Local Electrodynamics in higher dimensions?

["pi"mp]

Local Electrodynamics in higher dimensions??

So I am an unexperienced undergrad but the other day I had a few thoughts which are most likely crazy. I'm just wondering why they don't work. And whether the questions I'm asking are answered elsewhere.

So I've heard:

(i) Maxwell's equations break down on very, very small length scales. But Hermann Weyl showed they only work in (3+1)-dim spacetime.

and

(ii) Perhaps we haven't observed gravitons because they escape to higher dimensions after traveling only tiny length scales.

So I was wondering, is there some geometric way of thinking of the universe where locally, the universe is a higher dimensional space and they dimensions somehow coalesce or "smooth out" into the usual (3+1)-dimensions at larger lengths? Might Maxwell's electrodynamics be only approximate but break down locally?

I might not even be asking sensible questions and I certainly don't know enough mathematics to ask it more concisely, but any thoughts would be appreciated.

 

[Simon Bridge]

It's pretty much what string theory does ... what you do is curl the extra dimensions up real tight.

 

["pi"mp]

ah thank you...so the infinities that plague ED and QED, aren't these only problematic with point charges? Does the local geometry fix this?

 

[Simon Bridge]

No - the infinities that plague QED are not only problematic for point charges.

 

["pi"mp]

So thinking about my original post more now that I know more geometry, is the idea that the dimensions that you say are "curled up" locally, are from a vector or fibre bundle at that point on spacetime? Then the problematic point charges can be regarded as loops in the bundle but project down to a point still.