Dimensional Analysis, Planck length

Posted on 2007-10-04
Last Modified: 2008-01-09
Using dimensional analysis (and The Buckingham PI Theorem), you can approximate the Planck length, from:

  f(Lp, c, G, h) = 0

(Lp being the Planck length, and the other 3 being the obvious.)

The result being:  Lp = k.sqrt(Gh/c³) ~ 10^-35 m.

My questions though:

 1- How can you justify the assumption that Lp depends on c, G, and h?
 2- Why not include eps_0 (permittivity of free space), and e (elementary charge)? They are surely equally fundamental?

Question by:InteractiveMind
    LVL 84

    Accepted Solution

    One way to think of it is the scale at which Heisenberg uncertainty produces a black hole.
    eps_0 introduces a charge unit, which would need to be canceled
    e is dimensionless, so you can include as many factors of e or 2 or pi as you want.
    LVL 27

    Expert Comment

    the e he is referring to is the charge on the electron

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