  The persistent $a_\mu \equiv (g-2)/2$ anomaly in the muon sector could be due
to new physics visible in the electron sector through a sub-ppb measurement of
the anomalous magnetic moment of the electron $a_e$. Driven by recent results
on the electron mass (S. Sturm et al., Nature 506 (2014) 467), we reconsider
the sources of uncertainties that limit our knowledge of $a_e$ including
current advances in atom interferometry. We demonstrate that it is possible to
attain the level of precision needed to test $a_\mu$ in the naive scaling
hypothesis on a timescale similar to next generation $g-2$ muon experiments at
Fermilab and JPARC. In order to achieve such level of precision, the knowledge
of the quotient $h/M$, i.e. the ratio between the Planck constant and the mass
of the atom employed in the interferometer, will play a crucial role. We
identify the most favorable isotopes to achieve an overall relative precision
below $10^{-10}$.
