## Sunday, May 25, 2008

### Wormholes at the LCH?

The LCH is next to open. Hopefully supersymmetry and the Higgs boson will be found. But there are more possible things that we can find there. The recent Planck 2008 congress was devoted to that topic. You can see blog entries covering that in the Dmitry (non equilibrium phenomena) blog, concretely this entry, and previous ones (ok, the entry with the interview to Polyakov is not about Planck 2008, but it is worth reading anyway). Another ongress, PPC2008 was devoted to LHC, and string phenomenology in general. You can read blog entries about it in Tomasso Dorigos blog, particularly in this entry and subsequent ones (advise, there are a lot of them). Another coverage of the congress is here. If some reader has a lot of time and is interested in reading still more about scientific congress and phenomenology he could read the coverage that Marni Dee has made of neutrinos 2008. At the monet of writing this entry her las post is this.

Well, i am going to add some fuel into the phenomenology of LCH possible predictions in this post. I am going to talk about wormholes production in LCH. That possibility heavily relies in the large extra dimensions scenario. You can read a post in the thomaso dorigos series on PPC2008 about the subject, this. Also you could read my own post about large extra dimensions and warped geometries.

As I said in that entry one thing that can possibly found in the LHC, if the LED sceneries are true, are microblack holes. But that is not the whole history. One can find another things such as p-branes or wormholes. You can read about the formers in this paper. Advise, there they talk about a somewhat peculiar type of p-branes, cosmic branes, introduced in this other paper. I am not going to describe those papers, just quote the abstract, which is self explanatory:

We compute the cross section for p-brane creation by super-Planckian scattering processes
in a (n +4)-dimensional space-time with n−m flat large extra dimensions and m
flat small dimensions of size of the fundamental gravitational scale. We find that the
cross section for the formation of a brane with dimension 1 ≤ p ≤ m, completely wrapped
on the small dimensions, is larger than the cross section for the creation of a spherically
symmetric black hole. Therefore, in space times with asymmetric compactifications we
predict that branes are more likely to be created in super-Planckian scattering processes
than black holes. The higher rate of p-brane production significantly enhances possible
detection of non-perturbative gravitational events by future hadron colliders and cosmic
rays detectors.

Now I am going, at last, with the actual topic of this post. I will explain the resuoults of two papers, Time Machine at the LHC and If LHC is a Mini-Time-Machines Factory, Can We Notice?.

The first paper face the question of the actal calculation of the probability of the wormhole beeing formed. The second, the sing that it could leave in the LHC if it actually forms.

The first paper begins with a brief review of how calculation of black hole formation can be obtained. That subject is generically know under the name of "planckian scattering". He beguines with a "quantum gravity" approach, based on the wheeler-de Witt formalism. There the possibility of black hole formation is calculated by considering the kernell of the following transtion amplitude:

$\langle h'', \phi'',\Sigma''|h', \phi',\Sigma'i\rangle= \int exp{i/\hbar S[g,\Psi]}DgDh$

The key in that approach is to study the transition between geometries describing two particles and the geometry describing black holes (or wormholes). For the details the authors refers to the paper of arxiv gr-qc/9404036. which, unfortunately, is unavailable seemingly due to a corruption in the latex that arxiv uses to render the pdf.

Other approach discussed in that brief review of black hole formation is to suppose that that ultra-relativistic particles are represented by plane gravitational waves, which interacting collide and produce a black hole. For 3D geometry the energies required are not available in the LHC, but in the LED sceneries the thing changes. The Schwarzschild radius of a 4+n dimensional black hole of mass M = √s is approximately:

$r_o \approx M^{-1}_{4+n} (s/M^{2}_{4+n})^{1/2n +1)$

( is the square of the center of mass energy of colliding particles, M4+n is the 4+n dimensional Planck mass and the 4 dimensional Planck mass is given by:

