https://physics.stackexchange.com/questions/2721/what-is-the...> Remember that voltage is always expressed as a "potential difference." You can't measure the absolute value of voltage because everything is invariant when you add a constant voltage everywhere. That expresses a symmetry just like time translation invariance.
> When you bring in the magnetic field this invariance or symmetry can be generalised to a bigger gauge invariance transforming the electromagnetic potential as a vector field. Charge particles are also described by fields such as Dirac spinors, which are multiplied by a phase factor under the action of this symmetry, making it a U(1) invariance. Electric charge is the conserved quantity that Noether's theorem gives for this symmetry.
It sounds like violating this would mean that there was an observable difference between "zero electrical potential" and "nonzero electrical potential".
Temperature is another quantity that is usually measured solely in terms of the difference between two states, but -- apparently unlike electrical gauge -- in that case there is an absolute zero point which is distinguishable from other points.
It might be interesting to ask what would be conserved, but isn't now, if there were a temperature invariance analogous to gauge invariance.