I have been reading about superstring theory for a while, and it predicts 10-dimensional hyperspace. Apparently, in superstring theory the equations require the existence of these dimensions in order for there to be a certain symmetry, elegance, and rational beauty about the mathematical formulation of the theory. I was wondering if anyone could explain the equations predicting the dimensions, variable by variable, and why they predict these other dimensions, hidden from us by their paucity of magnitude.
That’s quite a request…
try GateControlTheory, Future Man, Ed3… I forget the other resident math wiz’s.
I really wish Alien Corpsicle Bath was still around… I always found him to be good at explaining physics.
String theorists are so immersed in the math that they don’t have time to keep up on the relevant physics in their own field. I strongly doubt that you would find anyone here who would have more then a ephemeral knowledge of it. You might want to start out with understanding the mathematics of general relativity because string theory is a highly geometrical framework. Its general relativity with Riemanns tensor equation taken to 11 dimensions. Remember elegant doesn’t mean simple. Try getting into vector calculus… for quantum mechanics, you can get Feynmann’s lectures off of the main torrent networks. http://www.mininova.org
ohh and I recommend “The Road to Reality : A Complete Guide to the Laws of the Universe”
the only piece of math i can remember reading has to do with tiny dimensions hidden inside the planck length. it doesnt really shed light on why there are extra dimensions, just makes it look cool.
so there are ‘wound’ strings which are little tiny circles that make protons, photons etc. and there are also ‘unwound’ strings which arent little loops but wrap around the entire universe, which curves around itself so the unwound strings are actually wound, they are just gigantic. like the 2d surface of a 3d sphere, the universe is the 3d surface of a 4d sphere, and the ‘unwound’ strings wrap all the way around the outside, as opposed to being little circles that float on top. once captain picard and friends ran into one of these, its just a gigantically massive, black-hole-density string stretching infinitely across the universe. i might be getting them mixed up, the wound might actually be the unwound. whatever.
so anyway, the properties of the particle that a string makes are determined in part by the radius of the string, in some complex way. this relationship between radius and properties (i think energy is the property directly related to it) relies on the planck length, a constant derived from something. (i think if a proton was the size of the solar system, the planck length would be a tree on earth. but it might be if the proton is the size of the galaxy or universe, i forget)
the interesting part is this: the properties created by a wound string (the one that makes particles) with a radius of ten times the planck length are exactly the same as an unwound string with 1/10th the planck length. (er uh, it might actually be that the wound string with 10 times the PL is the same as a wound string with 1/10th, and not an unwound one, i forget). it basically just means that there can be a miniature replicate version of the things we see if it gets small enough for some reason that we cant yet explain.
so its like if you smash particles into a tiny ball, they will pass a threshold into tiny land where they will have the exact same properties. they will be moving around in a “tiny” space way the hell smaller than a quark, and yet they will have the same properties. so it seems neccesary that its actually not a “tiny” space in all of the dimensions, and if they get in there, they must be freely moving around in those other, smaller dimensions that we on earth refer to as “tiny” because they just so happen to be “wrapped up” inside all strings.
i read about this in the Elegant Universe by michael greene, but he didnt say any of that stuff. he just said that there is a close relationship between strings that have an inverse relationship with the planck length (10 times it is equal in some way to 1/10th of it). i have wildly speculated that this clears up the enigma surrounding black holes (the enigma that was not solved by hawkings crappy radiation) and the big bang. when stuff falls into black holes, it gets real tiny in our universe, but actually spews outward into another dimension, while retaining all of the properties it originally had (which may be destroyed and redistributed in the form of pure energy and not atomic nuclei). not only does the original transfer into the black hole at the time of the supernova cause a single large intial explosion, but the semi-constant bombardment of that black hole with new matter that is floating nearby could inject our own universe with energy somewhere quiet out in the middle of the huge spaces that fill our universe. this could explain the mysterious dark energy that fuels the outward expansion of the universe.
its just crazy speculation, like all of string theory. less math backing up my speculation though. i like it better that way, because who the hell cares if im right, what difference does it make? just believe it!
I have found that string theory takes the Newton approach on math; if it doesn’t exist, make it up. It is our job to fill in the rest, and then debate over our different solutions
More like the Einstien approach. In adding extra dimensions we find the math becomes beautiful or “elegant”, and rather persausive. If you have a theory where equations such as Maxwells just magically “pop out of it”, well by glum I think you’ve got something, as does the majority of the sceintific community.
who came first The Newton or The Einstien. I pull facts out of the air that way I know there true…(no not really)