$M^2_{pl} \approx V_n M^{2 + n}_{4+n}$

Where Vn is the volume of the extra dimensions. This problem can be achieved using the Aichelburg-Sexl metric, which describe a particle at ultra relativistic speeds and is obtained by doing a Lorentz boost to the Schwarzschild metric and some convenient changes of variables. In the article the details of the calculations are not presented and the author refers to the literature. Maybe some reader is surprised why string theory is not mentioned in this article to analyze the formation of black holes. I guess that it is a good idea to give some things about it. Of course the ultimate reason to even bother about practical formation of black holes depends on warped dimensions. Although warped dimensions can be studied by classical general relativity in 4+1 dimensions (for one warped dimension) the practical motivation to do that depends on string theory. Ok, that was clear, I guess, so I´ll say some quick ideas about string theory and black holes. String theory can describe black holes of an special type, Reissner-Nordstrom black holes, using Dp-branes, and calculate it´s entropy. But the approach used to describe that black holes doesn´t say nothing about the actual formation of them. AS soon as in the eighties that question was studied by Veneziano who calculated the possibility of black hole formation by exchange of gravitons in a sting theoretic description. I don´t really know why exactly that approaches are not followed, but at least I leave Constance of their existence.

The article follows with a very brief introduction to wormholes. That is a topic widely discussed in the net. The reader can find references to it in many places. To avoid to make this entry too long I have made a separate entry in my other blog. I must apologize for English readers because the entry is written in Spanish, anyway, the actual url for it is this.

Anyway, in that entry I only discuss the basic of wormholes. For the article discussed here it is necessary to consider wormholes in a braneworld scenario. There, where the Universe is considered as a 3-brane embedded in a D-dimensional bulk, the four-dimensional Einstein field equations contain the effective four-dimensional stress energy tensor:

$G_{\nu\mu}= M^{-1}_{pl}.T^{eff}_{\nu\mu}$

The effective energy momentum tensor is a sum of the stress energy tensor of a matter confined on the brane, Tμv and correction terms that arise from a projection of the D-dimensional Einstein equation to the four-dimensional space-time. For some particular examples it is possible to show that the four-dimensional effective stress energy tensor violates the NEC meanwhile the total five-dimensional stress energy tensor does respect the NEC.

After discussing how wormholes are described in branworld sceneries the actual question of their formation is discussed. The approach followed mimetizes the approach followed for black holes. It is not very detailed and it is based in the following cross section:

$\sigma pp\rightarrow wh(s) \approx \sum_{i,j}\int_{\tau_m}^1 d\tau \int_{\tau}^1 dx/x fi(x)fj(\tau/x)\sigma ij\rightarrow wh(\tau s)$

Here √s is the center of mass energy, x and τ/x are the parton momentum fractions, and fi are the parton distribution functions. The parameter τm = M2min/s where Mmin corresponds to the minimum mass for a valid wormhole description.

σij→wh(s) is the geometrical cross section of the wormhole production and depends in a form factor F. The form factor F(√s/MD) incorporates the theoretical uncertainties in description of the process, such as the amount of the initial center mass energy that goes into the wormhole, the distribution of wormhole masses as function of energy. These corrections are similar to corrections in the formula for black hole production.

The second paper centers on the description of the observable traces of the existence of a wormhole. Much emphasizes is made in the possibility of the wormhole behaving as a time machine. For this it´s two motous must be shifting away at a considerable speed for some lapse of time. Anyway, the authors prefer to use MTM (minitime machine) instead of wormhole. Anyway the actual possibilities of detection discussed in the paper can be summarized as follows:

(i) change of the energy spectrum due to the frequency-filtration property of MTM,
(ii) possible production of anomalously energetic particles, accelerated by passing many times
through gravitational field inside the MTM,
(iii) acceleration of particle decays, since the proper time of a particle moving inside MTM can
strongly exceed the laboratory time,
(iv) CPT and naive unitarity violation (thermalization) due to effective non-local interactions
caused by MTM and to possible ambiguity in the population of closed world-lines inside MTM,
(v) collective effects due to conversion of a single particle into a bunch of its co-existing copies
within the MTM

## Sunday, May 18, 2008

### Black holes information distortion paradox

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:

"Although our
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:

$S(g, \Phi, f) =1/G\int d^2 V e^{-2\Phi}(R + 4g^{ab}$...

