  An explanation of the difference of the charge radius of the proton as
determined from the Lamb shift in electronic hydrogen and from elastic electron
scattering off the proton on the one side and the recent high precision
determination with muonic hydrogen on the other side is presented. It is shown
that the modification of the $2S_{1/2}$ and $2P_{3/2}$ wave functions by the
"Uehling potential" yields a correction to the theoretical Lamb shift of
$\delta (\Delta E_{\textrm{Lamb}}) = 0.302$ meV which has to be compared to
$\delta (\Delta E_{\textrm{Lamb}}) = 0.322(46)$ meV equivalent to the stated
radius difference. The explanation is based on the realization that the bound
state wave functions modified by the external "Uehling potential" have to be
propagated by the vacuum polarization propagator in order to give the correct
leading order Lamb shift. It is argued that a conflicting relativistic
calculation neglects this propagation aspect. The explanation demonstrates that
the Lamb shift is dynamically induced through the QED vacuum polarization and
is not only the result of a static external "Uehling potential" probed by a
test charge.
