Spontaneously broken mass

Understand

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 spontaneously broken.
• This remark is somewhat immaterial for the real world, where the correct space-time symmetries are encoded by the Poincar\'e group, which has no central charge.
• Yet it provides an explicit example of how superselection rules can be experimentally tested.