Alpha is 1/137th of what? (Fine Structure Constant)

[juniorcarty]

Hi. With regard to the Fine Structure Constant, I have been trying to figure out the practical applications of the formula in nature but have had difficulty trying to discern what the 137 denominator in the equation represents. ie, it is 1 137th of what? Or, 137 whats?

Is there a practical process in nature in which the relationship between the 1 and the 137 is patently manifest and describes the equation in a manner which is more accessible for a layman?

 

[Khashishi]

It is the strength of the electric force between two elementary charges, compared to hbar*c, reduced Planck's constant times speed of light.
hbar*c has something to do with the size at which quantum effects become important. So, you could interpret the fine structure constant as how important quantum effects are for the electric force.

 

[strangerep]

Hi. With regard to the Fine Structure Constant, I have been trying to figure out the practical applications of the formula in nature but have had difficulty trying to discern what the 137 denominator in the equation represents. ie, it is 1 137th of what? Or, 137 whats?

Is there a practical process in nature in which the relationship between the 1 and the 137 is patently manifest and describes the equation in a manner which is more accessible for a layman?

The Fine Structure Constant $\alpha$ characterizes the strength of the electromagnetic interaction between charged particles. Its value is not precisely 1/137 (see my link). It just happens to be quite close to that value. So far, we have no deeper explanation for its value -- we merely measure its value from the results of various high precision experiments.

$\alpha$ is one of the more intriguing constants of nature, since it is dimensionless -- meaning that its value doesn't depend on which system of units we choose.

As for "applications",... it affects all electromagnetic phenomena, both classical and quantum.

 

[secur]

Is there a practical process in nature in which the relationship between the 1 and the 137 is patently manifest and describes the equation in a manner which is more accessible for a layman?

It comes up in a number of places. The most intuitive, it seems to me, occurs in the ground state of a hydrogen atom. The speed of the electron is simply α times c, speed of light.

Of course "speed" is not observable but is calculated from the electron's momentum in the s-orbital.

 

[greswd]

It is the ratio between constant properties of the electric force of electrons and the energy of photons.

Why it has this value is unknown.

 

[A. Neumaier]

it is 1 137th of what?

It is approximately one 137th of 1. Which means, it is a pure number written approximately as a fraction.

 

[Jilang]

It is the square of the electric charge expressed in natural units divided by 4 pi.

 

[mathman]

Some history. Eddington at one time tried to show by numerical reasoning that 137 was exact. Even the best of them have crazy ideas.

 

[DennisN]

Is there a practical process in nature in which the relationship between the 1 and the 137 is patently manifest and describes the equation in a manner which is more accessible for a layman?

Hi juniorcarty, Sixty Symbols covered α in this clip: