  The question of whether Bose-Einstein condensation involves spontaneous
symmetry breaking is surprisingly controversial. We review the theory of
spontaneous symmetry breaking in ferromagnets, compare it to the theory of
symmetry breaking in condensates, and discuss the different viewpoints on the
correspondence to experiments. These viewpoints include alternative
perspectives in which we can treat condensates with fixed particle numbers, and
where coherence arises from measurements. This question relates to whether
condensates of quasiparticles such as polaritons can be viewed as "real"
condensates.
