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:
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.
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