Fine-structure constant

α 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.

The electrostatic CGS system implicitly sets 4πε0 = 1, as commonly found in older physics literature, where the expression of the fine-structure constant becomes

A nondimensionalised system commonly used in high energy physics sets ε0 = c = ħ = 1, where the expression for the fine-structure constant becomes[10]

The CODATA recommended value is [11] While the value of α can be determined from estimates of the constants that appear in any of its definitions, the theory of quantum electrodynamics (QED) provides a way to measure α directly using the quantum Hall effect or the anomalous magnetic moment of the electron.

The preferred methods in 2019 are measurements of electron anomalous magnetic moments and of photon recoil in atom interferometry.

One of the most precise values of α obtained experimentally (as of 2023) is based on a measurement of ge using a one-electron so-called "quantum cyclotron" apparatus,[12] together with a calculation via the theory of QED that involved 12672 tenth-order Feynman diagrams:[14] This measurement of α has a relative standard uncertainty of 1.1×10−10.

On the other hand, the large value of the corresponding factors in quantum chromodynamics makes calculations involving the strong nuclear force extremely difficult.

The value of the fine-structure constant α is linked to the observed value of this coupling associated with the energy scale of the electron mass: the electron's mass gives a lower bound for this energy scale, because it (and the positron) is the lightest charged object whose quantum loops can contribute to the running.

Based on the precise measurement of the hydrogen atom spectrum by Michelson and Morley in 1887,[b] Arnold Sommerfeld extended the Bohr model to include elliptical orbits and relativistic dependence of mass on velocity.

[c] The first physical interpretation of the fine-structure constant α was as the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the speed of light in the vacuum.

It appears naturally in Sommerfeld's analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines.

This constant was not seen as significant until Paul Dirac's linear relativistic wave equation in 1928, which gave the exact fine structure formula.

[27]: 407 With the development of quantum electrodynamics (QED) the significance of α has broadened from a spectroscopic phenomenon to a general coupling constant for the electromagnetic field, determining the strength of the interaction between electrons and photons.

The term ⁠α/2π⁠ is engraved on the tombstone of one of the pioneers of QED, Julian Schwinger, referring to his calculation of the anomalous magnetic dipole moment.

In the experiments below, Δα represents the change in α over time, which can be computed by αprev − αnow .

The first experimenters to test whether the fine-structure constant might actually vary examined the spectral lines of distant astronomical objects and the products of radioactive decay in the Oklo natural nuclear fission reactor.

[35][36][37][38][39][40] Improved technology at the dawn of the 21st century made it possible to probe the value of α at much larger distances and to a much greater accuracy.

In 1999, a team led by John K. Webb of the University of New South Wales claimed the first detection of a variation in α.

[41][42][43][44] Using the Keck telescopes and a data set of 128 quasars at redshifts 0.5 < z < 3, Webb et al. found that their spectra were consistent with a slight increase in α over the last 10–12 billion years.

In 2004, a smaller study of 23 absorption systems by Chand et al., using the Very Large Telescope, found no measurable variation:[45][46]

[47][48] King et al. have used Markov chain Monte Carlo methods to investigate the algorithm used by the UNSW group to determine ⁠Δα/ α ⁠ from the quasar spectra, and have found that the algorithm appears to produce correct uncertainties and maximum likelihood estimates for ⁠Δα/ α ⁠ for particular models.

In principle, this technique provides enough information to measure a variation of 1 part in 109 (4 orders of magnitude better than the current quasar constraints).

[54] The collecting area required to constrain ⁠Δα/ α ⁠ to the current level of quasar constraints is on the order of 100 square kilometers, which is economically impracticable at present.

Orzel argues[63] that the study may contain wrong data due to subtle differences in the two telescopes[64] a totally different approach; he looks at the fine-structure constant as a scalar field and claims that if the telescopes are correct and the fine-structure constant varies smoothly over the universe, then the scalar field must have a very small mass.

Both of these scientists' early criticisms point to the fact that different techniques are needed to confirm or contradict the results, a conclusion Webb, et al., previously stated in their study.

[72][f] Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms: There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon.

(My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place.

It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.)

In the late 20th century, multiple physicists, including Stephen Hawking in his 1988 book A Brief History of Time, began exploring the idea of a multiverse, and the fine-structure constant was one of several universal constants that suggested the idea of a fine-tuned universe.

We have seen that the charge of an electron is not strictly constant but varies with distance because of quantum effects; hence α must be regarded as a variable, too.