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

[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.