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.

## Tuesday, May 13, 2008

### The trouble with LQG

A través del excelente blog física en la ciencia ficción llegué a otro blog, la bella teoria. Supongo, no lo sé con certea, que eso de "la bella teoria" debería ir por la teoria de cuerdas, que en su momento alguna gente consideró matemáticamente bella y elegante. En todo caso en el blog ví que se trataban con cierta frecuencia temas sobre teoria de cuerdas (aunque no exclusivamente). También observé que algunas de esas entradas contenían algunos errores elementles. De hecho le señalé al autor uno en una de las entradas, a lo que me respondio dándome las gracias por el aviso. Posteriormente he visto algún que otro error, pero no me he molestado en írselos indicando uno a uno. Yo no me considero una autoridad en teoria de cuerdas ¿alguien aparte de Lubos Motl se atreve a asumir ese rol xD? y soy consiciente de que es probable que en este blog haya errores en algún que otro aspecto. Además el tono de ese blog es claramente divulgativo, para un público general y las entradas estan escritas de manera amena y cuidda (con fotos y cosas así). Dado que no hay en español muchos blogs (si es que hay algún otro) que cumpla similar función (yo, por ejemplo, oriento este blog a gente de un nivel de conocimientos bastante mas elevado) no tiene sentido ir señalando fallitos, que es algo que supongo podriá resultar irritante.

El caso es que el autor ahora ha ido a leer el polémico libro de Lee Smollin "the trouble with physics". Tras hacer una presentación del mismo en una entrada publico una segunda titulada Gravedad cuántica, continuando la revolución de Einstein Cómo quiera que es muy poco probable que la gente que lea su blog (y aparentemetne el mismo autor) este al tanto de los detalles de las "string wars" en los blogs Motl ,Distler, String Coffe y not even wrong, y de las críticas que los teoricos de cuerdas han elaborado sobre el estado actual de la LQG dejé una respuesta, que no ha recibido ulterior réplica dónde resumía algunas de ellas. Por su interés para los lectores de este blog dejo aquí esa respuesta:

"Salvador, lo que estas comentando es lo que se conoce cómo LQG. loop quantum gravity, o gravedad cuántica de lazos en español.

Dado que en tu anterior post hablabas del libro "the trouble with physics" asummo que has sacado de allí la información sobre este post. Aprovecho pués para comentarte ambos temas en esta respuesta.

Llevo siguiendo la LQG, a nivel técnico, no de divulgacion, desde el 2003, cuando se hizo populara en una hábil maniobra publicitria de algunos de su máximos represetantes. Fué un producto muy bien vendido, sobre todo mediante un paper de review de Robert Thieman. Te presentan la idea general, explicando cómo el programa de cuantización canónica lleva a que el operador área esta cuantizado. Luego hay argumentaciones de que, mediante algo conocido cómo "double special relativity", que extiende el formalismo de la relatividad especial al caso de una longitud privilegiada (la de Planck) se llega a que la velocidad de la luz en el vacio depende de la frecuencia, para luego señalar que los satelites GLAST podrian llegar a comprobar eso en un lapso de tiempo breve (su lanzamiento estaba previsto para el 2005).

