Noether's Theorem is really something I found extremely beautiful as a grad student, I always felt like Emmy Noether didn't really get the recognition she deserved.
My favourite way of explaining Noether's theorem to non-physicists is to think of it in terms of portal guns. If you have a portal gun that can freely create instantaneous travel between points in space, you can clearly see how momentum and energy are not conserved anymore. In fact, that's pretty much every mechanic in the game is designed to exploit that.
If spacetime is no longer translation and time invariant, momentum and energy are no longer conserved. Of course, this is a bit of a circular argument but the converse statement is also interesting to think about. If you claim you have a perpetual motion/infinite energy machine, somewhere along the line translation and time invariance are no longer a thing.
My favourite way of explaining Noether's theorem to non-physicists is to think of it in terms of portal guns. If you have a portal gun that can freely create instantaneous travel between points in space, you can clearly see how momentum and energy are not conserved anymore. In fact, that's pretty much every mechanic in the game is designed to exploit that.
If spacetime is no longer translation and time invariant, momentum and energy are no longer conserved. Of course, this is a bit of a circular argument but the converse statement is also interesting to think about. If you claim you have a perpetual motion/infinite energy machine, somewhere along the line translation and time invariance are no longer a thing.