““THE GOLDSTONE THEOREM It doesn't matter for our discussion that the broken symmetry of our world chooses a particular direction not in actual geometrical space but rather in an abstract space. There is one feature we can carry over from the previous consideration: Spontaneous symmetry breaking implies the existence of waves. The spin-waves in the ferromagnetic world of our model are replaced by excitations in the abstract space of particle properties, where the symmetry breaking actually occurs. In this world, there must be equivalent excitations, waves: The so-called Goldstone theorem says that every symmetry of the laws of nature that is not also a symmetry of the ground state implies the existence of an elementary particle; it even fixes the properties of that particle.””
