Understanding M Theory's 11 Dimensions

[vektruscen]

I've been reading into String Theory and M Theory lately and I think I have a general picture of what it's about, with the infinite parallel universes and whatnot. But this theory is built on the idea of 11 dimensions. I don't understand this.. how is it possible to imagine the 5th+ dimension? The difference, or leap, from the 2nd dimension to the 3rd is astronomical, as is the leap from the 3rd to the 4th. I find myself barely able to comprehend the basic idea of the 4th dimension in relation to our place in the multiverse, but it's completely beyond me and anyone else (I would assume) to grasp the concepts of a 5th or 11th dimension. The fundamentals seem light years beyond our imagination. How is it that scientists can talk of an 11th dimension, then?

 

[Golfer]

It's all in the mathematics

The concept of 11 dimensions come from the mathematics required to solve the equations of M theory. The description of strings require 3 dimensions [our normal concept of space] plus 6 additional dimensions in which the strings vibrate. These vibrations lead to all the elementary particles. These 6 dimensions are compacted to such a degree that they cannot be seen. That leaves 2 other dimensions. One of these dimensions is time which is required by Einstein's theory of gravity. That leaves one free dimension. Some cosmologists think this final dimension may also be required to define a string. The major problem is that no one has been able to solve the equations exactly. Approximations have to be used.

M theory has two things going for it. [1] It predicts a spin 2 Boson which is what gravity requires. [2] It unites Einstein's theory of gravity with the Standard Model of particle physics.

Thus, if the math requires 11 dimensions, then there are probably 11 dimensions.

 

[BenTheMan]

vek---

I don't know if there's a way to SEE 11 dimensions in your head. The best you can do is to draw projections and go from there.

 

[vektruscen]

'These 6 dimensions are compacted to such a degree that they cannot be seen.'

Are they within our universe? How big are they? What goes on inside of them?

 

[Coin]

'These 6 dimensions are compacted to such a degree that they cannot be seen.'

Are they within our universe? How big are they? What goes on inside of them?

As I understand things, the way that string theorists like to think about the extra six dimensions is as a "Calabi-Yau manifold". This is a particular mathematical way of describing the geometry of a space which is "curled up" in the way that the extra dimensions in string theory are believed to be curled up. Each Calabi-Yau manifold gives a different way of "curling". I think string theorists have some preferred way of visualizing these Calabi-Yau manifolds, but I'm not sure.

When we say the dimensions are "curled up" we mean that they loop back on themselves, so that the dimension has a "size" and if you travel the distance of that size you come back to where you started. The "size" of these dimensions would have to be absolutely tiny, like on the scale of the Planck length. So movements in these dimensions would make no difference to us. However althoughthese extra six dimensions are of no interest to macroscopic objects like us, since the equations of string theory behave differently depending on the details of the background geometry, the choice of calabi-yau manifold causes string theory to behave slightly differently.

There is also a version of string theory with "large extra dimensions". Here "large" means, like, as big as a centimeter. In this case our four dimensions are embedded in a larger space, but everything in our four-dimensional space is somehow "stuck" on the 4D manifold (except gravitons, which at least in some versions of this idea can leak out of the manifold into the "bulk"). I do not *think* this version of the theory is as popular as the version with small curled-up extra dimensions (?), but you hear about it sometimes because there is a specific side effect if it is true, which means it would be potentially possible to see evidence of it at the LHC.

 

[vektruscen]

wow, crazy.