Why strings, some answers.

It has been a few weeks that i dónt publish anything. I have been learning a few buch of things while.

I had posted in these blog some doubts about the foundations of string theory. I also posted some of them in physics forums. If you don´t want to push the link I´ll give you some of the answers I got:

Dmystifier:

here is no such thing as constituent points. A string can decay or snap only into other strings, and the lowest energy configuration is going to be stable. See some other recent thread here on a similar issue.
..............

R.X.

there are simply no constituent "points" on a string. Namely how could one possibly ever measure or see those? One would need to do a scattering experiment and bounce something off that string. But all what one can do is to take another string and use it "as a probe", ie, scatter it against the given string; what would come out from this experiment would be just other strings, because the only interaction that exists is splitting and joining of strings. This is related, as you say, to the notion of a minimal length scale beyond which one just cannot see. Thus, "points" on a string are not observable and thus, by the rules of quantum mechanics, are meaningless quantities.

One should not literally think about strings as little filaments made of "something else" - they are quantum mechanical oscillators and in order to understand them, one should not use too a naive classical intuition.


When he says that I mention it he refers that I had talked about T-duality . What is T-duality? Or better, what are dualities at all?

Well, dualities are symmetries betwen strings theories in diferents backgrounds or in betwen diferent string theories (or even betwen string theories and other theories)

The most widelly stuided, and may be the most important for the actual development of string theory, is T-duality. If you compactify some of the extra dimensions of a closed string theory in a circle of radious R you have in adition to the usual discretization of moment, propious of point particle physics a purely string efffect. It consist in that the closed string can wind around the circle a certain number of times usually denoted as w.

Well, the key point is that the observables of the theory (mass, scaterging amplitudes, etc) are invariante under the combined exchange:





There exist also T-duality for open strings. That duality is one of the ways D-branes make their aparition in string theory. And once you have the D-branes you can make some kind of T-duality among D-Branes (branes also can twist around compactified dimensions xD), but I will not extend myself in that questions. Only to mention that the entry (of today) of wikipedia in these topic mention that T-duality relates type II-A and type II-B superstring theories and that mixes betwen them the two heterotic strings. Right, but it is easier to study T-duality for the bosonic string to begin with the topic ;-).

Afther explainingg the T-duality to explian how it relates to the problem we have now. Well, the important part is the . these means that you can´t distinguish distances smaller that the radious of compactification because if you try to go there it is as if you would go to a greater radious.

These is the compactification radious, presumibly of the order of the planck size for usual scenaries of compactification, and not any characteristic legth of the string. So my claim in that post in physic forums was a bit diferent to the R.X. answer who addres the imposibility of seeing points to string themselves and not to the compactification.


Afther having discused these and considering self-explanatories the answers of demistifyer and R.X., what is my viewpoint about the dispersion of strings under evolution? The reader can judge himself. Myself I find the allegations, specially the last one of R.X. interesting and I´ll think about it. Anyway if the natural interpretation of the math is naive i guess it could be interesting to make a somewhat different formalism in wich that interpretation couldn´t appear. Maybe something as talking a bout a rule for an equivalence kind of points and the reasons why you that equivalence. Afther that you could explain that a very natural realzation of that equivalence class can be viewed as a mathemathical string. Of course these is just a very personal viewpoint, and one wich needs a further development.


To end these entry I reproduce here a diferent question about string theorie which I explain in that thread:


Investigating about a (very) older theory about extended objects, the knot theory of tompshon, tein, Maxwell (partially) and others inthe XIX century I discovered they had a very reasonable argument (withing the context of their knowledge of physics) for considering them. It came for a theorem in fluids mechanics with stated that once formed a vortex in a perfect fluid It would remain stable forever. In their times it was assumed that there was an universal prfect fluid, the ehter. But, of course, once the ehter theory was discarded the theory loosed any support (and Q.M appeared as a much better theory for the microscopial physic). Of course people who belive even nowadays in some kind of ether could claim for an string theory as vortex of that ether (well, maybe), but certainly mainstream string theory physicist hate ether (with good reasons, IMHO).

Maybe if there would be a way to see an string as a solitonic state of somtehing else I could see areason for an (at least partial) stability for them

By the way, in that times the tried to explain spectroscopic results as knotting of two or more vortex. That raised me a new question about string theory. Why strings can´t not knott around themselves?

I mean, if you would accept (as everybody does) that strings are (clasically) stable beeing quantum objects ther would be the possiblity of a closed string could be created in a knotted configuration with another closed string.

And a last question. These is about the polyakov integral and the admited interaction vertex (not confuse with vertex operators). It is allways showed that you can see an split of an string in another two, but, whay about a vertex in wich an string splits in thre, four, or in general N strings? What forbides the existance of that vertex?. I admit that perturbative theory with, vertex operators, dhem twists,moduly and teichmuller spaces is something wich I have readed a few times but I still don´t fullly understand. But towards my understanding works I don´t see a good reason for multisplitng vertex (or "knotting" vertex if we accept going from Rieman surfaces fto more general complex, algebraic curves with some singular points).

B.T.W. I mentioned in a past entry that LQG, had scenaries in which from "only gravity" the made to appear point particles (and may be even strings). Well, althoughtnot in deep but I readed some of the papers and I have a general vision of their arguments.

