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Local Electrodynamics in higher dimensions?

  1. Jul 30, 2013 #1
    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 gravitrons 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.
     
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  3. Jul 30, 2013 #2

    Simon Bridge

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    It's pretty much what string theory does ... what you do is curl the extra dimensions up real tight.
     
  4. Jul 30, 2013 #3
    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?
     
  5. Jul 30, 2013 #4

    Simon Bridge

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    No - the infinities that plague QED are not only problematic for point charges.
     
  6. Jan 5, 2014 #5
    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.
     
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