After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied …
The possible variation of the fine-structure constant, a, has inspired many people to work on modifications and/or generalizations of the current "standard" theories in which the electromagnetic field is involved. Here we first point out the amazing similarity between Bekenstein's model, describing the variation of α by a varying charge, and the Hojman-Rosenbaum-Ryan-Shepley torsion potential model. This observation invites us to consider a geometric theory of gravity in which a varying α originates from another kind of dynamic quantity of spacetime, i.e., vector torsion. Since the vector torsion field is weak and also not strongly coupled with fermions it is difficult to detect it directly. The detection of a time-varying α could thus provide some promising evidence for the existence of torsion.