A question of string v.s LQG derivation of BH entropy -

[ensabah6]

One question I have for LQG's derivation of BH entropy is this:

would any arbitrarily enclosed sphere in space, whether it's that of the surface of planet earth, or the moon, or the sun, not to mention BH's also have the same BH entropy since as I understand the calculation, it is merely counting spin network microstates on the surface of a black hole, but couldn't this also apply to any enclosed sphere? I understand that it is not volume extensive entropy but only surface entropy.

As for string theory, is the computation of bh entropy include the volume of the BH? Why hasn't it been able to reproduce Hawking results for ordinary astrophysical BH's if string theory is indeed a theory of QG.

 

[william donnelly]

The derivation of black hole entropy I know in LQG is the one by Ashtekar, Baez, Corichi, Krasnov (http://arxiv.org/abs/gr-qc/9710007) . Their derivation applies to "isolated horizons", which are essentially black holes in equilibrium. This constraint is applied at the classical level and causes some simplification that allows them to count the horizon states. I believe that most subsequent work is based on this approach.

In fact, I don't think any existing derivation of black hole entropy in LQG would apply to arbitrary horizons, let alone any enclosed sphere. But I would very much like to be proven wrong on this point.

 

[josh1]

Why hasn't [string theory] been able to reproduce Hawking results for ordinary astrophysical BH's if string theory is indeed a theory of QG.

You`ve got it backwards. It`s string theory and not lqg that has been able to produce the black hole area-entropy relation. In fact, It`s only string theory that has been successful in this regard. All lqg has been able to do is produce the proportionality between entropy and area, but not the correct constant of proportionality of 1/4, and it is the latter that presents the real challenge for any quantum theory of gravity. This is just one of many reasons why hardly anyone in the physics community takes lqg seriously. If you really want to understand what`s going on in high energy theory, learn string theory and learn it from string theorists and not lqg people.

 

[ensabah6]

You`ve got it backwards. It`s string theory and not lqg that has been able to produce the black hole area-entropy relation. In fact, It`s only string theory that has been successful in this regard. All lqg has been able to do is produce the proportionality between entropy and area, but not the correct constant of proportionality of 1/4, and it is the latter that presents the real challenge for any quantum theory of gravity. This is just one of many reasons why hardly anyone in the physics community takes lqg seriously. If you really want to understand what`s going on in high energy theory, learn string theory and learn it from string theorists and not lqg people.

The original papers in string theory was only in the special case of extremel BH, which do not exist in reality. The results are protected by SUSY. The results have been extended to near-extremel BH, but I am not aware that they have been generalized to all BH's.

 

[josh1]

The original papers in string theory was only in the special case of extremel BH, which do not exist in reality. The results are protected by SUSY. The results have been extended to near-extremel BH, but I am not aware that they have been generalized to all BH's.

You've failed to appreciate the significance of this, which is that this result must be produced for any black hole solution in string theory or any other theory of quantum gravity, whether or not the solution is that of an ordinary astrophysical black hole. If string theory hadn`t been able to produce the correct result, even if it is for unrealistic black holes, it would be inconsistent with the most important clue to quantum gravity we have. Like all other tests of consistency string theory has ever been subjected to, it passed this test with flying colors. The same cannot be said of any other competing theory of quantum gravity including lqg.

 

[Demystifier]

LQG predicts that entropy of ANY surface (not necessarily a surface of an isolated horizon) is proportional to the surface. The constant of proportionality is always the same, and can be adjusted so that it agrees with that in semiclassical gravity. However, LQG does not provide any new explanation of why entropy of a black hole should coincide with that of its surface.

String theory really explains why entropy of the black hole is proportional to its surface. Quantitatively, the constant of proportionality can be calculated explicitly only in some special (unrealistic) cases, but there are qualitative arguments for proportionality with the surface even in the general case.

 

[william donnelly]

Demystifier, could you give a url for the calculation of black hole entropy that does not depend on the isolated horizon constraints? The papers I have read on the arxiv all rely on the isolated horizon constraint, including those from this year.

 

[marcus]

LQG predicts that entropy of ANY surface (not necessarily a surface of an isolated horizon) is proportional to the surface. The constant of proportionality is always the same, and can be adjusted so that it agrees with that in semiclassical gravity. However, LQG does not provide any new explanation of why entropy of a black hole should coincide with that of its surface.

String theory really explains why entropy of the black hole is proportional to its surface. Quantitatively, the constant of proportionality can be calculated explicitly only in some special (unrealistic) cases, but there are qualitative arguments for proportionality with the surface even in the general case.

I had the same question as W.D. So I will just repeat for emphasis

Demystifier, could you give a url for the calculation of black hole entropy that does not depend on the isolated horizon constraints? The papers I have read on the arxiv all rely on the isolated horizon constraint, including those from this year.

Corichi has a recent series of papers on LQG BH entropy including one this year. There have been developments. Corichi also has a monograph in preparation on that topic. Nothing I've seen over the years corresponds to Demy.'s assertion as far as I can remember. So I think Demy. owes us a url. (would be interesting to have :-))

 

[josh1]

LQG predicts that entropy of ANY surface (not necessarily a surface of an isolated horizon) is proportional to the surface.

