Suppose we have some laws describing how possible states ought to behave and they are symmetric under a certain group. But suppose, however, the lowest energy solution, i.e. the stable solution is not symmetric under that group. This obviously means the lowest energy state is degenerate and performing a symmetry transformation on any such state would just lead to another such state. However, from the point of view of an observer in a state close to one of these states, it looks as if the symmetry of the dynamical laws are broken.
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