Q:

Why is momentum conserved?

- Bob (age 19)

Seattle, WA, USA

- Bob (age 19)

Seattle, WA, USA

A:

This time your short question has a fairly short answer. Noether's theorem.

Let's assume something more intuitive than momentum conservation. We'll assume that there are no special points in space, that until you have some particular stuff somewhere all of space is really just the same. Then we stop and think about what momentum is. In quantum mechanics (which is, so far as we know, everything) momentum just means "spatial derivative" with some constants. It's really easy to derive that since there's no spatial derivative to the fundamental properties of space, any closed system of interacting stuff doesn't change its total momentum over time.

Now I haven't gone through the calculation for you here, but I think now you can find it easily if you look.

Mike W.

Let's assume something more intuitive than momentum conservation. We'll assume that there are no special points in space, that until you have some particular stuff somewhere all of space is really just the same. Then we stop and think about what momentum is. In quantum mechanics (which is, so far as we know, everything) momentum just means "spatial derivative" with some constants. It's really easy to derive that since there's no spatial derivative to the fundamental properties of space, any closed system of interacting stuff doesn't change its total momentum over time.

Now I haven't gone through the calculation for you here, but I think now you can find it easily if you look.

Mike W.

*(published on 06/09/2011)*