What Do Dimensions 5-14 in String Theory Really Mean?

[Gear300]

There is also a proof for 26 dimensions...its somewhat arbitrary. Understanding the right amount seems to be the troublesome part.

 

[humanino]

There is also a proof for 26 dimensions...its somewhat arbitrary. Understanding the right amount seems to be the troublesome part.

26 dimensions applies to the bosonic string theory. If you want to include matter (supersymmetry on the worlsheet) you need fermionic degrees of freedom. This in turn requires 10 dimensions. Exactly, no freedom, the calculation is somewhat elementary (compared to the rest in this field).

Now there are additional developpements starting from those elementary, old, well known considerations. Add one dimension, that gets you to eleven, where an hypothetic M-theory lives, inspired from a unique supergravity theory in 11 dimensions. The 5 popular instances of superstring theory in 10 dimensions would be several limiting case of M-theory, explaining the web of dualities between them.

Even further, you can get more possibilities, but it gets more involved and less developped. Non-commutative geometry allows for several other dimensionalities, based on quaternions and octonions (I am honestly quite unfamiliar with that, even more than the whole thing anyway...). The thing that I am most intrigued with is the possibility to have a 4 dimensional twistor string geometry. Quite an amount of this business has been developped by Witten.

 

[Gear300]

The thing that I am most intrigued with is the possibility to have a 4 dimensional twistor string geometry. Quite an amount of this business has been developped by Witten.

I'm only an amateur (still a student), so I'm just wondering: is what you're referring to the concept of the 4th dimension of time actually being a spatial dimension?

 

[Kopachris]

I'm too lazy to read this entire thread before putting my two cents in, so sorry if this has been explained already.

String theory deals with gravity on a quantum level. I don't know the gory details of how the quantum mechanics is handled, but the gravity part is explained by having all particles be (or have in their centers) tiny vibrating strings. Of course, according to Einstein, moving things warp spacetime, just like what we see as gravity. So the tiny vibrating strings are warping spacetime, and we see it as gravity. The 10-26 dimensions are required to explain why gravity is so much weaker than the other forces: it actually isn't any weaker. Supposedly, gravity is diluted by the extra dimensions, so we only get a fraction of it. M-theory in particular helps illustrate this concept by having fermions be open-ended strings that are attached to membranes that are the dimensions. Gravitons, on the other hand (which have yet to be observed) would be closed-ended strings that would be free to float off of a lower dimensional membrane up to a higher dimension. (Well, some people visualize it as sinking, since they visualize the membranes as a lower dimension floating on top of a higher dimension, but that doesn't really matter.)

In particular, the amount of dimensions is dependent on the amount of potential energy (of something, I don't know what). All I know on that subject is that the discrepancies between the number of dimensions predicted by the various string theories arise from the different theories applying to different things (for instance, M-theory deals mostly with membranes, while there's a string theory that deals exclusively with bosons). Originally, it was thought that there was only one correct string theory, but physicists have started to see dualities between them all.

Or at least, that's how I understand it as the Science Channel and The Elegant Universe explained it.

 

[Dmitry67]

Are these 10,11,26 dimensions real or complex?

 

[Unilinear_Kev]

Are these 10,11,26 dimensions real or complex?

It seems the only thing that has been determined in this thread is that the word "dimension" and exactly how many of them there are seem to be relative to the poster and/or physicist. While we can define the word dimension, it tends to be open ended (which is why you're getting a lot of guesses as to how many there are). This is still really interesting physics and the reason I even registered for this BB.

It's to my understanding that most of these models for the number of dimensions are made from trying to explain 1st hand information that has yet to be explained using the traditional physics "4d". I also get an intense laugh out of "3.5d". Made me think of physics like a version of AOL: "you've got mass!" "you've got movement!".

 

[Dmitry67]

The word 'dimension' is not open ended, it is well defined in mathematics.

If you have 3D space, and each dimension is complex, you need 6 real numbers to define a point, however, still space is 3D and it is different from a 6D real space

 

[Aftermarth]

ok just chucking another idea out there...

in maths I am doing Vector Calculus and Linear Mathematics.
We do simple equations like finding spans and what not

But in the R3 plane, when you find a span of two linerly independant vectors, it is a plane in 3D space.
Given a R4 plane, when you find a span of 3 linerly independant vectors... what does that form? (Visualising things often helps me learn in this maths)

So it would be a complete R3 plane (x,y and z axes) all contained within another plane which we cannot visualise?