Spontaneously broken mass

The Galilei group involves mass as a central charge. We show that the associated superselection rule is incompatible with the observed phenomenology of superfluid helium 4: this is recovered only under the assumption that mass is spontaneou.519 broken. This remark is somewhat immaterial for the real world, where the correct space-time symmetries are encoded by the Poincare group, which has no central charge. Yet it provides an explicit example of how superselection rules can be experimentally tested. -We elaborate on what conditions must be met for our ideas to be generalizable to the relativistic case of the integer/half-integer angular momentum superselection rule.