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Fabri and Picasso (1966) showed that if the vacuum state $|0\rangle$ is translationally invariant, then the vacuum is either invariant under the internal symmetry, $Q |0\rangle = 0$ , or there is no state corresponding to $Q |0\rangle$ in the Hilbert space. The second case corresponds to SSB. The symmetry is hidden in that there is no unitary operator to map a physical state to its symmetric counterparts; instead, the symmetry is (roughly speaking) a map from one Hilbert space of states to an entirely distinct space. This is usually described as ‘vacuum degeneracy’, although each distinct Hilbert space has a unique vacuum state. […]