But this demonstration is a near-trivial result of the way that spin networks include degrees of freedom called links which by definition measure area.

A rather nontrivial example is the way that the entropy of highly excited strings is area-extensive. This is the string-black hole correspondence principle due to susskind. This is another one of many important clues string theory is giving us about black hole holography.

The constant of proportionality is always the same, and can be adjusted so that it agrees with that in semiclassical gravity.

The whole game is to produce the correct factor of 1/4. If a theory can`t do so, it`s wrong. What lqg needs is new physical input that fixes the immirzi parameter to produce the correct value. Not a single attempt has met with anything but utter failure.

The thing is that - and this is very important - lqg is a very simple theory and seems to offer no additional theoretical elbow room where such new physics could lurk. Precisely the opposite is the case with string theory.

However, LQG does not provide any new explanation of why entropy of a black hole should coincide with that of its surface.

It doesn`t provide any explanation, new or old.

String theory really explains why entropy of the black hole is proportional to its surface.

Well, it offers clues anyway.

Quantitatively, the constant of proportionality can be calculated explicitly only in some special (unrealistic) cases, but there are qualitative arguments for proportionality with the surface even in the general case.

The idea is to embed black hole physics in string theory by invoking the geometry of d-brane solutions with event horizons and then to use our knowledge of the spectrum of physical states of d-branes to explcitly count the number of states and compare the result to the area of the event horizon. However, this is not really an explanation of black hole holography, but it is no doubt an important clue.

 

[Demystifier]

William Donnelly and Marcus, see the derivation of black-hole entropy in the book "Quantum Gravity" of Rovelli. This book was also available online on the Rovelli's home page, but I do not know if this is still the case. I have not been reading the corresponding original papers of Rovelli, but I pressume that the same derivation can be seen there. The idea is very simple. The entropy of a surface is essentially the number of the degrees of freedom associated with the surface, so it is hardly surprising that the result is proportional with the surface (at least when the surface is much larger than the Planck surface).

 

[Sauron]

I have been reading the derivation of black hole entropy in string theory and there are a few aspects that I don´t see clear.

For example, the problem of uniquines. You can, as has explained josh, make somethin which resembles a black hole using a few kinds of d-branes and F-strings, ok. And you can count the number of states using CFT, o.k.

But, how can you be sure that there are not diferent ways to make the same black hole with another kind of branes/strings configuratiosn. If so the number of microstates would increase (Maybe there is some uniquines theorem anyway and simply I don´t know it).

 

[marcus]

William Donnelly and Marcus, see the derivation of black-hole entropy in the book "Quantum Gravity" of Rovelli. This book was also available online on the Rovelli's home page...

Demy, I have the book in hardcopy and back in 2003 used to read it online. Great book! but I would not consult it for BH entropy, there has been quite a bit written since Jan 2004 when Rovelli's text went to the publisher.

I could be wrong but I think if you check out 2006 and 2007 papers by Corichi (and references therein) you will be doing yourself a favor (if you are at all interested in LQG and BH entropy.)

It is certainly NOT the case that in LQG the entropy is simply proportional to the eventhorizon area! and the relation to area seems to depend somewhat on the size of the BH.

Corichi is preparing a review article on this. A lot has been written. The review article is not yet available but you should check out his recent papers in arxiv. Hope this helps

 

[josh1]

It is certainly NOT the case that in LQG the entropy is simply proportional to the eventhorizon area!

As a principled person who always argues honestly based on the facts as I understand them, I would only have included the exclamation mark if I believed I understood precisely what lqg does say about the area-entropy relation and was prepared to make my case in detail. You should note that one of the posting guidelines in PF requires members to back up their claims when asked and ignoring such requests when they are reasonable - especially when they do so on a regular basis - is a definite no no here. So please explain this strangely vague statement and enlighten us.

 

[josh1]

...how can you be sure that there are not different ways to make the same black hole with another kind of branes/strings configuration? If so the number of microstates would increase...

Yes, the entropy of a particular black hole may always be viewed as counting all of the ways it could`ve been made. But by a black hole we mean a particular solution of the theory. If a black hole involves different ingredients, the solution and hence the black hole - including the way it`s degrees of freedom are counted - will be different.

 

[william donnelly]

Yes, the entropy of a particular black hole may always be viewed as counting all of the ways it could`ve been made.

Do you have a reference for this argument? Specifically, why should the logarithm of the number of ways a black hole could have formed be the same as the entropy of the thermal state as seen by an observer outside the black hole?

I understand the statistical mechanical definition of entropy, I just don't see how "ways a black hole could be made" are the same thing as "black hole microstates".

 

[josh1]

Do you have a reference for this argument? Specifically, why should the logarithm of the number of ways a black hole could have formed be the same as the entropy of the thermal state as seen by an observer outside the black hole? I understand the statistical mechanical definition of entropy, I just don't see how "ways a black hole could be made" are the same thing as "black hole microstates".

