If there's a Charge distribution 4 Light-years away, static, we have a distinct value of Electric Field and Electric Potential where I'm measuring it through some wack-a-doodle apparatus at my home on earth.
Suppose I changed that charge distribution in an instant , it will take 4 years for the apparatus at my home to detect there's a change in Electric Field because photons are the mediators of the Electric Forces and Fields!
But what bout the Electric Potential? Is its change instantaneous? Or will it take 4 years? Or more? Or less?
If it's instantaneous, how so? Because the derivative of something instantaneous must not be taking 4 years for propagation! If it's 4 years or more or less, how so? Photons have nothing to do with Potentials! Or does it?
And what is the qualitative definition of potential?
I am looking for a deeper answer, rather than just "potential is the ability to do work".