nuro said:
When someone puts theory in quotations, puts stress on the word or end the sentence with the word and an upward inflection at the end I just want to pull out my golf club. =P
"I'm Ron
Burgundy?"
qwe said:
it seems to me that it would be a lattice, of n dimensions, with at least one dimension which is different from all the others (the time dimension) and perhaps other different types of dimensions (the folded, perhaps calubai-yubai (sp) dimensions) and three normal dimensions that macroscopic objects can travel through, and some 'background' (inter-brane) dimensions which gravity reaches through
thats four different types of directions to travel in!
1. normal (macroscopic) 3d connections between lattice points
2. time connections between lattice points
3. connections between lattice points along dimensions which are folded (small)
4. connections between lattice points linking brane to non-brane lattice points, allowing gravity and maybe other subatomic particles to escape our brane
Not quite.
There's time, 3 large spacial dimensions and 6 (or 7, if you're working in M theory) spacial dimensions which are curled up. A lattice implies there's a non-zero spacing between these folded up dimensions, there isn't. Pictures you see of the compact dimensions in things like The Elegant Universe are not literally true because it's hard to show a continuum of multidimensional objects on a TV screen.
The simplest (and pretty much only) example of a continuum of compact spaces would be a cylinder. You have an open dimension, which is the line which makes up the length of the cylinder. At each point along the line you have a circle. There's no gap between the circles, it's a smooth system. As Green described in TEU, if you view a cylinder from far enough away it looks like a line, so you can see how the compact dimension, ie the circle, works.
The branes are not seperated by different kinds of dimensions either. They are at different points in the compact space. To use the same cylinder example (but it's not visualisable in the same way), suppose you have a circle and at opposite sides of it you have a 3d 'sheet' (or volume or whatever geometry noun you feel comfortable with). One of the sheets (or 3-brane) will be our 'universe', where all the particles we see, including the particles which carry the electromagnetic, weak and strong forces, are stuck to. The other sheet will be a similar setup with similar matter. But matter from one brane cannot leave another, unless the branes collide. This is because all matter and forces, other than gravity, are formed by open strings and they must have their ends stuck to a brane. Gravity, however, is the result of graviton exchange and gravitons are closed strings and they can leave a brane, travel through the circular dimension and reach the other brane.
I've used a circular compact dimension as an example but you can construct models with as many branes as you like in the 6 or 7 dimensional compact spaces. The number of branes can have an effect on the properties of matter for reasons I can go into.
Oh and it's 'Calabi Yau'. And
technically (and this is something I actually corrected Wiki's string theory page on), Calabi Yaus are
approximations to the real string theory compact dimensions, because CYs have very symmetric properties and lack particular kinds of fields. Current development is to work out what happens when we no longer assume those kinds of fields are 'off' and unfortunately the mathematics we have is nowhere near as powerful as we need it to be. It's something I plan on getting into this year.
I can provide links to specific relevant papers if needs be.