I`ve come across this way of saying things a number of times, but only in the context of black holes, but I don`t have a reference. But it`s not meant in a literal way. As you know, a microstate is a collection of excitations that represent one possible configuration of a system. We then think in terms of "building" the system out of the excitations of a particular microstate with the complete collection of all possible micrsostate then representing in this sense the "different ways of building" the system.

 

[Demystifier]

Demy, I have the book in hardcopy and back in 2003 used to read it online. Great book! but I would not consult it for BH entropy, there has been quite a bit written since Jan 2004 when Rovelli's text went to the publisher.

Marcus, could you specify what exactly is wrong with the simple analysis presented by Rovelli in his book? The fact that later other people made a more complicated analysis does not convince me that the earlier simpler analysis is wrong. Can you explain, in simple terms, in what sense the later results represent an improvement?

In my opinion, scientific papers are often too polite, in the sense that they often hesitate to say explicitly what are the drawbacks of earlier papers on that subject. For that reason you can understand the point of a new paper only if you already studied all earlier papers on that subject.

 

[marcus]

In my opinion, scientific papers are often too polite, in the sense that they often hesitate to say explicitly what are the drawbacks of earlier papers on that subject. For that reason you can understand the point of a new paper only if you already studied all earlier papers on that subject.

Yes! But maybe this politeness has a good reason.
Remember that this is an area of expertise of Corichi---maybe he has the best judgment. He was one of the authors of the original 1997 paper Asht. Baez Corichi Krasnov, and of those four he is the only one who is currently working on it.

Moreover he is writing a review of the whole LQG/BH entropy subject.

Corichi has chosen not to directly attack earlier work and point out its limitations in an obvious way. I would understand if you think it "too polite". But maybe he is behaving with correct amount of politeness.

This business has been going on for 10 years. There have been gradual refinements. There is still room for people to disagree.

Where I personally stand (as an observer, not researcher) is not so important but I will tell you frankly that at first I was dubious of Corichi's work and gradually I am finding it more and more convincing. Partly this is because of the work by Ghosh and Mitra around the same time (2005) which seems to corroborate Corichi. Partly it is the fact that he is using computer models and brute force. I have a lot of respect for brute force number crunching as an alternative to theoretical/analytical----both are fallible so one should try to do both as a check on each other.

The Indians, Ghosh and Mitra, are very analytical, so Corichi numerical approach complements theirs.

Corichi is a prominent organizer of the Loops '07 international LQG conference this summer in Morelia. I am sure that this summer's conference will have a lot about BH!

Probably the earlier work of ten years back should be honored and quietly improved on

 

[josh1]

Hi marcus,

You posted the following:

Demy, I have the book in hardcopy and back in 2003 used to read it online. Great book! but I would not consult it for BH entropy, there has been quite a bit written since Jan 2004 when Rovelli's text went to the publisher.

I could be wrong but I think if you check out 2006 and 2007 papers by Corichi (and references therein) you will be doing yourself a favor (if you are at all interested in LQG and BH entropy.)

It is certainly NOT the case that in LQG the entropy is simply proportional to the eventhorizon area! and the relation to area seems to depend somewhat on the size of the BH.

I think that the site guidelines (not to mention considerations of simple respect of other members) obligate you to respond in some meaningful way to the following question posted by Demystifier:

Marcus, could you specify what exactly is wrong with the simple analysis presented by Rovelli in his book?

 

[william donnelly]

I can't speak for Marcus, but I find the Krasnov/Rovelli approach to black hole entropy a little circular. They start by assuming the area is the only relevant macroscopic quantity for the black hole and so count the number of states for a fixed area. This quantity must be a function of the area by definition.

 

[josh1]

I find the Krasnov/Rovelli approach to black hole entropy a little circular. They start by assuming the area is the only relevant macroscopic quantity for the black hole and so count the number of states for a fixed area. This quantity must be a function of the area by definition.

It could turn out that the correct degrees of freedom of black holes really are explicitly area-extensive. But then being the correct theory, it would produce the correct factor of 1/4. The failure of lqg to achieve this emphasizes that producing the correct factor of 1/4 can only follow from a theory that identifies the correct degrees of freedom of a black hole and that these degrees of freedom are certainly not the links of spin networks.

 

[william donnelly]

Failure seems a bit strong. Admitted, loop quantum gravity has its problems, but I don't think the presence of a single free parameter is one of them. I don't know of any reason to believe the Immirzi parameter should not take on the right value to reproduce the Bekenstein-Hawking entropy.

 

[josh1]

Failure seems a bit strong.

Maybe "failure-ish"?

I don't know of any reason to believe the Immirzi parameter should not take on the right value to reproduce the Bekenstein-Hawking entropy.

Some piece of new physics is needed to fix the immirzi parameter, and I can`t deny that it`s possible that this physics lives in some undiscovered part of lqg. It`s just that lqg seems too simple for there to be anywhere such new principles could hide.

