1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Derive Planck Length in terms of c, G, and h_bar

  1. Feb 20, 2009 #1
    1. The problem statement, all variables and given/known data

    a. The first part of this problem was to derive the escape speed (Vesc) for a star of mass M and radius R.

    b. The second part is where I am having trouble. It says to equate the Vesc calculated above and derive a formula for Planck length in terms of c, G, and h_bar.

    2. Relevant equations

    This is from the Heisenberg uncertainty section for position and momentum so:

    [tex]\Delta[/tex]X * [tex]\Delta[/tex]P = h_bar/2

    E = mc2

    3. The attempt at a solution

    The escape velocity I calculated from part a was Vesc = [tex]\sqrt{2GM/R}[/tex]

    Equating Vesc to C gives:

    C = [tex]\sqrt{2GM/R}[/tex]

    Am I supposed to assume that [tex]\Delta[/tex]p = Mc and solve for [tex]\Delta[/tex]x using the Heisenberg uncertainty principle?

    I have tried a couple of different methods and I can't get this to simplify down to the form I need. I am pretty sure this is an easy problem, I just am not seeing the trick.
     
  2. jcsd
  3. Feb 20, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    According to Wikipedia the Planck length is defined as sqrt(hG/c^3)
    I think it is just a way to get units of meters out of those fundamental constants.
    I don't think it has a physical meaning, except in quantum mechanics which doesn't seem to apply to the problem you have.
     
  4. Feb 20, 2009 #3
    Ok I think I am getting close to this one:

    c=[tex]\sqrt{\frac{2GM}{R}}[/tex]

    M=[tex]\frac{c^2 R}{2G}[/tex]

    Using the Heisenberg Principal:
    [tex]\Delta[/tex]X [tex]\Delta[/tex]P = [tex]\frac{h_bar}{2}[/tex]

    [tex]\Delta[/tex]P = c M

    Solving this for [tex]\Delta[/tex]X
    [tex]\Delta[/tex]X = [tex]\frac{G h_bar}{c^3 R}[/tex]

    How do I get the square root and get rid of the R? :frown:
     
  5. Sep 21, 2010 #4
    Gravity level
    c =under root of (2GM/R)
    where R=L (Planck's Length) on gravity level
    so c =under root of (2GM/L)

    Uncertainty principle
    uncertainty in momentum x uncertainty in position = reduced Planck constant/2
    mv x L = reduced Planck constant/2
    here on quantum level, Uncertainty in position is Planck length and velocity is c (velocity of light)
    mcL= reduced h/2
    m=reduced h/(2cL)

    put the value of m in value of c in gravity level
    c square = 2 G reduced h/(2cL*R)
    c square = 2 G reduced h/(2cL*L)
    where R=L (Planck length on gravity level)
    Derive L (Planck length) from above equation.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derive Planck Length in terms of c, G, and h_bar
Loading...