Eur. Phys. J. H 39, 591–613 (2014)
https://doi.org/10.1140/epjh/e2014-50044-7

Attempts at a determination of the fine-structure constant from first principles: a brief historical overview

¹ Department of Physics, Missouri University of Science and Technology, Rolla, 65409-0640 Missouri, USA
² MTA–DE Particle Physics Research Group, P.O. Box 51, 4001 Debrecen, Hungary

^a e-mail: ulj@mst.edu

Received: 19 July 2014
Received in final form: 27 October 2014
Published online: 4 December 2014

Abstract

It has been a notably elusive task to find a remotely sensical ansatz for a calculation of Sommerfeld’s electrodynamic fine-structure constant α_QED ≈ 1 / 137.036 based on first principles. However, this has not prevented a number of researchers to invest considerable effort into the problem, despite the formidable challenges, and a number of attempts have been recorded in the literature. Here, we review a possible approach based on the quantum electrodynamic (QED) β function, and on algebraic identities relating α_QED to invariant properties of “internal” symmetry groups, as well as attempts to relate the strength of the electromagnetic interaction to the natural cutoff scale for other gauge theories. Conjectures based on both classical as well as quantum-field theoretical considerations are discussed. We point out apparent strengths and weaknesses of the most prominent attempts that were recorded in the literature. This includes possible connections to scaling properties of the Einstein-Maxwell Lagrangian which describes gravitational and electromagnetic interactions on curved space-times. Alternative approaches inspired by string theory are also discussed. A conceivable variation of the fine-structure constant with time would suggest a connection of α_QED to global structures of the Universe, which in turn are largely determined by gravitational interactions.