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- Why does Newton's Third Law actually work? 10 answers
I can sort of see why Newton's third law makes sense, since if I sit on an office chair and push at my desk, I move away from it. Apparently this happens because when I push the desk, the desk pushes me back with an equal and opposite force. I've been told that Newton came up with his law through similar experiences. But why must Newton's third law be true in the sense he defined force in his second law? While I can believe that when I push something, I'm also being pushed back, but why is it that the product of mass and acceleration must be the same for both of us (except for the sign)? I've asked this before and I've been shown that it works because of conservation of momentum in collisions. But this seems circular, as usually I have seen conservation of momentum in collisions derived using Newton's third law.
EDIT: I'm aware that there are other ways to produce conservation of momentum as a whole, such as Noethers theorem, but I'm more interested in knowing how the third law was thought of in Newton's time.