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String number density - does it make sense?

  1. Jul 24, 2006 #1
    On a blog I came across a strange question:

    "Does it make sense to speak about the number of
    strings found in a volume of space?"

    Could anbody comment on this? I would be
    interested if one has to imagine string theory
    as filling all of space with strings Or branes),
    or whether this is the wrong visualization.

    Frank

    [Moderator's note: one can construct the "number of strings" operator in a
    perturbative treatment of string theory - much like you can talk about
    the number of particles and/or the level of the harmonic oscillator.
    However, both in quantum field theory and string theory, this quantum
    number is a bit problematic. It is certainly not conserved. In QFT, it
    depends on the energy scale at which you understand the system - because
    with a high enough scale, you find very many gluons inside the proton,
    to say an example. The "number of particles" behaves strangely when
    you include interactions. The latter statement is also true in string
    theory. The real physical objects at nonzero coupling are not just the
    "bare 1 string" that you know from g=0. LM]
     
  2. jcsd
  3. Aug 4, 2006 #2
    frank_k_sheldon@yahoo.co.uk wrote:

    > On a blog I came across a strange question:
    >
    > "Does it make sense to speak about the number of
    > strings found in a volume of space?"


    > [Moderator's note: one can construct the "number of strings" operator in a
    > perturbative treatment of string theory - much like you can talk about
    > the number of particles and/or the level of the harmonic oscillator.
    > However, both in quantum field theory and string theory, this quantum
    > number is a bit problematic. It is certainly not conserved. In QFT, it
    > depends on the energy scale at which you understand the system - because
    > with a high enough scale, you find very many gluons inside the proton,
    > to say an example. The "number of particles" behaves strangely when
    > you include interactions. The latter statement is also true in string
    > theory. The real physical objects at nonzero coupling are not just the
    > "bare 1 string" that you know from g=0. LM]


    I was always looking for answers to the comment, but saw the
    moderator's note only today.

    To continue on the QCD analogy, the number of strings would
    thus depend on the energy. I suppose this also correct for empty space.
    Thus the number of strings in empty
    space will depend on the energy. (Correct?)
    If this is so, can we give numbers?
    I suppose that at 10^19 GeV (Planck energy), the number is maybe one
    string per mm^3 (or probably one string for any volume whatsoever),
    whereas at 1 eV it is very high. Is this correct?
    And if so, can one give an estimate for the number of strings at 1eV
    in flat empty space? (Or does one need to specify some other
    condition?)

    That is really an interesting issue!

    Frank
     
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