The most relevant new of this month was, probably, the announcement of the MAGIC discovery of indications of the possibility that light speed could depend on its frequency. The relevant paper is this.

it has been discussed in some blogs (Lubos, Peter Woit, Sabine) and some forums (for example physics forums or, in Spanish, migui´s forum. See the links of these blog to search them if you are interested). I will not add too much about it, at least not still. Just to state that, if truth, it would, probably, be a signature of a quantum gravity effect, and that would be the first quantum gravity effect ever observed, which is, of course, a very, very important thing.

The reason why these could be a sign of quantum gravity is also an interesting thing. LQG people reach to that conclusion from two sides. The best known one comes from the side of canonical LQG. There they state that the area operator has a discrete spectrum on the kinematical Hilbert space and that is an strong suggestion (but not necessarily a definitive one) that there is a minimum length. They have tried to probe the same result directly for the length operator but until now they have obtained only preliminary results because of redundancies on the quantization procedure (or something like that). Also it has been criticised that in the full, dynamical, Hilbert space the discreteness of the area operator could fail. Of course Lubos Motl and the stringy community knew that these result of discreteness made no sense long time ago. Pity that I have not seen a careful mathematical proof of their wordy arguments. Well, anyway, once you have a minimal length you can make a DSR (double special relativity) theory and get modified dispersion relations for the propagation of particles and you get the desired result presumably observed. DSR theories have many problems and nowadays seem to have derived into something named ESR (extended special relativities) which in some way results into some kind of nonconmutative geometry.

Other way, worst known, in which LQG people arrive to this kind of results is from a certain limit of spin foams which results, agian, into an NCG, see for example these paper for the details.

It is interesting to note that in fact any generic NCG (non conmutative geometry)could, potentially, give rise to a breaking of Lorentz symmetry and, hence, to a frequency dependent speed of light. Critical string theory could result, through a non zero vev (vacuum expected value) of the NS-NS antisymmetric tensor give rise to an effective theory describable by an NCG. Seemingly these would mean that critical string theory could explain these result, but in view that Lubos Motl doesn’t point in these direction maybe I am missing something. Also it is courius to note that critical (super)string theory is formulated in ten dimensions to avoid both, the conformal anomaly and, related to it, the Lorentz invariance. Even thought a solution of it, the NCG limit, violates Lorentz symmetry. Theses is not new, the solutions of a theory need not to respect the symmetries of the lagrangian.

Well, these are ways in which some could achieve the MAGIC ideal result (if the alternative explanations with no new physics could be discarded). But the paper doesn’t rely on any of these. It is related to a very special kind of strings, the Liouville strings. I had a previous knowledge of theses, and also of the fact that the mainstream string community had not in good estimate the works of their mayor proponents, Nanopoulos, Mavramatos, and all. I had inquired some people of the string community about these Liouville strings when it was announced in the CERN courier that they predicted the vacuum frequency dispersion of speed treated in these post (B.T.W. it is important to note that at least in the CERN courier paper the clearly stated that LQG perditions and Liouville string predictions were in the opposite direction, I have not seen people being to precise about these concern now).

At that time, 2003. I preferred to study LQG, which looked very promising at that time, and I didn’t pay mayor attention to Liouvile strings, the treatment of then in the Hatfield book "quantum field theory of point particles and strings" was dissuasory enough. For someone who doesn’t know anything about Liouville strings a quick comment. You treat the conformal factor of the world-sheet metric as an independent field. In the end it results into a Lagrangian for it which resembles something related to something previously known as Liouville field (I don’t know the exact reason). The problem is that the lagrangian contains an exponential of the field so it is very hard to work with it. In the Hatfield book it is shown that these problem is related to the fact that the 2d bosonic fields of the world-sheet don’t decouple from the 2d gravity and that means that you are doing 2D gravity. It was studied through matrix models (not the same matrix models related to M theory) and at least in the epoch of the Hatfield book they didn’t allow a reasonable formulations in D<25, that is, they didn’t allow a formulation of string theory in four dimensions which was the main goal of that theories. Probably later the have had some improvements, still i am not too sure.

My idea, when I first tried to think how Liouville strings could result into the MAGIC effect was very obvious; they brooked Lorentz invariance, which was enough. But I begun to read the papers linked in the announcement article and I got shocked. They talked about decoherence, hawking radiation, the role of the Liouville field as an emergent time and the role of spacetime foam as the source of the effect. Separately any of these statements seem bizarre, but together, well, at last I understood why Lubos didn’t even mention "liouville strings" in his entries about these announcement ;-).

I didn´t read in deep any of the papers of nanopoulos and all, but I have made some partial readings related to some of the aspects. I’ll speak a bit about the spacetime foam (not to confuse with the LQG community spin foams). The idea of spacetime foams dates back to wheeler. The idea is that at small scale the quantum fluctuations of the metric become very important and the plane spacetime disappears. In that "foam" could, at least it is cited so in the usual divulgation, happen unusual things, such as topological changes of spacetime. These could result in the virtual formation, and annihilation, of things such as black holes, and also, wormholes (a bit more on these later).

