A few days ago a friend of mine, graduate theoretical physician, but not an active physician nowadays, and an ocasional reader of this blog,let me know of a new in the media versing about a resolution of the "black hole information paradox". The new was published in many webs, for example here. By the same time a thread was opened in physics phorums about the topic, concretelly Physicists Demonstrate How Information Can Escape From Black Holes based in LQG.
Ok, I suposse that I would have to somehow give an opinion about the new. I have waited a bit to see if, apart of physics phorums people, some of the big (or even not so bigs) ones on the blogosphere said something about the particular. Afther all Astekhar, the mainauthor of the paper behind the new, is one of the greatests personalities in LQG (the whole field begins with a work of him about new variables in canonical gravity) and the theme is very catchy, to say the less. For some reason there has not been such an entry in referential blogs, so I´ll try to give my humble opinion abot the particular.
First of all to say that I find that the claim of the new somewhat distort the actual nature of the achivement. Suposedly the paper solves the questions in the framework of LQG. Afther all in the news release you can read:
"Once we realized that the notion of space-time as a continuum is only an approximation of reality, it became clear to us that singularities are merely artifacts of our insistence that space-time should be described as a continuum."
The idea of discrete space-time strongly suggest that they are talking about LQG. Well, in the physics porum post somone pointed to the arxiv paper behind the news release, concretelly this, Information is Not Lost in the Evaporation of 2-dimensional Black Holes. The first bad thing comes in the title, "2-dimensional black holes". That is they solve the problem in a simplified modell, that always opens the possibilitie that the problem could not be solved in the full environment, afther all 3-d quantum gravity is very diferent from 4-d one.
Anyway, let´s see what is going on. In the last post I talked about LQG and I did a brief description of how LQG treats black holes (or at least one of the ways they do it when they face the singularity problem). As not every reader of this blog is assumed to speak spanish I´ll re-explain it. They don´t work in the full LQG framework but in modell with reduced simmetry. They get the Scharschild solution (a solution for vacuum Einstei equations, statif and with radial symmetry) and write the hamiltonial constraint equation fo it. They treat the radious as a discrete time coordinate. That results in a diference equation that can be solved and they show that they can evolve the solution for negative values of the radious, so they, seemengly, advoid the central singularity. Before reading the paper of Astekharet all I tried to figure how they could have procceded. To begin with the information paradox problem is related to matter in the vecinity of the horizont. So they would need to introduce in the description mttr in some wayor another. The original work of Hawkings that raised the whole problem used a fiexed Schwarschild background and an scalar field propagating in it. By the properties of quantization of fields in a courved backgrounds it was known that a vacuum state contianing no particles for aan observer is transformed in a state containg particles by a bogoliougov transformation for another non inertial observer. Playing with that, and with the conformal diagrams of black holes, Hawking derived that black holes actually emit radiation, in thermal quilibrium. That raises the problem that the black hole aan evaaporate because that procces. But the b-h was formed by matter in a pure state, and the thermally described matter is in a mixed stte, so the evolution would be not unitary (that is a bried description of the problem we are trating, for the ssafe of someone wouldn´t know it). Canonical LQG, the one in which Astekhar usually works, normally trates pure gravity, althought it can describe non fermionic matter also. Knowing that I thoguht that they would use some variant of the singularity removal approach including a klein-gordon field. Well, I was too naive.
They work in something called "Callen-Giddings-Harvey-Strominger (CGHS) black holes". I had not previous knowledge of that model, but the names behind it sound me "stringy", in particular Strominger is mainly an string theorist. Well, I was not wrong this time. The paper makes begins with a brief description of the hawking problems, some previous aproachs to the solution (açone by Hawking himself aaproach based in the maldacnena AdS/CFT corresondence) and just afther that talks about some workd in the early ninties triying to solve it in a toy two dimensional modell, the CGHS.
Just before writing the actual equation of the model the aouthor make a very courious advise:
considerations are motivated by loop quantum gravity, in
this Letter we will use the more familiar Fock quantization
since the main argument is rather general"
So they say that we are not going to see a formalism related to LQG, alathought LQG is behing the scene. Well, that means taht we must belief in LQG, but we are not ging to see it. Ok, lets belive, at least for a while. Let´s see (part of)the lagrangian describing the model:
Now it is when one can beguin to be really surprised. We have that Phi is said to be a dilaton. But a dilaton is a field related to string theory. All of the strings theories have a dilaton. So we are in a modell inspired by string theory (an aspect that it is not mentionesd anywhere in the paper). R is the curvature and f is an scalar field. Well, ok, no problem, someone would expect their appearence.
Afther that they introduce the equatios associated to the lagrangian and begins the task of finding solutons resembling a black hole suited for their purposes. First they affront the classical case. They do it in a perturbative, recoursive, way. That is, they choose a candidate metric, calculate the stress tensor for the fields and reintroduce it in the Einstein equation. By dong that they find that the metric an develope a singularity that they can identify as a proper black hole.
Afther that they consider a quantized version, they add hats xD). Not, serously, they use a fock space tratement (in teh spirit of the Wald aproach to quantization in courved backgrounds, but this time quantizing the metric also). They afrront the uestion of quantization (solving the conmutator eqations to say that) by a bootstrapping procedure, a recoursive way similar to the classical one. They do the suual stuff of identifiying the average values with the classical solutions,but they face a problem when the metric becomes singular, and they cann not continuate the bootstraping. Afther that they use another procedure, a mean field approach MFA. They argue that the e relevant part to solve the information paradox depends on the behaviour of the MFA in the near future ifinity and with some 3 extra sumptions ( they explain that two of them aare commonly accepted and that the other is very natural) they can calculate the S-Matrix and se that it is unitary.
Well, the detaills of how valids are the asumptions (2-D space time, MFA, asymtotic regions, etc) is something that, fourtunately, I don´t need to judge. The key point that I want to raise is that what we see in the paper is very, very, far from any formalisms related to LQG. So to claim that this can be seem as a trioumph of LQG, if they don´t bring a future a paper (or smewhat point me that I am missing something important) where they addapt the calculations to something more LQG like, is to somewhat distort the truth. Or, at least, a too propagandistic deformation of facts ;-).
P.S. Seriously, I would like to leave this tasks to the famous physicists bloggers. For example, I am still wating Sean Carrol to post about the 't Hoof paper I writted about two posts above.