Help: Planck Scale and Fine Structure Constant

[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"!

 

[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

 

[1Truthseeker]

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

 

[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.

 

[1Truthseeker]

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

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

 

[Bob S]

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

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 = m_ec²α²/(2cR)

where m_ec² is the electron mass and R is the Rydberg constant.

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

R_E//m_ec² = α²/2 which is unitless and therefore scale independent.

Bob S