Can We Make Sense of Dissipation without Causality?

Relativity opens the door to a counterintuitive 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.

Automated summary

Two observers can only disagree on the stability of a state if perturbations exit the light cone. If a perturbation exits the light cone and changes with time due to dissipation, there will always be two observers who disagree on the stability of the state. Stability is a Lorentz-invariant property of dissipative theories only if the principle of causality is respected.