De ahí pasan a argumentar que deducen la entropia de un agujero negro, reproduciendo la fórmula conocida mediante la aproximación semiclásica de que depende de una potencia del área. No entran en los detalles, que dependen de una construccion de relatividad general poco conocida llamada "isolated horizonts" (y también de el concepto relacionado de "dynamic horizonts". Cómo casi nadie esta familiarizado con eso conceptos consiguen que en una primera lectura uno no caiga en que en el cálculo se esta asumiendo, como punto de partida, que la entroia depende del área. Además la teoria de la LQG tiene un parámetro libre, concido cómo parámetro de inmirizzi. Ajustando ese valor se consigue que la fórmula obtenida se ajuste. Total, que el único punto medianamente serio del cálculo es que el área esta cuantizada qu ehay que dividir el área total entre la unidad mínima de área para encontrar el número posible de microestados.

Luego pasan a cosmologia. Anuncian qu econsiguen demostrar el "rebote", es decir que no puede haber un big crunch pués usando factores cuánticos se comprueba que el colapso se detiene en un radio mínimo y luego hay un nuevo big bang. Claaro, eso no se hace dentro de la teoria completa sino restringiéndose a "minisuperespacios", es decir, subgrupos de las métricas posibles. Vale, se admite que es una aproximación, el problema es que no dan ningún criterio que permita hacerse una idea de cuan buena o mala es esa aproximación.

Por cierto, la LQG canónica, basada directamente en la gravedad clásica de Einstein y luego cuantizada de un modo raro, presuntamente no perturbativo, es estática. Para tener un espaciotiempo dinámico tiene que irse a un formalismo lagrangiano (las spinfoams). El caso es que las spin-foams no parten de la relatividad de Einstein sino de unas teorias clásicas que con ciertas restricciones, son más o menos clasicamente equivalentes a la relatividad de Einstein. Además hay varias de ess teorias clásicas y cada una lleva a una teoría cuántica esencialmente diferente.

Y bueo esas dos son las líneas fundamentales, pero aparte hay otras que asumen de partida que el espaciotiempo es discreto, lo cuál es mucho suponer. Y no quda muy claro la relación entre ellas.

Mas importante es que esas teorias cuánticas deberían tener un limite clásico que reprodujera la gravedad clásica de Einstein. Pué sbien, no han conseguido eso de una manera medianamente clara (lo mejor que tiene es obtener, mediante una serie de aproximaciones de dudosa justificación) reproducir, en el marco de algunas spinfoams algo que debería ser similar al potencial de Newton.

Vamos, que no digo yo que la LQG sea un sinsentido, pero desde luego tiene muchos problemas bastante serios.

Respecto a su mejor punto, la posibilidad de confirmación de la dispersión de la luz en el vacio, al final los satélites GLAST han tardado muchísimo en lanzarse, (deben estar a punto de salir ahí fuera por estas fechas). Un experimento en tierra hace unos meses dió un resultado preliminar en esa línea, pero no es conluyente (y hay ciertas teorias de cuerdas, bastante raras todo sea dicho, las cuerdas de liouville, que predicen algo similaar. De hehco fué un fisico de cuerdas quien hizo populñaar ese experimento).

Y, por si no esta claro, la teoria de cuerdas también es una gravedad cuántica, así que no se puede presentar esto cómo si fuera le más de lo más en gravedad cuántica y dejar de lado la teoría de cuerdas.

En fín, no me parece mal que comentes sobre la LQG, pero cuidado, que no es oro todo lo que reluce con es gente."

Bien, tras esa entrada Salva ha publicado otra . Más allá de los agujeros negros. No he leido "the trouble with hysics, sólo los comentarios, unos favorables (en la comunidad LQG) otros adversos, así que no tengo la certeza, pero si la firme sospecha, de que los datos de esa entrada salen de ese libro. En cualquier caso lo que si conozco es el tema específico tratado (agujeros negros en LQG) pués lei en su momento unos cuantos artículos originales sobre el particular. La entrada en sí no contiene ningún error, pero creo que es interesante que complete la respuesta que reproduje antes para explicar aalgo respecto a la singularidad de los agujeros negros en LQG.