You know, the euclidean quantum gravity program lost it`s popularity because it predicted a gravitational phenomenon called wormholes which occurred below the Planck scale. If correct, euclidean quantum gravity would have to produce a constant that tells us at what scale below the Planck scale wormholes do occur, but it couldn`t. Now euclidean quantum gravity is used only because it seems to capture some properties that could very well be relevant to quantum gravity or quantum cosmology.

Another example is the consistent histories approach to quantum cosmology. It aimed to show how classical physics emerges from quantum mechanics. To do so it introduced the notion of quasi-classicity as an interpolater between quantum mechanical behaviour and purely classical behaviour. The problem was there was nothing in this theory that could be used to identify under what conditions quasi-classical behaviour appears.

The same is true of lqg. It is seductive, but without an argument to establish how it connects with ordinary gravitational physics, it cannot succeed, and a rather large majority of physicists in this field are quite certain it never will.

 

[jal]

Some piece of new physics is needed to fix the immirzi parameter

I'm listening tell me more.
jal

 

[marcus]

one trouble with outsiders discussing LQG is that the field doesn't hold still---various "LQG-like" off-shoots develop.

Some currently-researched LQG-like approaches don't have an Immirzi parameter. Others make it have physical meaning so that it could in principle be determined experimentally in lab (not from Black Holes! from other stuff I gather). One doesn't know which of the approaches are correct

it would be a big job to say in an accurate and balanced way what the situation is

I can't take the time to look up the arxiv links but I will give author names and you or anyone interested can use the search engine at arxiv to find the papers if you want.

1. Rovelli and Freidel have several papers together or separately where the Immirzi has a physical meaning, tells something about nature that is in principal measurable in laboratory---this doesn't have to do with black holes, it has to do with particle physics, keyword torsion comes up, have to see the articles

2. a defining event for the LQG community is the QGQG school now in progress. The person who is teaching the LQG series of lectures is Thomas Thiemann. He has a new version of LQG called AQG and I am not sure that it has an Immirzi parameter. Maybe we can ask some PF people who are attending the school: Francesca is one and F-H is another.

3. Sergei Alexandrov and Etera Livine have a variant of LQG with no Immirzi, they call it "covariant LQG". Recently Alexandrov Buffenoir Roche came out with a new version, just in the past 6 months---no Immirzi.

4. a lot of the LQG community's research is spinfoam based or GFT (group field theory)----so there would be no Immirzi AFAIK. I could be wrong.
At the QGQG school, the people teaching the spinfoam approach are Laurent Freidel and Etera Livine.

 

[marcus]

to a lot of people it is the LQG community which they want to talk about because it is the main rival to string research

but then they get talking about vintage 1995 canonical LQG or whatever, and it misses the point, because the community is already 10 years down the pike and moving fast.

So a lot of confusion and misleading talk arises, which i will try to straighten out some.

An important issue is CONTACT WITH ORDINARY GRAVITY. Everybody should have noticed when Rovelli and team derived gravitons in a spinfoam context in 2005. After one of their papers in August 2006 he said what I put in sig

essentially we got Newton gravity starting from scratch

This was published in major journal articles and also in popular media, so I would guess anybody who follows QG knows about it.

But there have been a lot of other cases of this by other LQG people in the past 2 years---in several different special cases and contexts: different from Rovelli's spinfoam context. More an more often when i scan the literature i am seeing the phrase correct classical limit turning up. Always so far in a special case, not yet a totally general solution to the problem.

It is old news that you get the correct classical limit in LQC. But it came up last year in a particular case Bojowald was working on where it wasnt even LQC it was a new version he'd developed of LQG! I also saw it in a recent paper of Magueijo. And the correct classical limit came up in Thiemann's talk at KITP if i remember correctly. It seemed to interest folks so they gave him a second hour.

So it seems that you get a bunch of critics of the LQG community who stonewall it and say "LQG has nothing to do with gravity!"
But they are talking about something that doesn't have much to do with the actual stuff the LQG community is working on! The approaches the community actually works on DO seem to be reaching out and contacting classical gravity here and there these days.

A lot has happened in the past 2 years. A lot of new faces besides the original pioneers (Rovelli, Smolin, Ashtekar). A lot of variations, new approaches. so it is hard to get it right if you have a static picture.

It may be that vintage 1995 LQG has nothing to do with gravity---I don't know I watch progress on a lot of different fronts. But the LQG community's job is to adapt and evolve the stuff they work with. Which they have over the past 10 years almost beyond recognition. And the past 2 years progress seems to me to have been especially rapid.

this year we SHOULD be seeing a new book from Cambridge University Press called Approaches to Quantum Gravity, towards a new understanding of space time and matter which includes work by 20 or so people. It is edited by Dan Oriti (in Renate Loll's group at Utrecht) and it should give us some better perspective on what the LQG community is doing
(the mention of matter in the title is important---LQG people are very much into discovering matter and QFT Feynman diagrams in their spinfoams these days----matter turning out to be a facet of geometry----look up Laurent Freidel papers he has many about this starting in 2005)

so anyway, Oriti's book will help clarify and define the field----and gradual increasing contact with classic gravity as one aspect.
And we will hear more from the Loops '07 conference in Morelia, this summer. And hopefully we'll hear from some of the people now attending that QGQG school.

