# Help: Planck Scale and Fine Structure Constant

1. Dec 9, 2009

### 1Truthseeker

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?

Thanks!

-Truth

PS - my apologies, it should read "Planck Constant"!!

Last edited: Dec 9, 2009
2. Dec 9, 2009

### Bob S

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

3. Dec 9, 2009

### 1Truthseeker

Both describe the very very tiny. I would like to know the difference between them. And how they are related, if at all?

4. Dec 9, 2009

### diazona

$$\alpha = \frac{e^2}{\hbar c\,4\pi\epsilon_0}$$
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.

5. Dec 9, 2009

### 1Truthseeker

Why is the reduced Planck constant inversely proportional to the fine structure constant?

Last edited: Dec 9, 2009
6. Dec 10, 2009

### Bob S

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