As part of a science project, I have to give a presentation to my classmates about a topic of my choice (within some constraints) – and I chose symmetry, and it's importance in physics. One important aspect that I think must be talked about is Noether's Theorem.

Now, of course the statement of the theorem itself is very impressive, but I feel like it lacks intuitional backing. I could go up there are start talking about infinitesimal transformations of fields, but even that gets very complicated very quickly (and the mathematics can't be over an Algebra 1 level or I'll completely lose them).

What I'm instead thinking is taking one specific example of a system, and showing that if some symmetry is true, then something else is conserved.

But I can't think of any examples. Is there any specific example of a system where it is easy to explain why translation symmetry implies conservation of momentum in that system, or some other symmetry implies some other conservation? If not, how can I go about demonstrating Noether's Theorem in an intuitive way to a class of 8th graders?

## Best Answer

Explaining Noether's theorem to 8th graders may be hard, as even the simplest special case of the theorem requires some calculus to state. However, if we're talking about why one example of an invariance corresponds to one example of a conservation law, there are some calculus-free arguments you can make. I'll mention one example, energy (whose conservation law is a little different from the others); hopefully others will follow.

Imagine if the laws of physics or parameters therein varied over time; imagine, for example, if gravity became stronger tomorrow. Today, lift an object onto a shelf, which requires some work equal to the GPE it's gained. Lower it to its previous position tomorrow, when gravity is stronger. The GPE loss will exceed the GPE gain today. Boom! You've made energy out of nothing.