Exploring the Inter-Relationship of Nature's Constants

[jsc314159]

Hello all.

I only have a few posts here so I am somewhat new to the forum. I have been reading a number of the posts though and I am favorably impressed by many of the responses. I am also somewhat new to LaTex so please forgive my mistakes with it.

I am interested in learning more about the fine structure constant $$\alpha$$, where

$$\alpha = e^2/\hbar c \sim 1/137$$

e = elementary charge

$$\hbar = h/2\pi$$, h is Planck's constant

c = the speed of light in a vacuum

Another way of writing the fine structure constant is

$$\alpha = \frac{\hbar/mc}{a_0}$$

m = mass of an electron

$$a_0$$ = the Bohr radius

I understand that the fine structure constant is dimensionless and is one of those enigmatic fundamental constants that pops up in the study of nature.

I further understand that it is used in electrodynamics, how? Where else is it used?

What are the leading explanations as to why it exists and why it might take on the value it has?

Does it relate to other numbers like Pi, e, the number of spatial dimensions in the universe?

What do you think?

John

 

[pam]

You could try this thread for starters.

https://www.physicsforums.com/showthread.php?t=220773

 

[jsc314159]

Sorry, I didn't know a thread already existed on this topic. I suppose that is what the search function for.

jsc

 

[adc-fc]

Hello John,

You have laid out the basics for calculating the fine structure constant and may be interested in some further information about the constants of nature given on the website at the following link: (...) - Please read the attachment for my full reply -

... So the inter-linking of the constants seems to be open to expansion in line with specific theories, and the constants themselves appear to be constants of dimension in some cases, providing the mathematical link between expressions of different fields of physics, and in other cases definite parameters to associate with specific body and particle, for example Planck’s constant is the angular momentum of the electron.

Do you John, and others, have some more expressions extending the inter-relationship between the constants of nature?

Adc-fc