I am a mathematician and I asked this question briefly and my question became closed may be -I don't know- because physicist don't used to apply the method of "proof by contradiction". This is a very powerful method in many aspects and could give new intuition.

We know for sure that total momentum of every closed physical system is conserved (for simplicity take classical physics).

Noether's theorem says this conservation $(q)$ is result of this: every physical experiment is the same when we only translate our lab is space $(p)$.

So we have a inference like this: $$p \Rightarrow q$$ Proof by contradiction uses the logical fact this result is exactly the following: $$\sim p \quad \Rightarrow \quad \sim q.$$ Now let we want to prove conservation of momentum in every closed system. Let's the result is false, that is "SUPPOSE" there is a system by non-conservative momentum. Then to Noether's theorem be true we find "THERE IS" a physical experiment which alters by only spatial translation.

Could you design such an experiment explicitly? (of course by supposing that there is a system with non-conservative momentum. this is just a logical assumption and there is not such a thing in the real world.)

I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know  - because physicists don't used to apply the method of "proof by contradiction". This is a very powerful method in many aspects and could give new intuition.

We know for sure that total momentum of every closed physical system is conserved (for simplicity take classical physics).

Noether's theorem says this conservation $(q)$ is result of this: every physical experiment is the same when we only translate our lab is space $(p)$.

So we have a inference like this: $$p \Rightarrow q$$ Proof by contradiction uses the logical fact this result is exactly the following: $$\sim p \quad \Rightarrow \quad \sim q.$$ Now let we want to prove conservation of momentum in every closed system. Let's the result is false, that is "SUPPOSE" there is a system by non-conservative momentum. Then to Noether's theorem be true we find "THERE IS" a physical experiment which alters by only spatial translation.

Could you design such an experiment explicitly? (of course by supposing that there is a system with non-conservative momentum. this is just a logical assumption and there is not such a thing in the real world.)