(ex) Nuclear physicist here... (computers pay better) The Wikipedia page isn't bad. https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org

(ex) Nuclear physicist here... (computers pay better) The Wikipedia page isn't bad. https://en.wikipedia.org/wiki/Noether%27s_theorem https://en.wikipedia.org/wiki/Noether%27s_theorem > Its Lagrangian is rotationally symmetric: from this symmetry, Noether's theorem dictates that the angular momentum of the system be conserved, Let me explain that in human terms. :) Let's take an example of a moon moving in a circle around a planet. (We're assuming a spherical cow here, as I know the orbit is actually an ellipse). If the gravitational well is rotationally symmetric, then the moons orbit has to go at the same rotational velocity, all around the circle. The moon can't change velocity willy-nilly, because something has to change the velocity, and we just said that the gravitational well is symmetric. Which means "smooth", and no "bumps" in it. On the other hand, if the rotational velocity changed, you'd know there has to be "bumps" in the gravitational well. Because something has to change the velocity. It's a simple concept in the end. If something happens, something else has to cause it. If there's a cause, there has to be an effect. Noether's principle is really the "next level" of cause and effect. If certain kinds of causes happen, then certain kinds of effects also have to happen. And if you see certain kinds of effects, you know they have to have certain kinds of causes. But it's sexier if you spin it with math words like Lagrangians and Hamiltonians. :)