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# Fine-structure constant

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The fine-structure constant, often denoted by the Greek letter α, is a dimensionless quantity[?] frequently encountered in atomic physics. It was introduced into physics by A. Sommerfeld in 1916, and is sometimes called the "Sommerfeld fine-structure constant". In the theory of quantum electrodynamics, it represents the strength of the interaction between electrons and photons.

The fine-structure constant α is defined as

$\alpha = \frac{e^2}{4\pi\epsilon_0\hbar c}$
where e is the charge of an electron, π is pi, h = h/(2π) is Dirac's constant, c is the speed of light in vacuum and ε0 is the permittivity of the vacuum.

In cgs units, electrical charges are measured in a way which results in the factor 4πε0 becoming equal to one:

$\alpha = \frac{e^2}{\hbar c}$

Since α is a dimensionless quantity, its numerical value is independent of the system of units used. This value is

α = 0.007 297 352 533(27),
it is commonly listed by the value of its inverse 137.035 999 76(50).

The fine-structure constant has been of interest to physicists because its value does not seem to be directly related to any obvious mathematical constant. In the standard model, the fine-structure constant is inserted to the theory externally.

The small value of the fine-structure constant is important in allowing calculations using quantum electrodynamics. Quantum electrodynamics allows one to break up a quantum mechanical problem into a power series of α and the small value of α creates a situation in which the terms corresponding to higher orders of &alpha become unimportant. By contrast, the large value of the corresponding factors in quantum chromodynamics make calculations involving the strong force extremely difficult.

One controversial explanation of the value of the fine-structure constant invokes the anthropic principle and argues that the value of the fine-structure is what it is because stable matter and therefore life and intelligent beings could not exist if the value were something else.

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