone. Most people believe that LQG was DOA. I don't think that's a productive view. I think it's worth studying, but even if I was interested in researching LQG, it's harder to secure an academic appointment with a background in LQG than strings.

I doubt you are in line for any academic appointment whatever, with whatever background!

You strike me as a self-taught loner---a hobbyist to use your term---pretending to speak for a professional research majority to which you do not belong.

How you got "Spin foams" confused with the main LQG area, I cannot understand. Very different stages of development.
Shouldnt talk so confidently about stuff you don't understand.
Yr understanding seems mainly on the verbal level----not physical.
Noticed this in your denial that a binary system can lose rest mass by gravitational radiation, which went on post after post.

 

[marcus]

Originally posted by jeff
Just to be sure here, you believe that LQG's low energy limit and couplings to matter are understood. Correct? If so, when did this happen. Do you have the landmark papers at hand, because if you do, I'd love to see them.

jeff you still have not responded to my request that you
provide links to back up your personal speculations aired here at PF.

something in "Spin Foams" hardly counts, it is a new field investigating 4D combinatorial models.

To back up your rather wild innuendo you need a link by some mainstream authoritative figure explaining why standard background-independent quantum gravity (LQG) is "dead on arrival" as you colorfully put it.

 

[marcus]

Originally posted by jeff
You have no right to expect me to divulge my identity. I've reported this post to the administrator.

Jeffery you have already "divulged" your identity many times in your posts on Usenet------sci.physics.research

You wouldn't get in such trouble if you did not have the habit
of pretending to be an academic.

You have referred to yourself here at PF as in "high energy research"

as belonging to the "professional researchers" community

but these appear to be merely your private fantasies and pretense

If you really think you are in line for academic appointment as you recently indicated----and should guide research decisions on whether string or loop is more academically respectable or currently has more faculty positions, then good luck

 

[marcus]

Originally posted by jeff
marcus,

You haven't answered my question about whether you believe that finding the low energy limit of and coupling matter to LQG has been solved. It's a simple yes or no. What's the problem?

I won't be giving you anymore physics answers to your physics questions until you start doing the same for me.

That is simple defensiveness, I am sure you realize. You have made extravagent suggestions of fatal flaws and I have challenged you to provide links-----to critiques by reasonable people.

You provided one link---it was a canard, a fake answer, not having to do with LQG but with a recent spinoff still in early stages of development.

Now, because you cannot come up with links to justify your assertions you are thinking up excuses why you shouldn't have to.

You are aware of my sense that string theories are flawed because they depend on a flat undynamic space time at the very outset.

Background independent Quantum Gravity, by contrast, is an attempt to quantify general relativity. Many of the recent papers (2002,2003) make liberal use of matter fields. No responsible person claims, as you do, that the theory will prove incapable of accomodating matter!

Your reasoning about this is, I think you realize, not rigorous and seems to be wishful thinking. It doesn't demonstrate a logical necessity.

You have not shown that there is any conclusive problem with LQG. But certainly the theory is under development! Every aspect is being worked on and no final answers have been given---which would involve experimental tests.

The LQG approach to Quantum General Relativity is, it appears, a lot LESS vague about its testable predictions than are Stringy models. LQG is obviously MORE clearly complete and nearer to being testable. It is part of a effort to quantize geometry that has been going on since before 1962 (Wheeler's "Geometrodynamics") and with which flat fixed-background stringy models have nothing to do.

All active areas of theoretical research are to some extent vague until conclusively tested by observation---and may afterwards be modified and retested. LQG, which doesn't try to explain all the forces and particles in the world but merely to quantize General Relativity (hard enough!, something string-folk avoid!) is LESS vague and LESS apt to be fundamentally flawed and NEARER to being productively testable. But still there is no clearcut answer yes or no to your question----never will be till final experimental tests.

I think the question is just a defensive ploy because you want an excuse not to back up your statements

 

[marcus]

I'm getting bored with your bickering.
Will have to start ignoring your posts till they get a little more sensible