 

[Demystifier]

I can't speak for Marcus, but I find the Krasnov/Rovelli approach to black hole entropy a little circular. They start by assuming the area is the only relevant macroscopic quantity for the black hole and so count the number of states for a fixed area. This quantity must be a function of the area by definition.

I agree. But can you explain in simple terms how other LQG approaches (presumably with isolated horizons) avoid this circularity?

 

[josh1]

one trouble with outsiders discussing LQG is that the field doesn't hold still

So now your holding yourself out as an lqg insider and the rest of us as outsiders? Boy you`ve got a lot of nerve given the lack of specifics in your posts.

...various "LQG-like" off-shoots develop. Some ...approaches don't have an Immirzi parameter.

The problem isn`t the immirzi parameter. The problem is the failure to recover general relativity. We can express this difficulty in terms of the immirzi parameter in those variants of lqg that have one, or in different terms in those that don`t.

On the other hand, string theory reduces in the low energy limit to various classical supergravities from which one can write down a classical metric involving event horizons of various types and then analyze these solutions, including in some cases calculating the entropy which yields the correct value in all cases considered so far.

More an more often when i scan the literature i am seeing the phrase correct classical limit turning up.

And from this we`re suppose to learn what exactly?

Others make it have physical meaning so that it could in principle be determined experimentally in lab (not from Black Holes! from other stuff I gather).

This has already been discussed since it is just another way of trying to identify new physics in lqg that would fix the value of immirzi to the correct one. None of these approaches have succeeded either.

The fact that so many different approaches to lqg are available and none of them have succeeded is screaming at us that these ideas are fundamentally wrong.

By contrast there are no variants of string theory, just as one would expect from a correct theory.

 

[josh1]

Hi jal,

You asked me to expand on my remark that some piece of new physics is needed to fix the immirzi parameter. Unfortunately, in the absence of any real progress on this issue, there isn`t a hell of a lot more to say. Maybe you had something more specific in mind?

 

[jal]

Marcus}
Some currently-researched LQG-like approaches don't have an Immirzi parameter. Others make it have physical meaning so that it could in principle be determined experimentally in lab (not from Black Holes! from other stuff I gather). One doesn't know which of the approaches are correct

Thanks. I am looking in the paths that you have mentioned.

josh1
Maybe you had something more specific in mind?

Well!... I am gathering in my blog what I think would end being citations for a new approach.
Do we need to open up a new thread to discuss another paper?

http://arxiv.org/PS_cache/gr-qc/pdf/0703/0703135.pdf
Loop quantization of spherically symmetric midi-superspaces
Miguel Campiglia1, Rodolfo Gambini1, Jorge Pullin2
27 March 2007

We quantize the exterior of spherically symmetric vacuum space-times using a midi-superspace reduction within the Ashtekar new variables. Through a partial gauge fixing we eliminate the diffeomorphism constraint and are left with a Hamiltonian constraint that is first class. We complete the quantization in the loop representation. We also use the model to discuss the issues that will arise in more general contexts in the “uniform discretization” approach to the dynamics.

p.12 If one adopts the point of view commonly used in loop quantum cosmology, that the quantum of distance should have a minimum value, then one would not expect to take the limit ρ going to zero, but to keep the parameters at a minimum value. In such a case one could expect to eliminate the singularity. This is plausible since then the triads would likely not go to zero.

I would think that this can be achieved by applying/obeying the Quantum Minimum Length Structure (QMLS)
Since a 2d surface is being analysed... would it be too hard to use these results to get a better understanding of a membrane?
jal

 

[william donnelly]

I agree. But can you explain in simple terms how other LQG approaches (presumably with isolated horizons) avoid this circularity?

Sure. The isolated horizon approach starts by quantizing in the same manner as ordinary lqg, but the manifold has a boundary. Then they apply the isolated horizon constraint - this is a classical constraint on the boundary that forces it to be a horizon. Then they count the number of states of the boundary Hilbert space. In essence this space should contain all the observables of the horizon, not just the area.

The other advantage of the isolated horizon calculation is that it seems to match the value derived from the quasinormal modes of a Schwarzschild black hole, under certain assumptions about the edges intersecting the horizon.

Of course the down side is that they have applied an extra classical constraint that shouldn't be there. It really restricts the applicability of their derivation.

 

[william donnelly]

Regarding the ways to fix the Immirzi parameter, those I know of are:
- Black hole entropy
- Quasinormal modes of Schwarzschild black holes (Dreyer)
- Fermion scattering (Perez and Rovelli)
The entropy has been studied a lot, the quasinormal modes less so, and the fermion scattering very little as far as I know. I don't think this constitutes "no progress".

 

[josh1]

Regarding the ways to fix the Immirzi parameter, those I know of are:
- Black hole entropy
- Quasinormal modes of Schwarzschild black holes (Dreyer)
- Fermion scattering (Perez and Rovelli)
The entropy has been studied a lot, the quasinormal modes less so, and the fermion scattering very little as far as I know. I don't think this constitutes "no progress".

