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Disturbing moving fluids

In Newtonian physics, the excitation spectrum of a fluid is the same in all reference frames, up to a trivial shift. In special relativity, this is no longer the case. Relativity of simultaneity causes different inertial observers to measure markedly different excitation spectra, with stability being the only property known to be Lorentz invariant in all causal theories. Here, we show that, under a certain Onsager-like symmetry principle (which applies to kinetic theory and transient hydrodynamics), it is possible to place rigorous bounds on phase velocities, eigenmode convergence radii, spectral gaps, and equilibration rates in any inertial frame, using only information about the rest frame spectrum at zero wavenumber. The conventional intuition coming from time dilation is also shown to lead to generically wrong predictions, but becomes accurate if the fluid is non-relativistic in the rest frame.