  The Wigner little group for massless particles is isomorphic to the Euclidean
group ${\rm SE}(2)$. Applied to momentum eigenstates, or to infinite plane
waves, the Euclidean "Wigner translations" act as the identity. We show that
when applied to finite wavepackets the translation generators move the packet
trajectory parallel to itself through a distance proportional to the particle's
helicity. We relate this effect to the Hall effect of light and to the
Lorentz-frame dependence of the position of a massless spinning particle.