This is the naive view. Stringy theorists claim that S-duality changes drastically this scenario. The reason is as follows, when you get some string theory in weak coupling you can prove that it´s correspondent in strong coupling is another string theory (or maybe M-theory or F-theory in certain circumstances). For example, the dual object of a fundamental string is a D1-brane. Also there is duality between different branes (including duality between D-branes and NS5 branes). How this duality prevent the spacetime foam? It is somewhat obvious once one thinks about it. The strong coupling theory corresponds to the limit where the spacetime foam would appear and instead of it one gets another string theory. I have not had time to think to much about these, but I see some possible subtleties. The first one is that the S-duality is obtained by some heuristic arguments in perturbative theory which can be extended to non perturbative one with the help of supersymmetry. That raises the question of how much these dualities are related to supersymmetry or to D-branes. These could seem irrelevant, but not necessarily. In open string theories (for example, the bosonic one) D-branes appear as diritlech conditions for the extrems of the open strings. You don´t need supersymmetry and RR charges and all that for the existences of that D-branes. I have no notice of the search of string dualities for the bosonic string, but naively one would spect that still the S-dual of an fundamental bosonic string would, again, be an D-1 brane, but I can´t say for sure.

In fact all these could seem totally uninteresting to someone. I still think that to clarify the exact role of supersymmetry in the dualities is basic, after all pure (non stringy) supersymmetric theories also have branes and maybe there is some kind of S-duality betwen point particles and 0-branes and these would mean that supergravities also forbid the spacetime foam. But by now my concern about spacetime foam will go into anther direction, the (noncritical) Liouville strings.

If the reader makes a google search (s)he will find that in closed string theory there are also D-Branes, introduced as boundary states in the conformal theory (see, for example, my previous post about these theme). The interesting, for this post, fact is that also noncritical (closed bosonic) strings can be shown to have D-branes. If the S-duality depends exclusively in the existence of D-branes that would mean that there is no reason for the existence of spacetime foam in Liouville strings, contrary to the claims of Nanopuollos at all. On the other side if the S-Duality depends on supersymmetry it is expected that (super)Liouville strings (the relevant ones if the theory must reflects the reality which has fermions) would also have S-duality and so no spacetime foam. The obstacle for these would be the existence of D-branes, but as far as I see the Liouvile strings would have the same R-R sector, and charges, and so some kind of D-branes, in the appropriate dimensions, so one would expect definitively no spacetime foam. Well, that is what I expect previous to a careful reading of that papers, why didn´t i did it?

Well, that leads me to the last topic of the post, the wormholes. I assume by now that all my readers have the intuitive idea of what a wormhole is. I´ll make a separate post in this topic anyway. This time I´ll just say a few things. On one side one of the ideas of Wheeler is that they could be formed in the space time foam. After all the continuous evolution of a metric can, in general, drive one for spaces with a certain topology to others with a different one.

But if one studies carefully general relativity one learns that there are some theorems stating that if causality must be respected everywhere there cannot be such transitions in topology. Also quantum tunnelling between different topologies could be ruled out under certain reasonable assumptions. Wheeler seemingly ended by trying to achieve something different. Instead of absolute changes in topology you could search for effective changes, i.e. that the transition point between topologies would be of subplanckian size, but not a point. Anyway, I know that string theory claims that it allows topology changes in space time. And also it describes wormholes. In fact (transversable) wormholes relies for it’s stability in some special matter, or, in the presence of a positive cosmological constant. The discovering of these constant in the actual universe has launched an interest in wormholes in the string community, specially in the Randall-sundrum sceneries. I begun to study some papers, but I got somewhat lost and searched for some guidance. I have found very interesting, and very useful, the book by M. Vissier: "lorentzian wormholes" (1996, springer verlag). It is focused in "relativistics" viewpoint on white holes and I am not sure if he says anything about string theory. Also it is previous (I gues) to the discovery of the accelerating universe. And it is somewhat old. But still so it is being one of the most interesting books I have readed for a time, it is very well writing and results easy to understand, at least if you have a good basic in GR. When I would have readed this book (or a relevant part of it) I will try to read the papers of nanopoulous and comment on them. Oh, yeah, I am also reading occasionally a classical (1993) paper in closed string field theory inthe BV antifield formalism. I have confident knowledge that it is, even today, a relevant paper and that you need to read it if you are interested instring field theory. But compared to the Witten open string field theory, and it´s results about tachyon condensation I find these paper terribly boring, yeah, I know that is of topic to these post but...I needed to say it!!! ;-)

## Friday, August 31, 2007

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