One usually says that sound waves in a crystal, ie. phonons, are Goldstone modes of the broken translation symmetries. However, fluids have sound waves and also translation invariance. In fact, it's obvious that the sound mode of the fluid is the same sort of pressure wave as a longitudinal phonon. So it seems the fluid has one "phonon" and the crystal has three.
Does this "phonon" come from a broken symmetry?
I was thinking it probably is the dilation symmetry of the vacuum which is broken by having a nonzero density fluid. Did anyone try to explain sound in fluids this way? It seems interesting because in this case one has to redo the counting of Goldstone modes for the crystal because more symmetries have been broken.