Why? What`s your definition of progress? Failing in many ways rather than only one?

 

[william donnelly]

In your words "some piece of new physics is needed to fix the immirzi parameter". This is exactly what the papers I referenced provide. I didn't want those in this thread to misinterpret your post as saying that nobody is thinking about or trying to solve this problem.

 

[josh1]

In your words "some piece of new physics is needed to fix the immirzi parameter". This is exactly what the papers I referenced provide. I didn't want those in this thread to misinterpret your post as saying that nobody is thinking about or trying to solve this problem.

Fair enough, but are they really any closer now to a solution then they`ve been in the recent past?

 

[Demystifier]

Then they count the number of states of the boundary Hilbert space. In essence this space should contain all the observables of the horizon, not just the area.

Still, one should not be surprised to obtain that the number of states of the horizon increases linearly with the area of the horizon. Isn't it slightly circular as well?

By contrast, string theory counts the number of states INSIDE the black hole, not on the horizon, so it is really nontrivial to obtain that this number is proportional to the horizon area. In this sense, string theory really provides an EXPLANATION for the proportionality with the area, whereas LQG, at best, provides a confirmation.

 

[william donnelly]

Yeah, that's a good point. Both derivations require a priori that the black hole entropy depends only on the horizon degrees of freedom. What is missing is some argument for why these are the relevant degrees of freedom.

One thing that is almost certain is that loop quantum gravity is not compatible with the hypothesis that the Bekenstein-Hawking entropy counts the number of internal states of the black hole. But this hypothesis is not a given, and there exist arguments against it.

 

[josh1]

...the number of states of the horizon increases linearly with the area of the horizon.

The entropy increases linearly with the area of the horizon while the number of states goes as the exponential of the area. Since I`m sure you know that the entropy is the log of the number of states, I`m guessing that this was just a careless error.

By contrast, string theory counts the number of states INSIDE the black hole...

The counting of states of black holes made out of D-branes or anything else in string theory as it`s currently understood doesn`t say anything about where the actual degrees of freedom they count are. It could very well turn out that the true degrees of freedom of black holes do indeed live in some sense on their event horizons.

These sorts of black holes are represented by classical supergravity solutions analogous to ordinary black hole spacetime metrics. Just like ordinary black hole metrics are functions of the mass and perhaps charges carried by the black hole, the metrics for black holes made out of D-branes are functions of how many of each type of D-brane there are and the various charges they may carry. The difference is that we can use our knowledge of D-branes to count the number of states and then independent of this compute the area of the event horizon in terms of the same quantities. We then find that the log of the number of states and the event horizon area are related by the correct area-entropy law. But there is still a (classical nonstandard) singularity and we just don`t know what the physical implications of that are.

 

[ensabah6]

The entropy increases linearly with the area of the horizon while the number of states goes as the exponential of the area. Since I`m sure you know that the entropy is the log of the number of states, I`m guessing that this was just a careless error.



The counting of states of black holes made out of D-branes or anything else in string theory as it`s currently understood doesn`t say anything about where the actual degrees of freedom they count are. It could very well turn out that the true degrees of freedom of black holes do indeed live in some sense on their event horizons.

These sorts of black holes are represented by classical supergravity solutions analogous to ordinary black hole spacetime metrics. Just like ordinary black hole metrics are functions of the mass and perhaps charges carried by the black hole, the metrics for black holes made out of D-branes are functions of how many of each type of D-brane there are and the various charges they may carry. The difference is that we can use our knowledge of D-branes to count the number of states and then independent of this compute the area of the event horizon in terms of the same quantities. We then find that the log of the number of states and the event horizon area are related by the correct area-entropy law. But there is still a (classical) singularity and we just don`t know what the physical implications of that are.

Isn't the whole point of quantum gravity to remove classical singularities?

 

[josh1]

Isn't the whole point of quantum gravity to remove classical singularities?

Pretty much, but there are other aspects of gravity that need to be understood better as well.

 

[ensabah6]

Pretty much, but there are other aspects of gravity that need to be understood better as well.

Until that happens, would it be fair to say that at present, string theory fails as a candidate theory of quantum gravity for it fails to produce a theory in 4D, with broken SUSY, with a mechanism, that removes classical singularities?

I agree that loop quantum gravity also fails btw.

 

[josh1]

Until that happens, would it be fair to say that at present, string theory fails as a candidate theory of quantum gravity…?

Firstly, string theory is a true blue quantum theory of gravity and it is also the only such theory known. Why can we say this? The reason is that string theory includes gravitons, and in the limit of low energies reduces to various supergravities containing general relativity.

But what about LQG? Isn`t it a quantum theory of gravity too? To the best of our knowledge, although it is a quantum theory of something, that something seems not to be gravity. This should be surprising because the starting point of LQG is general relativity. But in fact this is also the problem in that to believe in LQG, one must also believe that general relativity remains a valid basis for quantization all the way up to Planck scales and this is inconsistent with everything we do know, not only about quantum gravity, but also from our knowledge of the other interactions.

