  We construct and analyze the Standard Model of electroweak and strong
interactions in multiscale spacetimes with (i) weighted derivatives and (ii)
$q$-derivatives. Both theories can be formulated in two different frames,
called fractional and integer picture. By definition, the fractional picture is
where physical predictions should be made. (i) In the theory with weighted
derivatives, it is shown that gauge invariance and the requirement of having
constant masses in all reference frames make the Standard Model in the integer
picture indistinguishable from the ordinary one. Experiments involving only
weak and strong forces are insensitive to a change of spacetime dimensionality
also in the fractional picture, and only the electromagnetic and gravitational
sectors can break the degeneracy. For the simplest multiscale measures with
only one characteristic time, length and energy scale $t_*$, $\ell_*$ and
$E_*$, we compute the Lamb shift in the hydrogen atom and constrain the
multiscale correction to the ordinary result, getting the absolute upper bound
$t_*<10^{-23}\,{\rm s}$. For the natural choice $\alpha_0=1/2$ of the
fractional exponent in the measure, this bound is strengthened to
$t_*<10^{-29}\,{\rm s}$, corresponding to $\ell_*<10^{-20}\,{\rm m}$ and
$E_*>28\,{\rm TeV}$. Stronger bounds are obtained from the measurement of the
fine-structure constant. (ii) In the theory with $q$-derivatives, considering
the muon decay rate and the Lamb shift in light atoms, we obtain the
independent absolute upper bounds $t_* < 10^{-13}{\rm s}$ and
$E_*>35\,\text{MeV}$. For $\alpha_0=1/2$, the Lamb shift alone yields
$t_*<10^{-27}\,{\rm s}$, $\ell_*<10^{-19}\,{\rm m}$ and $E_*>450\,\text{GeV}$.
