  The spontaneous breaking of boost invariance is ubiquitous in nature, yet the
associated Goldstone bosons are nowhere to be seen. We discuss why some
subtleties are to be expected in the Goldstone phenomenon for spontaneously
broken boosts, and derive the corresponding quantum mechanical,
non-perturbative Goldstone theorem. Despite similarities with more standard
Goldstone theorems, we show by examples that ours can be obeyed by quite
unusual spectra of low-energy excitations. In particular, for non-relativistic
Fermi liquids, we prove that it is obeyed by the particle-hole continuum. To
the best of our knowledge, this is the first example of a Goldstone theorem
obeyed by a continuum rather than by (approximately stable) single-particle
Goldstone boson states.