On one hand there is the Smollin-Markopoullous-Billson Thmpson paper. It is formulated in the framework of canonical (or hamiltonian) quantum gravity and it is based on preoon models. Beeing based on canonical L.Q.G it has no dynamics (because the hamiltoninan of LQG is a constraint, that is null, so it can´t give any evolutions, at leas in a conventinal way. That also true for the, easier, ADM hamiltonian of gravity).

On the other hand is the Baratin-Freidel model. It is based on spin-foams version of LQG (you can so it as the "lagrangian" version) has dynamics. They argue that from an scenary of pure gravity they can reproduce the Feyman diagram of any point particle (or even maybe of an string). They did it first for 2+1 gravity and recentlly for 3+1 gravity. That´s their claim. But as far as i have seen they introduce by hand the feyman diagram, rewrited in the spin-foam technologie so it doesnt appear in a dynamic scenary form pure gravity. Anyway I need to read it in more detaill so don´t trust these preliminary drawback as definitive.

And for now that´s all folks.


P.S. I hate these stupid scripts who try to correct the html synthax. They don´t like pure html and they try to convert it into XHTML. In the proccess they try to correct things as spaces or non asccii elements in the source etiquete of an image tag. But if that img tag is LaTeX code for a public LaTeX server that can corrupt the code and the images are not seen. But it is even worst. It try to obligate you to use XHTML but the page itself is not XTHML, and you have not access to the head etiquetes (or at least not in any reasonably easy way) so you cant make a doctype declaration wich would allow you to use MathML, wich would be an alternative to Latex. I´ll try to correctlly publish the latex images if there is sme way to prevent the self correction of html, but i am not sure if it will be possible today. If so it could be you don´t see the images (formulaes) correctly

Why strings II

Well, apart of these ontological questions we always could listen to Feyman and go with the "don´t think, calculate" premise. But, can we?

The fundamental calculational tool in string theory is the polyakov path integral. If you read the correponding chpaters in the string books they aregue that one virtue of string theory if that you don´t need so many feyman diagrams and taht you basically need one kind of vertex, the one in wich an incoming string separates in two outgoing ones. By a lorentz transformation that vertex is shown to be equivalente to ones in wich you have two incoming strings who join in a single one.

In QFT (sdecond quantized theory) you get a prescritpion on how the Vertex are form teh form of the lagrangian. In perturbative string theory they are put "by hand".

My question, of course is, why no other diagrams?. For example you could have a diagram with tow incoming and two outgoing strings, or an string breaking in more than two pieces. In fact you could, as far as i see, have an string breaking itself in an arbitray n of strings, and i don´t see that you could reduce these case to the simple one.

But i recognice that these could easily be a missunderstanding on the polyakov integral, may be someone could explain me if it is so.

Why strings?

There are considerable amounts of blogs which attack string theory.

Some of the argued reasons against it are things like: "they require additional non-observed dimensions", "they don’t make predictions and so they are not refutable", et, etc, you can see the "not even wrong" blog to find many of them.

I particularly have a problem with string theory far before all these questions even appear in the theoretical development. For me the problems begin at the very idea of an string as a basic object.

I mean, in the macroscopic world you can have an string. We know that we can describe it in terms of component (atoms) which keep joined themselves by means of their electronic interactions.

But, what about "fundamental" strings? What keeps them joined? I mean, we can think that we have some one-dimensional region of space witch shares some common features which differ from the ones of their environment and that is what we can call an string. The question is , why does it remains joined under time evolution?

I find that it would be natural to expect that their component point evolve in a manner that makes them to separate and we end up without an string any more.

Of course you can simply postulate that the string keeps joined. But for me it is an unsatisfactory situation. How could we circumvent it?

Well, let’s look at what we know. Where else do we have strings?

Well, there are another kind of strings apart from the one made of atoms. The cosmic strings. They appear as topological defects when a phase transition occurred. Similar topological defects happen in condensed matter physic. Could we think of a preliminary sate of the universe which went under some phase transition leaving as a result topological defects such as strings and branes?

Recently loop quantum gravity physic has presented some ideas which I thought could hold some light in these directions. I am referring to a paper by Friendklin (i will edit these later to put the arxiv) in which they claim that beginning from an spin foam model of pure gravity they obtain one-dimensional topological defects which behaves as particles. At least that is the promise. Until now it is a 2+1 spin foam model. And it is well known that gravity in that dimension is a pure topological theory (that is, not local degrees of freedom, only global ones). It is expected soon a new paper where the result is extended to 3+1 dimensions.

My problem with that article is that in some point it is introduced some hint that seems a lagrangian of a point particle which status is greatly an-explained and wich is the basic of the rest of the article. I am waiting for the next 3+1 article before doing a harder effort to understand these theory.

Anyway, is there another reason why string could keep joined under evolution? Maybe, the key word here is "evolution". I´ll do a separate post about these possibilities sometime later.

But of course you always can accept that strings (or branes) keep joined as a postulate, as seemingly everybody does without even worrying about how bizarre these notion could be and keep doing formalism. If you adopt these viewpoint the goodness of string theory relays in their good mathematical properties and ultimately in experimental confirmation.

P.S. Latex: