when a continuous symmetry is broken, we say that the ground state is just one of the possible ground states, and there is no energy cost in moving from one to the other..
why doesn't the state keep changing with the slightest perturbation (production of goldstone boson).
why don't we have a different ground state every time we do an experiment.
and what if we had different possible ground states that are not symmetric (but equal in energy),, then every time we have a phase transition we could get a field with a different mass.
sorry for the question being unclear, I barely understand this.