# What is the relation between Noether's theorem and uncertainty relation? [duplicate]

According to noether's theorem, "if a system remains invariant under some translation then there exists a corresponding quantity which remains conserved."

E.g.

the invariance of physical systems with respect to spatial translation (x)(in other words, that the laws of physics do not vary with locations in space) gives the law of conservation of linear momentum(p);

invariance with respect to rotation (Ø)gives the law of conservation of angular momentum(l);

invariance with respect to time(t) translation gives the well-known law of conservation of energy(E)

But surprisingly these related quantities are related to each other by some other way also( p,x and E,t) i.e. uncertainty relation. Is this just a coincidence or some mechanism behind it?

Symmetry≈ conservation ≈ uncertainties?