  We show that the full spurionic symmetry of Galilean-invariant field theories
can be deduced when those theories are the limits of relativistic parents.
Under the limit, the non-relativistic daughter couples to Newton-Cartan
geometry together with all of the symmetries advocated in previous work,
including the recently revived Milne boosts. Our limit is a covariant version
of the usual one, where we start with a gapped relativistic theory with a
conserved charge, turn on a chemical potential equal to the rest mass of the
lightest charged state, and then zoom in to the low energy sector. This
procedure gives a simple physical interpretation for the Milne boosts. Our
methods even apply when there is a magnetic moment, which is known to modify
the non-relativistic symmetry transformations. We focus on two examples, taking
the non-relativistic limits of scalar field theory and hydrodynamics.
