Why do dimensions curl up or expand?

[Trollfaz]

In string theory, the universe can have 9-10 spatial dimensions and the reason why we experience 3 is because those higher dimensions compactify. Under right conditions the extra dimensions can decompactify into the macroscopic dimensions we see. Why do some dimensions curl up or expand? Is energy required to curl up the extra dimensions

 

[Vanadium 50]

Why do some dimensions curl up or expand?

Happens when they get wet. Fabric of space and all.

The question seems to presuppose that they have a natural size and something causes them to deviate from it - this "cause" you mention. That's not necessarily true.

 

[Cepatiti]

Under right conditions the extra dimensions can decompactify into the macroscopic dimensions we see. Why do some dimensions curl up or expand? Is energy required to curl up the extra dimensions

Are you referring to this paper: The fate of four dimensions ? Personally, I didn't know that paper. I didn't check, but does it have a lot of follow-up papers?

Some remarks related to your question:

As far as I know, there is no well-established model in string theory explaining why some dimensions are compact and others not.

Another question to ponder is why these compact dimensions remained small during the cosmic inflation. Here I read something in the past about cosmic strings, which stated that during the inflationary epoch, cosmic strings were wrapped around the compact dimensions, thus preventing them from expanding. Unfortunately, I do not have a reference for this anymore.

 

[haushofer]

In string theory we compactify by using fluxes of fields. This can already be done in GR with an electromagnetic field. You can compactify one spatial dimension and keep it small by using a flux from the EM-field. But that solution will be unstable.

To me, this flux compactification reeks a bit like fine tuning. And why just 6 dimensions compactified? Nobody knows. People were primarily happy to use the geometry of this 6d spaces to explain features of standard models, and saw the former curse of extra dimensions as a new blessing.

 

[berkeman]

Some trolling nonsense has been deleted from the thread and the thread is reopened.

 

[ohwilleke]

In string theory, the universe can have 9-10 spatial dimensions and the reason why we experience 3 is because those higher dimensions compactify. Under right conditions the extra dimensions can decompactify into the macroscopic dimensions we see. Why do some dimensions curl up or expand? Is energy required to curl up the extra dimensions

The theory has 9-10 spatial dimensions in the first place to motivate the weakness of gravity relative to the Standard Model forces and to allow for mathematical beauty.

The theory has compactified dimensions because we need them to conform to observation.

Alternately, the theory doesn't use compactified dimensions at all, and instead confines Standard Model forces but not gravity to four dimensional branes. This also has the virtue of providing a dumping ground on branes we don't live on for particles and forces that the theory predicts that aren't seen.

But a theoretical motivation or mechanism for compactification is more of a open problem than it is something that there is an answer at the ready to address.