Local Symmetry
Intuitive
A prototypical example of a system with local symmetry is a grid of completely black balls.
TODO IMAGE GRID OF BILLARD BALLS.
We can rotate each ball individually and no observer could tell the difference. Hence this system has a local rotational symmetry.
The symmetry vanishes as soon as we put a little red dot onto each ball. Now it's easy to keep track of the orientation of each ball and there is no longer any local symmetry.
Concrete
In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
Abstract
The motto in this section is: the higher the level of abstraction, the better.