To truly appreciate why string theory dominates high energy theory requires one understand a lot of physics. Knowing phrases like “supersymmetry breaking” or “extra dimensions” or little pieces of propaganda from here and there doesn`t really help much. To learn about string theory and why there isn`t a lot of serious doubt about it`s ultimate correctness requires you do a lot of work. It`s just very difficult dealing with this sort of question because it requires one explain what string theory does do successfully and this is a long and complicated story.

By contrast, LQG is so simple that once you understand string theory it`s childs play to see why LQG was dismissed long ago by nearly everyone. Since then, some disgruntled scientists having lost their battle in the arena of science are now trying to win it in the court of public opinion, which is ridiculous since laymen cannot really be expected to know the difference.

Alot of this sort of thing goes on at PF vis a vis a bunch of people who aren`t scientists and who really don`t understand either lqg or string theory, so watch out. One particular trick they use is to make it look like their taking a "balanced" approach to lqg and string theory. They`re like religious zealots saying that one should consider both creationism and evolution equally but really they just want to suck you into the creationism club. The people who do this are easy to identify. They`re unable to answer technical questions or explain what they mean in technical and precise terms.

I agree that loop quantum gravity also fails btw.

Drop the word "also".

 

[marcus]

my two cents from the sideline is that it seems really important for LQG-critics to make the point (a shaky one) that LQG does not have a demonstrated correct classical limit.

But LQG is actually a manyheaded beast and some variants in some cases have gotten a correct classical limit, or closer to it, in the past couple of years.
Whether a particular version has reached the finish line depends on the standards you set up to judge by. But there has been obvious and undeniable progress. I cite the papers now and then but no one wants to read the "bad" news---LQG critics don't anyway.

The latest thing from Bojowald was part of this development. I posted the link.
His thing is that LQC ALREADY HAS a correct limit and he is setting up to deal with a sector of LQG by perturbing around LQC.

there are a bunch of other cases of this getting closer to the goal thing
======

anyway the question I'm curious about is where does this extreme need to deny{/b] come from? It gets so intense that someone who simply points out they have a number of variants (spinfoam, GFT, AQG...) and there's definite progress in this area can even get attacked personally!

why can't LQG-critics relax and allow that the approaches that the LQG-community is working on are getting some contact with classical gravity?

I think it is a kind of anxiety---feeling that things are not so fine with string these days---so that they really need the feeling of being the "only game in town". it is a necessary delusion that supports a needed feeling of security and esteem. Well that's a theory

 

[josh1]

...some variants [of lqg] in some cases have gotten a correct classical limit, or closer to it.

Allow me to translate: no variant of lqg has gotten the correct classical limit or moved closer in any unambiguous sense. If it we`re otherwise it would be big news, just like the whole quasinormal mode business was until it was realized that it was just a fluke since it worked for only one very special case.

Whether a particular version has reached the finish line depends on the standards you set up to judge by.

What is this suppose to mean?

But there has been obvious and undeniable progress...

Really? Do tell!

The latest thing from Bojowald...is that LQC ALREADY HAS a correct limit and he is setting up to deal with a sector of LQG by perturbing around LQC.

Please explain.

why can't LQG-critics relax and allow that the approaches that the LQG-community is working on are getting some contact with classical gravity?

There are few critics of lqg in the physics community since nobody really cares about lqg. But if they ever do make contact with classical gravity, people will definitely take an interest. But no such contact has been made, and it is the consensus that none can ever be made, but few spend much energy explaining this because it just doesn`t matter.

I think it is a kind of anxiety---feeling that things are not so fine with string these days---so that they really need the feeling of being the "only game in town". it is a necessary delusion that supports a needed feeling of security and esteem. Well that's a theory

This is just baloney.

 

[Sauron]

Josh, I guess you can't know what people at physics forums know or what does not´t know. If we go to it John Baez post here from time to time and I guess you will agree that he knows LQG. I also have seen posts from Lubos Motl and I suspect he knows "at least a little" string theory ;).

But in fact this is also the problem in that to believe in LQG, one must also believe that general relativity remains a valid basis for quantization all the way up to Planck scales and this is inconsistent with everything we do know, not only about quantum gravity, but also from our knowledge of the other interactions.

I don´t fully agree with these and I´ll try to explain you why. On one side you can argument that by the renormalization group flow (solved at one-loop or so) the intensity of the gauge forces will become as important as the gravity forces at some regime. Well, I don´t deny it but on the other side if you get one individual gauge theory it is self consistent. It could be conceivable a world where only one such force would exist and we could quantize it and it would be a theory of everything. Yeah, it is not the world we live but it would be a mathematically self consistent theory.

I guess the same reasoning applies to gravity. You could be interested in the behaviour of it and wonder if you can make a mathematically self consistent theory of it even if you know that by doing so you are not getting an answer for the world we live. But still so I see it like a very interesting thing to investigate.

