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Fractional dimensions in superstring duality

  1. Jul 24, 2004 #1
    Instead of superstrings having 10 unitary dimensions (6 of compactified space and 3+1 of ordinary spacetime), imagine these 6 compactified spatial dimensions being of fractal value (3/6=1/2) relative to the 3 apparent dimensions of space.

    This corresponds as a dimensional duality to the 6 dimensional phase space of quantum mechanics, where each of three orthogonal dimensions is assigned both a spatial and a momentum phase (6/3=2).

    Is there any merit to this pattern being a legitimate duality?
     
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  3. Jul 25, 2004 #2
    Why 10 Dimensions?

    When strings vibrate in space-time, they are described by a mathematical function called the Ramanujan modular function.26 This term appears in the equation:27

    [1-(D - 2)/24]
    where D is the dimensionality of the space in which the strings vibrate. In order to obey special relativity 9and manifest co-variance), this term must equal 0, which forces D to be 26. This is the origin of the 26 dimensions in the original string theory.

    In the more general Ramanujan modular function, which is used in current superstring theories, the twenty-four is replaced by the number eight, making D equal to 10.28

    In other words, the mathematics require space-time to have 10 dimensions in order for the string theory to be self-consistent, but physicists still don’t know why these particular numbers have been selected.


    http://www.ecf.utoronto.ca/~quanv/String/string9.html
     
  4. Jul 25, 2004 #3

    selfAdjoint

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    Yes, and the numbers arise for physical reasons (cancelling anomalies). You can't build a consistent string theory in other than 26 dimensions or a consistent superstring theory in other than 10.
     
  5. Jul 25, 2004 #4
    I like the link - it's fairly understandable. Forget the "duality" I mentioned, but couldn't the "compactification" of the 10 minus 4 extra dimensions take place as with 6 fractal dimensional values that fit just as well our apparent 4-dimensional spacetime?
     
  6. Jul 25, 2004 #5

    selfAdjoint

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    Yes, you can play tricks with compaction. See my post on the string computation of Bekenstein entropy. Here they take 10 dimensional branes and superstrings, compact five of the 9 spatial dimensions onto circles, and work in the resulting effective 5 dimensional Minkowsi spacetime. Perfectly reasonable, but note that the argument doesn't just ignore the compacted dimension; what happens in them is just as important as what happens in the "big" dimensions.
     
  7. Jul 25, 2004 #6
    Rather than imposing the familiar "compactified" dimensions on the Planck scale, I am proposing that extradimensions can be considered interstitial to integral-value spacetime by assigning them fractal values. Fractal space is just as effective as compactified space in representing the resonances underlying physics.
     
  8. Jul 25, 2004 #7
    That's a pretty tall order considering the predictability that is required from one length to another? In terms of discrete states of existance, you should see more alliance with LQG. Look up quantum gravity in the Monte Carlo effect.



    what is being discribed makes sense in this as well.


    There are certain realizations that must be understood in D5 branes? The fifth dimension has been realized here?


    Could someone explain?
     
    Last edited: Jul 26, 2004
  9. Jul 26, 2004 #8
    There are problems with this picture.

    http://www.nature.com/nature/journal/v411/n6841/images/411986af.0.jpg

    Maybe if we look at displacement??????????

    Physicists also measure the extra dimensions in terms of the energy needed to probe them. A particle accelerated to 1 trillion electron volts (TeV) has, according to standard arguments from quantum mechanics, a wave aspect with a wavelength of about 2 x 10–19 m. It can therefore explore facets of the subatomic world on that scale. Doubling the energy means seeing features half that size, and so on. So far, the smallest length scale observable with accelerators is a little greater than 10–19 m.

    The idea of extra dimensions dates back to at least the 1920s. At that time, physicist Oskar Klein, building upon work by mathematician Theodor Kaluza, added a curled-up fifth dimension to the familiar universe in an ingenious but unsuccessful attempt to unite the forces of electromagnetism and gravity.

    Physicists believe that the four forces—electromagnetic, weak, strong, and gravitational—were joined as a single superforce at the time of the Big Bang. In theory, they could merge only if the forces were about the same strength under conditions of high energy. However, gravity is much weaker than the others.

    As some researchers today explore extra dimensions, they are on the lookout for implications regarding unification of the four forces. Other scientists striving for models that unify the forces have found extra dimensions a useful tool.


    http://www.sciencenews.org/articles/20000219/bob1.asp


    I had to tie posts together
     
    Last edited: Jul 26, 2004
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