In continuation of another question about Noether's theorem I wonder whether there exists some kind of relationship between this theorem and the Heisenberg uncertainty principle.
Because both the principle and the theorem relate energy with time, momentum with space, direction with angular momentum. When this is a general fact then e.g. electrical charge and electrostatic potential(*) should be partners in an uncertainty relationship too. Are they?
I feel that these results look so basic and general that I hope that a pure physical reasoning (without math or only with a minimal amout of math) exists.
Also compare this question where again momentum and space are connected, this time through a Fourier transform.
(*) i.e. electric potential and magnetic vector potential combined.