We report a new measurement of the ratio $h/m_{\mathrm{Rb}}$ between the Planck constant and the mass of $^{87}\mathrm{Rb}$ atom. A new value of the fine structure constant is deduced, $\alpha^{-1}=137.035\,999\,037\,(91)$ with a relative uncertainty of $6.6\times 10^{-10}$. Using this determination, we obtain a theoretical value of the electron anomaly $a_\mathrm{e}=0.001~159~652~181~13(84)$ which is in agreement with the experimental measurement of Gabrielse ($a_\mathrm{e}=0.001~159~652~180~73(28)$). The comparison of these values provides the most stringent test of the QED. Moreover, the precision is large enough to verify for the first time the muonic and hadronic contributions to this anomaly.
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.