  We study electroweak interactions in the multiscale theory with
$q$-derivatives, a framework where spacetime has the typical features of a
multifractal. In the simplest case with only one characteristic time, length
and energy scale $t_*$, $\ell_*$, and $E_*$, we consider (i) the muon decay
rate and (ii) the Lamb shift in the hydrogen atom, and constrain the
corrections to the ordinary results. We obtain the independent absolute upper
bounds (i) $t_* < 10^{-13}{\rm s}$ and (ii) $E_*>35\,\text{MeV}$. Under some
mild theoretical assumptions, the Lamb shift alone yields the even tighter
ranges $t_*<10^{-27}\,{\rm s}$, $\ell_*<10^{-19}\,{\rm m}$, and
$E_*>450\,\text{GeV}$. To date, these are the first robust constraints on the
scales at which the multifractal features of the geometry can become important
in a physical process.
