# Help: Planck Scale and Fine Structure Constant

• 1Truthseeker
In summary, the Planck scale is a very small unit of measurement that deals with the very tiny. The FSC is a scale that deals with the very large. They are related in that the reduced Planck constant is inversely proportional to the 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"!

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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

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

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

diazona said:
$$\alpha = \frac{e^2}{\hbar c\,4\pi\epsilon_0}$$
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?

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1Truthseeker said:
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 = 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

## 1. What is the Planck Scale?

The Planck Scale is a unit of measurement used in theoretical physics to describe the smallest possible scales of space, time, energy, and mass. It is named after physicist Max Planck and is also known as the Planck length, Planck time, Planck energy, and Planck mass.

## 2. How is the Planck Scale related to quantum mechanics?

The Planck Scale is related to quantum mechanics in that it is the scale at which quantum effects become significant and the laws of classical physics break down. At this scale, particles and energy behave in ways that are not described by classical physics, but rather by quantum mechanics.

## 3. What is the significance of the Fine Structure Constant?

The Fine Structure Constant, also known as alpha, is a dimensionless number that describes the strength of the electromagnetic interaction between charged particles. It is a fundamental constant in physics and plays a crucial role in describing the behavior of matter at the atomic and subatomic level.

## 4. How is the Fine Structure Constant related to the Planck Scale?

The Fine Structure Constant is related to the Planck Scale through the concept of renormalization. In theoretical physics, renormalization is a mathematical procedure used to remove infinities that arise when trying to combine quantum mechanics with general relativity. The value of the Fine Structure Constant at the Planck Scale is thought to be a fundamental constant that describes the structure of the universe.

## 5. What are the current theories about the Planck Scale and Fine Structure Constant?

There are various theories about the Planck Scale and Fine Structure Constant, including the idea that they may be related to the concept of a multiverse or that they may hold the key to understanding the fundamental laws of physics. However, these theories are still being explored and there is currently no definitive answer or consensus on their exact nature or significance.

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