  Frohlich, Morchio and Strocchi long ago proved that Lorentz invariance is
spontaneously broken in QED because of infrared effects. We develop a simple
model where consequences of this breakdown can be explicitly and easily
calculated. For this purpose, the superselected U(1) charge group of QED is
extended to a superselected "Sky" group containing direction-dependent gauge
transformations at infinity. It is the analog of the Spi group of gravity. As
Lorentz transformations do not commute with Sky, they are spontaneously broken.
These abelian considerations and model are extended to non-Abelian gauge
symmetries. Basic issues regarding the observability of twisted non-Abelian
gauge symmetries and of the asymptotic ADM symmetries of quantum gravity are
raised.
