  Relativity opens the door to a counter-intuitive fact: a state can be stable
to perturbations in one frame of reference, and unstable in another one. For
this reason, the job of testing the stability of states that are not
Lorentz-invariant can be very cumbersome. We show that two observers can
disagree on whether a state is stable or unstable only if the perturbations can
exit the light-cone. Furthermore, we show that, if a perturbation exits the
light-cone, and its intensity changes with time, due to dissipation, then there
are always two observers that disagree on the stability of the state. Hence,
''stability'' is a Lorentz-invariant property of dissipative theories if and
only if the principle of causality is respected. We present 14 applications to
physical problems from all areas of relativistic physics, ranging from theory
to simulation.
