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

Abstract

It has been a notably elusive task to find a remotely sensical ansatz for a calculation of Sommerfeld's electrodynamic fine-structure constant αQED ≈ 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 αQED 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 αQED to global structures of the Universe, which in turn are largely determined by gravitational interactions.

Solutions for Series of Exponential Equations in Terms of Lambert-W Function and Fundamental Constants

“…In Equation (1.1), when n = 2 and y = 10, the equation becomes The solution 137.129 is close to the inverse of the fine structure constant 137.036 [14]- [21] which is dimensionless.…”

Gravitational Interactions and Fine-Structure Constant

“…The analogy of the leading (Schrödinger) term in Eq. ( 13) for the nonrelativistic contribution to the bound-state energy (under the replacement α G → α QED ) may encourage us to look for connections of gravitational and electromagnetic interactions on a more global scale, possibly, using scaling transformations [19]. Indeed, the first attempts to unify electromagnetism with gravity are almost 100 years old [20,21].…”

Derivation of the Planck and Fine-Structure Constant from Assis's Gravity Model

“…We will show that such a minimum energy condition appears naturally if we use Weber's electrodynamics and a gravitational model that derives gravity from electromagnetism using the Weber force (listed as one of the candidate theories by Jentschura and Nándori [1]). We can then calculate Planck's as well as the fine structure constant only using electromagnetism.…”

“…Many attempts have been made to find a viable analytical formula to derive the fine-structure constant using quantum electrodynamics (QED), algebraic identities as well as conjectures based on classical and quantum field theories as recently reviewed by Jentschura and Nándori [1] without convincing success. Planck introduced the quantum of action as an adhoc assumption in order to correctly predict the black-body radiation.…”