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Help: Planck Scale and Fine Structure Constant

  1. Dec 9, 2009 #1
    Could someone explain the relationship between the FSC and the Planck Scale? What are they in relation to each other. I know what the Planck Scale is, and I even have a loose understanding of the FSC, but what of them in contrast and comparison? And how does the FSC affect QM, if at all?



    PS - my apologies, it should read "Planck Constant"!!
    Last edited: Dec 9, 2009
  2. jcsd
  3. Dec 9, 2009 #2
    I am not sure I understand your question. One of the beauties of the fine structure constant is that it is unitless, i.e., independent of any scale or system of units.
    Bob S
  4. Dec 9, 2009 #3
    Both describe the very very tiny. I would like to know the difference between them. And how they are related, if at all?
  5. Dec 9, 2009 #4


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    [tex]\alpha = \frac{e^2}{\hbar c\,4\pi\epsilon_0}[/tex]
    That's the relationship... both of them are numbers that keep popping up in important physics formulas. They're universal constants. I'm not really sure what else you're after.
  6. Dec 9, 2009 #5
    Why is the reduced Planck constant inversely proportional to the fine structure constant?
    Last edited: Dec 9, 2009
  7. Dec 10, 2009 #6
    The reduced Planck constant is given by

    h-bar = e2/(4πε0cα).

    So the reduced Planck constant is scale dependent on a lot of factors, excluding only 4, π, and α, which are scale independent (unitless).

    A better question is why does the reduced Planck constant depend quadratically on the fine strucure constant in

    h-bar = mec2α2/(2cR)

    where mec2 is the electron mass and R is the Rydberg constant.

    Most fundamental is the ratio of the Rydberg energy RE = 13.606 eV to the electron mass:

    RE//mec2 = α2/2 which is unitless and therefore scale independent.

    Bob S
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