Exploring the Inter-Relationship of Nature's Constants

In summary, John, the fine structure constant is a fundamental constant that is used in electrodynamics. It is believed to have a link to other constants of nature, such as Pi, e, and the number of spatial dimensions in the universe.
  • #1
jsc314159
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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 [tex]\alpha[/tex], where

[tex] \alpha = e^2/\hbar c \sim 1/137 [/tex]

e = elementary charge

[tex] \hbar = h/2\pi [/tex], h is Planck's constant

c = the speed of light in a vacuum

Another way of writing the fine structure constant is

[tex] \alpha = \frac{\hbar/mc}{a_0}[/tex]

m = mass of an electron

[tex]a_0[/tex] = 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
 
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Sorry, I didn't know a thread already existed on this topic. I suppose that is what the search function for.

jsc
 
  • #4
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
 

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What is the fine structure constant?

The fine structure constant, denoted by the symbol α, is a dimensionless constant that characterizes the strength of the electromagnetic interaction between elementary particles. It is approximately equal to 1/137 and is a fundamental constant in quantum electrodynamics.

How is the fine structure constant calculated?

The fine structure constant is calculated by dividing the elementary charge squared by Planck's constant multiplied by the speed of light. It can also be derived from other fundamental constants such as the permittivity of free space and the electron charge-to-mass ratio.

Why is the fine structure constant important?

The fine structure constant is important because it is a fundamental constant in physics that governs the strength of electromagnetic interactions. It also appears in many equations and theories, such as quantum electrodynamics and the Dirac equation, and is used to explain phenomena such as the splitting of spectral lines.

Can the fine structure constant change?

The fine structure constant is currently believed to be a constant value, meaning it does not change over time or in different physical conditions. However, some theories suggest that it may vary in extreme environments, such as the early universe or near black holes.

How is the fine structure constant related to the speed of light?

The fine structure constant is related to the speed of light because it appears in the formula used to calculate the speed of light. This is because the speed of light is determined by the permittivity and permeability of free space, both of which contain the fine structure constant.

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