I was reading the brief wikipedia entry on string and there it says that strings are one-dimensional "unlike an elementary particle which is zero-dimensional, or point-like. Quarks and electrons are thought to be made of strings." The part about zero-dimensional entities being made of one-dimensional ones is not easy to understand for me, could someone clarify this?
They are two contrasting concepts, not complementary ones. Wiki is using careless language here. Within the context of quantum field theory, elementary particles are considered to be zero-dimensional points. Within the context of string theory, elementary particles are considered to be 1-dimensional strings.
Thanks, bapowell, that makes more sense. I was almost sure that paragraph was badly expressed if not wrong. Another question, also from that page, a string in motion sweeps a surface called worldsheet. Analogous to the worldlines of classical field theory. Is the high number of dimensions in string theory related to the fact that it deals with worldsheets instead of worldlines?
Yes. It is more directly a result of the fact that string theory is essentially a 2-dimensional conformal field theory defined on the string worldsheet, where the spacetime dimensions are internal degrees of freedom (the fields defined on the worldsheet carry indices that range over the spacetime dimensions.) In order for this field theory to be consistent (e.g. possess Lorentz symmetry, etc), only certain dimensionalities are allowed.
I'm trying to get a very basic understanding of string theory, and have some more questions. Please excuse my ignorance Apparently in some string theories like M-theory something called M-branes ¿replace?/¿complement? strings as the structure of elementary particles. So for instance we have 2-branes, 3-branes etc depending on their dimensionality, and I guess analogously to strings and 2D world sheets, 2-branes in motion generate 3D world volumes. And so on, so that the maximum M-brane has M=D-1 with D referring to the dimensionality of the string theory space. To bring it closer to a more comfortable knowledge zone for me, I would think of a world tube from relativity as a 3-brane in 4-spacetime, would this be right? Also what is the difference between the diffferent types of branes, like p-branes, D-branes, M-branes etc?
As Powell mentions, the spacetime dimensions provide degrees of freedom that are required to give strings the characteristics we observe in particles. Numbers and shapes of dimensions determine the vibrational modes. I think it was Ed Witten who realized that string theory, via his "M theory" includes ingredients besides one dimensional strings. Somebody coined 'p- branes' to describe multidimensional strings with 'p' a whole number from 0 to 10...p-branes turn out to be heavier than strings. In the Steinhardt-Turok cyclic universe, it is the collision of branes that causes 'bangs'....they propose that branes are not smooth multidimensional objects but rather that they ripple..so collisions occur at different points and different times giving rise to quantum irregularities that are believed to precipitate particles. A graviton, for example, is among the lowest energy string vibrations and it's strength is proportional to the length of the string. The Braneworld scenario is one where our untire universe lies within a three brane. p-branes are 'sticky' and the ends of most strings stay attached; we say such strings are open and their freedom is restricted. Gravitons are un attached loops and may drift off into higher dimensions...hence gravity is very weak. Last night on Science Channel I see Lisa Randall has a theory that gravitons actually leak from the multiverse into our universe. apparently this solves a number of interesting issues. Anybody know?? Check out Wikipedia for more on BRANES or membranes. There are some distinctions between Polchinski's p-branes and Dirichelt [D] branes.....I've forgotten... edit: Brian Greene's FABRIC OF THE COSMOS has chapter upon chapter about strings and branes...a used copy is cheap...no math....
Yes, these are the Randall-Sundrum (RS) models, of which there are two types. RS1 attempts to resolve the hierarchy problem by postulating the existence of two branes bounding a 5th compact dimension: one brane has Planck-scale gravity. The gravity of this brane leaks across the 5th dimension which is highly warped due to the presence of the Planck brane. This warping attenuates the strength (hence, scale) of the gravitational interaction across the 5th dimension so that on the 2nd brane gravity is perceived to be weak. The problem with this model is that the 2nd brane must have a negative cosmological constant. The RS2 model deals with only a single brane situated transverse to an infinite 5th dimension. The significance of this model was to illustrate that GR can be recovered from a theory with extra dimensions even when the extra dimension is infinite. The key again is a strong warping of the extra dimension to that gravity remains more or less localized on the Planck brane: any leakage is exponentially suppressed by the warping.
