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Planck distance and less dimensional gravity

  1. Apr 22, 2012 #1
    If we imagine 2+1 dimensional gravity, I think that this influences on Planck distance and time.
    Because attraction between two bodies can be described:

    [tex]F = m_1 m_2 G/r [/tex]

    F= force, m are masses, G is changed gravitational constant and r is distance between two bodies.
    So G does not have the same dimension as a common our 4D G. So calculation of Planck's distance is different.

    How it is with this?
     
  2. jcsd
  3. Apr 22, 2012 #2

    mfb

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    Staff: Mentor

    You would have to modify other forces, too - or you get a really strange universe.
    While this is no problem for Coulomb's law, the other features of the Standard Model are a bit tricky, as they are made for our 3+1 dimensions.

    Anyway, you could get a different mass in some way.
    This is usually done with a higher-dimensional gravity. If these additional dimensions are compact, you can introduce a new scale for them and calculate a modified Planck mass. This is usually done to lie within reach of the LHC ;).
     
  4. Apr 22, 2012 #3
    In 3+1 dimensions, dimensionless masses of particles are calculated as:
    [tex]
    \mu_e^2=m_e^2 G/(\hbar c)
    [/tex]
    In 2+1 this is not possible with the above mentioned 2+1 dimensional G. So, what is changed, [itex]\hbar[/itex], m, or the above formula, or what else?
     
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