SuperString theory

[Aki]

I am reading Kaku's Hyperspace and he says the superstring theory could only exist in a universe with 10 or 26 dimensions. Then he says 16 of the 26 dimensions have been compactified, so 26-16=10. I don't really understant this part, could somebody please explain what this means? and why superstring theory would only work with 10 or 26 dimensions

 

THanks

[Tormod]

It's been a while since I read Kaku's book, but there are in fact a lot of theories about superstring, the most common these days (I think) is the so-called "M-theory".

 

Some variations of these theories require 9 spatial dimensions plus 1 time dimension, while others require 10 + 1. The 10 or 26 dimension thingy is puzzling to me as well and I have no good explanation for it.

 

However, there is a good site out there on superstrings:

http://www.superstringtheory.com/

 

It has lots of interesting articles and educational stuff on superstrings.

 

Tormod

[Freethinker]

Another great site for info about Superstring theory is from the PBS special on "The Elegant Universe"by Brian Greene.

 

Lots of good discussion and some well made animations to help understand the concepts.

 

http://www.pbs.org/wgbh/nova/elegant/

 

I think the number of dimension required for various superstring theories is still open. But Greene seems to find 10 to be the prefered count.

[Bo]

The 26 Dimensions come from the theory of the so called bosonic string. 'Bosonic' here means basicly that the strings have no spin (i hope the concept of spin is known, otherwise let me know).

The problem is: We want string theory also to describe particles with spin (fermions). One of the cases you can consider then is Supersymmetry (basicly a symmetry between bosons and fermions). This leads to the theory of Superstrings. Here the requirement is to have 10 dimensions.

Further one can go from 10->4 dimensions by compactification. (rolling up dimensions to such a size they're not noticable to us any more).

As to why String theory only works in 10 dimensions: this is highly mathematical... But i'll try somethig (bosonic case, this is slightly easier)...

A string has a certain number of excitations. But each excitation has D (# dimensions) degrees of freedom. furthermore there are some requirements that distinguish between 'physical' and 'nonsense (e.g. the expectation value to find a particle is negative)' strings. If you do this properly then eventually you can get a state of which you are sure that it is physical, however if you apply the constraints for a physical stat you get D=26.

I think this is as clear i can explain it without mathematics....

Bo

[Aki]

Bo: No, I'm not very familiar with the concept of spin. I read about it, but I'm still confused. If you don't mind, please explain it to me. Thanks.

 

Tormod: about the theory that require 11 dimensions (10 spatial and 1 time) , isn't that the supergravity theory, which came before the superstring theory, and it was proven that it doesn't work or something. Correct me if I'm wrong

[Tormod]

Aki: Maybe. It's been a while since I read up on these things. I hope Bo or some else can explain it!

 

Tormod

[TeleMad]

Concering why string theory requires 11 dimensions, anyone who has Brian Greene's "The Elegant Universe" can get the general idea by reading pages 201 - 204

[Bo]

Supergravity does not put any requirements on the number of space-time dimensions; that is something that only happens with string theory (for as far as i know...).

The fact that you sometimes see 10 and sometimes 11 as the number of dimensions comes from the following: Basic superstring theory needs 10, but there are suggestions that the theory actually lives in 11 dimension, but 'movement' in the 11th dimension is not possible. Rather our position in the 11th dimension fixes physical parameters (like the value of the speed of light etc.) But i don't know much about this and i'm not sure how widely accepted this is.

 

As to the subject of spin: there is in classical mechanics a property called angular momentum. This is basicly the momentum (mass*speed) for a rotating object. If we use quantum mechanices to calculate the angular momentum of for example an electron that orbits a nucleus, we get 2 sets of sollutions. One of these sets we can identify with the motion of the electron around the nucleus and thus is the equivalence of the classical angular momentum. This is called 'orbital angular momentum'. The other set on the other hand appears to be an intrinsic property of the electron (like charge or mass). This is called spin. Conceptually you can visualise this (the visualisation isn't correct but that doesnt really matter) as the electron tolling around its own axis. The electron can have 2 values for its spin. this is called 'spin up' and 'spin down' (or in the previous picture: the electron spinning right or left). Other particles can have more 'spin orientations. some extra info can be found here: http://hyperphysics.phy-astr.gsu.edu/hbase/spin.html#c3

 

bo

[maddog]

Sorry to wake up an old post. It is just I feel compelled to speak.

 

Yes, both Kaku's book "Hyperspace" and Brian Greene's book Elegant Universe are great.

I personally like Greene's book for covering this subject more thoroughly and explaining

clearly.

 

:)

However, I must point out a few inaccurate statements made on this post. What distinguishes

Bosons from Fermions is the spin. However, Bosons have integral spin and Fermions have

half-integral spin. Bosons are typically seen as the force carriers and Fermions are seen

as the particles (that have mass). Thus one would think that Bosons are massless (like the

photon). Actually untrue. The Z particle, a carrier of the weak force (only particle I know

of that has 0 spin) actually has a mass (the value I would have to look up).

 

As for 10 vs 26 dimension for which string theory it is a matter of when. Early on in the

life string theories, a conjecture analogous to the Kaluza-Klein theory which Einstein had

studied in about 1918 that attempted to unify gravity with electromagnitism. This hypothesis

added an arbitrary number of dimension where the number worked out 26 dimensions

total. It was later learned that this version of string only accounted for Bosons (massless

at that) and was therefore limited. It was notions from Supersymmetry that spawned

the 10 dimensional version and Superstrings was born (mid 80's I think). Adding a dimension

was to create a quantum description for gravity (inline with Supergravity). Kaku in his

book and later book of his, describes that M-theory as bridge between 5 self-consistent

and contradictory string theories.

 

I am in fact reading brand new book (2004) called "A first course in String Theory" by

Barton Zwiebach of MIT. This is a first as a textbook on String Theory at an undergraduate

level in physics. In it is the latest findings (except maybe the goof by Hawking this last

summer).

 

I know I am rambling. For that, my apologies. :)

 

Maddog

[Tormod]

Sorry to wake up an old post. It is just I feel compelled to speak.

I'm sure we have a lot of loose threads than can do with some reactivation.

 

I know I am rambling. For that, my apologies. :)

I was going to say...finally someone who can write half-spin and half-integral spin without even adding a wiggly finger.

 

Oh, you did. :)

 

Seriously, excellent post!