Thanks for the info, Naty1. Trying to keep it one thing at a time at the moment. About the braneworld, how can it model our universe as a 3-brane, is it also a string theory? I thought all string theories had at least 10 dimensions. EDIT:Ok, After reading the article in wikipedia I think I got this one, according to this brane cosmology, our entire universe can be a brane but there are more branes(kind of parallel universes?) and therefore more dimensions,right? Also can anyone confirm my analogy above about the world tube as a 3-brane evolving in time?
exactly. That's not a good analogy if I understood your wording..///.consider a point particle in SPACE.... if you trace out it's worldline in SPACETIME it is still a zero dimensional entity in Space. A THREE BRANE is a three dimensional entity in SPACE.
Sure, a world-tube is 4-dimensional, its spacelike section are 3 dimensional hypersurfaces, that is like 3-branes in SPACE, isn't it?
Regarding elementary particles, the search for the origin of matter means the understanding of elementary particles. And with the advent of holism, the understanding of elementary particles requires an understanding of not only their characteristics, but how they interact and relate to other particles and forces of Nature, the field of physics called particle physics.
Let us find an application: 1) Is any electron a 2-dimensional charged and closed surface (in extenso a small ball) orbiting around, example given, a proton at some quantized distance? or 2) Is the electron a 2-dimensional surface in a sort of equilibrium with different forms (depending on the available quantized energy) centered on the proton with total charge e and mass at rest m_{e}? For any of these two proposed alternatives, where does a model involving a string come into the play, thus justifying the discussion here: "strings and elementary particles"?
OK, electrons, quarks etc.. in string theory. I'll start off by stating that nobody really knows how an electron manifests itself in string theory, unless they know and haven't told anyone ;) Lets first think about a weak-coupling scenario (where strings don't like to interact strongly, so that we can still talk about what individual strings actually do..) and then we'll move on to a strong-coupling scenario (where strings like to interact so strongly that their stringy nature becomes less and less clear..). One idea that I like is that an electron corresponds to an open string (in its lowest energy level) that is stretched between two stacks of intersecting D-branes. The number of D-branes in each stack is important. Each endpoint of the open string can attach to any of the branes in a given stack. Furthermore, there is a rotational symmetry, or U(1) symmetry, associated to every brane. If one of the two stacks has 2 branes, then the symmetry becomes U(2), 3 branes lead to U(3), etc. Therefore, if we have two stacks of branes, the first stack having 1 brane and the second having 2 branes, the resulting symmetry is U(1)xU(2), which is almost U(1)xSU(2), the symmetry group (one could say one of the key defining properties) of electrons. How to get SU(2) from U(2) is tricky, and one usually ends up with extra U(1)'s. How to get the right masses is even trickier ... Nevertheless, continuing along these lines, the Standard Model spectrum has symmetry group U(1)xSU(2)xSU(3), so you can imagine having 3 stacks of intersecting D-branes, each stack having respectively 1, 2 and 3 branes. (Here you're suppose to imagine a triangle, each side of which corresponds to one of the three stacks.) Then, all the ways you can imagine open string attached to these three stacks of branes correspond to all the particles of the standard models, and more ... One common example is that these D-branes are in fact D6-branes, so that there are 4 large dimensions (corresponding to the observed world), and 6 extra dimensions associated to these stacks of D6-branes, which have open string attached to them. The total dimensionality is 10, as required by anomaly cancellation conditions. OK, that's a weak coupling manifestation of the standard model. However, there are indications that in fact our world lives in the strong-coupling limit of string theory ... (and that is unfortunate for the poor people like myself who like to be able to compute things!) In the strong coupling limit an extra dimension becomes visible, large, and the total dimensionality is now 11: this is the realm of M-theory. In fact, one can go quite far along these lines ... Acharya, Kane and Kumar have been voicing for years that M-theory (on a G2 manifold, don't ask what this is .. ) gives rise to the standard model spectrum with a Higgs of mass 125 Gev (!), long before the LHC result was out (see http://arXiv.org/pdf/1204.2795.pdf and references therein), claiming in fact that this is a GENERIC PREDICTION! Hope that helps! Wakabaloola