Fine Structure Constant
The fine structure constant, written α, is the dimensionless number that measures the strength of the electromagnetic interaction between elementary charged particles. Its value is close to 1/137.036, and because it is a pure number — independent of any choice of units — it is often taken to be the single most fundamental quantity in physics.
The standard account
Arnold Sommerfeld introduced the constant in 1916 while extending the Bohr atomic model to elliptical orbits, in order to account for the fine structure — the small splitting of the spectral lines of hydrogen. In SI form it is written α = e²/(4πε₀ħc), combining the elementary charge, the permittivity of free space, the reduced Planck constant and the speed of light. The units cancel. The current recommended value is α ≈ 1/137.035999, known to better than a part in 109, making it one of the most precisely determined numbers in science; it is measured independently through the electron's anomalous magnetic moment, through atom-recoil experiments with caesium and rubidium, and through the quantum Hall effect.
α turns up wherever charge and light meet. It sets the ratio of the electron's velocity in the first Bohr orbit to the speed of light, the ratio of the Compton wavelength to the Bohr radius, and the size of each successive order in the perturbation expansion of Quantum Electrodynamics — which is why QED calculations converge so usefully.
What no accepted theory supplies is a reason for the number. Nothing in the Standard Model predicts 137.036 rather than any other value; α is put in by hand, and in quantum field theory it is not even a constant but a running coupling that grows at higher energies (reaching roughly 1/127 at the mass of the Z boson). Feynman called it "one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man." Arthur Eddington's attempts in the 1920s and 1930s to derive it as exactly 136, and then 137, from combinatorial arguments are the best-known failure. Whether α has been constant over cosmic time is an open observational question: analyses by Webb and collaborators of quasar absorption spectra have repeatedly reported small spatial or temporal variation, while other groups analysing similar data, together with constraints from the Oklo natural fission reactor and from atomic-clock comparisons, find none.
On this wiki
Because the constant is unexplained by the received theory, deriving it from a physical model is a standing goal for the researchers catalogued here — the reasoning being that a theory which produces 137.036 from structure has earned its keep.
Reginald T Cahill treats α as a fundamental parameter of his process-physics in-flow model of gravitation, arguing in Gravitation, the "Dark Matter" Effect and the Fine Structure Constant (Apeiron, 2005) that the anomalies usually attributed to Dark Matter — the borehole g anomaly and the flatness of spiral-galaxy rotation curves — are governed by α rather than by unseen mass. It is one of the more specific quantitative claims on this wiki, and it ties the constant directly to cosmology rather than to atomic physics.
Harold Aspden built his aether theory around the derivation of the electron's anomalous magnetic moment and related constants from vacuum structure rather than from renormalized field theory; see A New Approach to the Problem of the Anomalous Magnetic Moment of the Electron (1977) and Physics Without Einstein. William C Daywitt's Planck-vacuum programme takes a similar line at a deeper level: in The Planck Vacuum (Galilean Electrodynamics, 2010) he argues that a polarizable vacuum state is the common source of the gravitational, fine-structure and Planck constants alike, and works out consequences in Origin of the Compton and de Broglie Relations (2008).
Others attack the number directly. Theodore D Mitsopoulos asks what it physically means in The Physical Meaning of the Fine Structure Constant (1985). Jeffrey M Lee argues from atomic orbital geometry for a revised value in The True Value of the Fine Structure Constant Revealed (2005). Paul A Stowe, working from a continuum-mechanical alternative to QED, proposes in The Fine Structure Constant (2000) that α is not fixed at all but varies with the dielectric constant of the medium in which it is measured. Thomas N Lockyer derives fundamental constants from particle geometry in Fundamental Physical Constants Derived From Particle Geometric Structures (2008). Martin Kokus looks for the constant at the largest scales in The Fine Structure Constant and Cosmic Structure (Journal of New Energy, 2003), and Arnold G Gulko gives a derivation in terms of charge and Planck's constant in Derivation of the Fine Structure Constant in Terms of the Electric Charge and Planck's Constant (1993).
A dissenting note within the dissident camp comes from Edward Kapuscik, who argues in Physics Without Physical Constants (1994) that the basic equations of Newtonian mechanics and Maxwell electrodynamics contain no physical constants at all, and that constants enter only when a theory is applied — which would make the search for a formula for α a search in the wrong place.