The superfluid vacuum theory was proposed to understand some features of the vacuum (aether) from the emergence point of view. Although made up of non-relativistic atoms, the low-energy excitations of the superfluid, i.e. the phonons, are said to be "relativistic". I know that the superfluid phonons do have the linear dispersion $\omega = c k$, and the low-energy effective theory is Lorentz invariant. Also the superfluid is inviscid, so that the aether has no drag force. But I still doubt that the special relativity can really emerge in the superfluid. Because I can not show the following statement: The velocity of sound in the superfluid is the same for all inertial observers, regardless of their relative motion to the superfluid. I believe this should be a fundamental feature of relativity, but I do not see how to prove it. The velocity addition formula for sound is not the same as that for light. So I am very confused when people say that the phonons are relativistic. Any understanding of the emergent relativity in superfluid would be appreciated.