Fine-structure constant

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Numbers

$\alpha$:

0.0072973525675 +/- 1.09e-11

$\alpha^{-1}$:

137.035999113 +/- 2.03e-7

Definition

The fine-structure constant $\alpha$ is the dimensionless physical constant defined as $\alpha = e^2/(2 \varepsilon_0 c h)$, where $e$ is the elementary charge, $\varepsilon_0$ the electric constant, $c$ the speed of light in vacuum, and $h$ the Planck constant.

Comments

(1)

$\alpha$ may not be constant [3].

(2)

The constant is also called the Sommerfeld constant after Sommerfeld's 1916 treatment of spectral fine structure [1].

Programs

(P1)

Python

from scipy.constants import physical_constants
physical_constants['fine-structure constant']
physical_constants['inverse fine-structure constant']

References

[1]

Arnold Sommerfeld, "Zur Quantentheorie der Spektrallinien", Annalen der Physik Ser. 4, Bd. 51 (1916).

Links

[2]

Wikipedia: Fine-structure_constant

[3]

Wikipedia: Is_the_fine-structure_constant_actually_constant?

[4]

Wikipedia: History_of_measurements

[5]

NIST CODATA: fine-structure constant

[6]

NIST CODATA: inverse fine-structure constant

Similar tables

Proton-to-electron mass ratio — another dimensionless measured physical constant stored together with its reciprocal

Data properties

Entries are of type: real number

Table is complete: yes (it holds $\alpha$ and its reciprocal $\alpha^{-1}$, the two forms published by NIST; each stored interval is the union of the 2014-2020 measurements widened to five standard uncertainties, so it spans measurements that disagree rather than tracking a single adjustment)

Sources of data: [4], [5] and [6] for the CODATA 2022 check

Reliability: The stored real intervals are the union of the 2014-2020 measurements displayed in [4], each widened to five standard uncertainties. The measurements used are CODATA 2014, Aoyama et al. 2017, Parker et al. 2018, CODATA 2018, and Morel et al. 2020. Also note (1).

How well the digits are known: measured

How they were obtained:

Not computed: the values come from experiment. The attached generator parses the parenthesized standard uncertainties, widens each of the 2014-2020 measurements to five standard uncertainties, and stores their union.

The CODATA 2022 values from [5] and [6] lie inside these unions, so adding them leaves both entries unchanged.