  The proton size has been found, with a $6\,\sigma$ statistical significance,
to be larger by 4% when it is measured relatively to the electron than to the
muon [Pohl2010,Antognini2013]. We solve this proton radius puzzle by accounting
for the relativity of the proton scale. The proton to electron and proton to
muon scale ratios are obtained by direct measurement, but their comparison
requires a conversion to electron reference which is currently made by assuming
the usual law of scale ratio composition, $\rho_ {pe}=\rho_ {p\mu} \times \rho_
{\mu e}$. Using instead the special scale relativistic law $\ln \rho_
{pe}=(\ln\rho_ {p\mu}+\ln\rho_ {\mu e})/(\ln\rho_ {p\mu} \ln\rho_ {\mu
e}/(\ln\rho_ {\mathbb{P} e})^2$, where $\mathbb{P}$ denotes the Planck
length-scale, the two determinations of the proton radius, showing now a ratio
$1.009 \pm 0.008$, recover their agreement within about $1\sigma$. The proton
radius puzzle therefore provides one with a highly significant test of the
special scale relativity theory.
