Fine-structure constant

In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by ${\displaystyle \alpha }$ (the Greek letter alpha), is a fundamental physical constant that quantifies the strength of the electromagnetic interaction between elementary charged particles.

It is a dimensionless quantity (dimensionless physical constant), independent of the system of units used, which is related to the strength of the coupling of an elementary charge ${\displaystyle e}$ with the electromagnetic field, by the formula ⁠${\displaystyle \alpha ={\tfrac {e^{2}}{4\pi \varepsilon _{0}\hbar c}}}$⁠. Its numerical value is approximately 0.0072973525643 ≈ ⁠1/137.035999177⁠, with a relative uncertainty of 1.6×10⁻¹⁰.

The constant was named by Arnold Sommerfeld, who introduced it in 1916 when extending the Bohr model of the atom. ${\displaystyle \alpha }$ quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887.

Why the constant should have this value is not understood, but there are a number of ways to measure its value.

In terms of other physical constants, ${\displaystyle \alpha }$ may be defined as:

where

Since the 2019 revision of the SI, the only quantity in this list that does not have an exact value in SI units is the electric constant (vacuum permittivity).

The electrostatic CGS system implicitly sets ⁠${\displaystyle 4\pi \varepsilon _{0}=1}$⁠, as commonly found in older physics literature, where the expression of the fine-structure constant becomes