When looking at What, in simplest terms, is gauge invariance? question, the OP in the last paragraph asks this:
In many high school physics calculations, you measure or calculate time, distance, potential energy, temperature, and other quantities. These calculations very often depend only on the difference between two values, not the concrete values themselves. You are therefore free to choose a zero to your liking. Is this an example of gauge invariance in the same sense as the graduate examples above?
The answers all explain gauge invariance but don't answer the quoted paragraph.
Here is my example.
Take the Lagrangian for a simple pendulum:
$$L(q,\dot q)=\frac{1}{2}ml^2\dot q^2+mgl\space cos(q)-mgz_0$$
where the last term is there because of how defined where the origin of our coordinate system is (i.e. from where we measure the height of the mass that is swinging on the pendulum).
Since that last term is not a function of either $q$ not $\dot q$ it will always vanish when we do the Euler-Lagrange equation, so it we conclude that it is not important from where we measure the height of the bob.
So the Lagrangian is, in a sense, invariant of the height of ground state. Is this an example of gauge invariance? If not does this invariance have any other name?
To clarify why this question is different from the linked one:
- I am asking about if this concrete example is an example of gauge invariance?
- I am not asking what is gauge invariance in general.
- This is about invariance in CM and not in QFT or GR.