I´ll try to give you another thing why i find interesting LQG. In ordinary gauge theory (not to say in string theory) you are doing perturbation theory around some classical vacua's. And the content of the theory is very different depending on the vacua's you choose. An "elementary" case is the Higgs mechanism. If you quantize the unbroken symmetry you have a theory for a tachyonic 0 spin field and a few massless vector and fermion fields. But if you quantize around the minima obtained after spontaneous symmetry breaking you get a bunch of massive non tachyonic fields (and also some massless fields because not all symmetry is broken).

The point is that you have a quantum theory of two limits (vacua) of a classical theory, but you don´t have a quantum theory which describe simultaneuosly all the limits. If you would have a non perturbative quantum theory of a gauge + fermions + higgs fields, which would you think that its "classical limit" would be? the broken symmetry or the unbroken symmetry theory? I know "tachyon condensation" program try to answer a somewhat similar question in the bosonic string, but I am not sure if it is succesfull or if address the questions such I am formulating it.

Well, I guess that if you try to do a non-perturbative quantization of gravity, which seems to be a most complex theory than gauge theories (I am aware of the maldacena conjecture) it very easily could be that it would exist more than a "classical" limit. In fact it would be interesting to see what the LQG program could say of the "ordinary" gauge theories, maybe it could give a description of all the ranges of the theory, i.e. to have a quantum description of how you go from a vacua to another vacua.

And if we wonder about what LQG must do realize that by quantization in curved backgrounds we know that a matter + gravity in a coordinate system is equivalent to a theory with only gravity in another system, so that raises, i think, the question of which would be the "rgitht" description of classical vacua in quantum gravity. Related to these, from my viewpoint, is the question that in gauge theories you have a classical nonlinear theory. Them you choose a vacua and from there you make a quantum theory, which is a linear theory. I seriously doubt that these perturbative quantum theories represent the whole history. Until you have a nonperturbative quantization I think you don´t have a quantum description of all the regimes of a gauge theory.

Well, of course you have S-dualities that relate the weak coupling of some theories to the strong coupling of another, but I don´t think dualities are as powerful as it would be to have a nonperturbative quantum description of the theory in the whole regime.

Just to conclude a question about the stringy calculation of the black hole entropy. Ok, you make a description of a 5-D black hole by wrapping D5, D-2 branes around a torus, and counting the states of open strings that connect these branes (well, these is just a part of the history of course). also you can have different descriptions using dualities and whatever you want. And you can describe 4-D black holes as well. But, and these is my question, none of the configurations of branes+strings which allow to describe black holes are well suited to describe the world we live. I mean, they don´t allow to describe the observed standard model. But if I think of a massive body falling into the event horizon of a black hole I guess I still could describe, at least for an amount of (proper) time the matter of the object by the same kind of strings + branes hat live outside the event horizon. I don see how we would expect to map the outside description of the out of the black-hole to the in of the b-h. Well, maybe these last question makes not too much sense, but I am just now trying to appreciate the details of the stringy description.

In definitive, even if LQG wouldn´t be a theory of quantum gravity I still think it could seed light in some aspects of quantum theory. I don´t see any clear reason why people would study LQG. Personally I am triying to understand both, strings and LQG and compare them and see where they agree and differe. I neother see why one approach can´t get ideas from the other, at least to some extent.

 

[Demystifier]

The entropy increases linearly with the area of the horizon while the number of states goes as the exponential of the area. Since I`m sure you know that the entropy is the log of the number of states, I`m guessing that this was just a careless error.

Of course, thanks for the correction.

By the way, although I also find string theory more promising than LQG, I believe that there is at least one great achievement of LQG that deserves great respect. It removed UV divergences essentially from the requirement that quantum theory should be explicitly diffeomorhism-invariant (with respect to diffeomorphisms in 3-dimensional space). It can be compared with string theory, whose one of the greatest successes is removal of UV divergences essentially from the requirement that quantum theory should be explicitly invariant with respect to conformal transformations of the 2-dimensional world-sheet.

Also, as one can complain that LQG has not yet been fully successful in obtaining classical general relativity, one may equally complain that string theory has not yet been fully successful in obtaining general relativity in 4 dimensions. Both theories have some results in these directions, but none is yet fully successful.

In fact, many physicists will say that string theory is not really physics, but pure mathematics. I have never heard that somebody said that for LQG.

 

[R.X.]

In fact, many physicists will say that string theory is not really physics, but pure mathematics. I have never heard that somebody said that for LQG.

.. because this loose set of different setups with shaky rules can't even be called mathematics...

 

[marcus]

... this loose set of different setups with shaky rules...

real theoretical physics, at a growth boundary, has often been just this I believe (a loose set of different setups with shaky rules)
you give a good description, not necessarily of lqg but, of an evolving branch of physics theory in general. bravo

 

[Demystifier]

.. because this loose set of different setups with shaky rules can't even be called mathematics...

LQG is at least wrong. String theory is not even wrong.

I am just kidding, of course. I find both approaches interesting and promising.
Few years ago I liked LQG more, now I like strings more, but it can change again.