An exact expression for the fine structure constant

In summary, the conversation discusses the relationship between the fine-structure constant (\alpha), the probability for an electron to emit or absorb a photon, and Schwinger's first term of the electron's magnetic moment anomaly (\mu). It is noted that \alpha, with a value of 1/137.03599911, is a function of \mu and that using the exact value of pi results in a value for \alpha that falls within the measurement range. The significance of this finding is uncertain.
  • #1
Hans de Vries
Science Advisor
Gold Member
1,094
30
Just for the record:


[tex]\ \alpha^{-\frac{1}{2}}\ +\ \alpha^\frac{1}{2}\mu\ =\ e^{\pi^2/4}[/tex]


Where [itex]\alpha[/itex], the fine-structure constant = 1/137.03599911 (46)
and [itex]\mu=1+\frac{\alpha}{2\pi}[/itex] is Schwingers first term of the electrons
magnetic moment anomaly which is a function of [itex]\alpha[/itex] as well.

[itex]\alpha^\frac{1}{2}[/itex] is the probability for an electron to emit or absorb a photon.

Fill in 1/137.03599911 for [itex]\alpha[/itex] and you'll get for pi:

3.14159265263 which only differs in the 10th digit with the real value:
3.14159265358...

Using the exact value for pi results in a value for the fine structure
constant of: 1/137.03599952837 which is within the measurement range.

Does it mean anything? maybe, maybe not.

Regards, Hans
 
Physics news on Phys.org
  • #2

FAQ: An exact expression for the fine structure constant

What is the fine structure constant?

The fine structure constant is a dimensionless physical constant that characterizes the strength of the electromagnetic interaction between elementary particles. It is denoted by the symbol α and has a numerical value of approximately 1/137.

What is the significance of the fine structure constant?

The fine structure constant plays a crucial role in understanding the behavior of atoms and molecules, as it determines the strength of the interaction between charged particles and the electromagnetic field. It also appears in various fundamental equations in physics, such as the Dirac equation and the Schrödinger equation.

How is the fine structure constant calculated?

The fine structure constant is calculated by taking the square of the elementary charge (e) and dividing it by two times the Planck constant (h) and the speed of light (c), multiplied by the permittivity of free space (ε0). This gives the value of approximately 1/137.

Has the value of the fine structure constant changed over time?

There is currently no evidence that the value of the fine structure constant has changed over time. It is considered to be a fundamental constant of nature and is expected to remain constant in the future. However, some theories suggest that the fine structure constant may have varied in the early universe.

What is the exact expression for the fine structure constant?

The exact expression for the fine structure constant is α = e2/(4πε0hc), where e is the elementary charge, ε0 is the permittivity of free space, h is the Planck constant, and c is the speed of light. This expression is a combination of several fundamental constants in physics and is used to calculate the value of α with high precision.

Similar threads

Replies
4
Views
948
Replies
12
Views
2K
Replies
3
Views
1K
Replies
1
Views
2K
Replies
7
Views
2K
Replies
6
Views
2K
Back
Top