I was looking through some reference material, and I came across this:
In the situations in which we cannot follow details, we need to know some
general properties, that is, general theorems or principles which are consequences
of Newton’s laws. One of these is the principle of conservation of energy, which
was discussed in Chapter 4. Another is the principle of conservation of momentum,
the subject of this chapter.
According to the text, energy and momentum are conserved as a consequence of Newton's Third Law.
But then I did some searching and it seemed that the conservation laws were much more fundamental than Newton's Third Law. The sources suggest that the action-reaction pairs are necessary for momentum to be conserved, so they are a consequence of the conservation of momentum.
Which is a consequence of which? Will it be right to treat one as a consequence of the other?
Best Answer
As far as the actual physics is concerned, it is meaningless to talk of whether conservation of momentum is "more fundamental" than Newton's third law -- you can axiomatise classical physics in either way -- from Newton's laws, from conservation laws, from symmetry laws, from an action principle, whatever. You can prove the resulting theories are equivalent, in the sense that all the alternative axiomatic systems imply each other.
In terms of understanding, it makes sense to have multiple different frameworks in your head -- a symmetry-based framework is really good intuitively, especially once you understand Noether's theorem, while an action principle is the most powerful and also more useful when you leave the realm of classical physics. Treating Newton's laws as axioms isn't a great idea -- it's mostly just historically relevant.
When you learn more advanced physics, conservation of momentum will start "feeling" more fundamental -- this is simply because momentum is an interesting quantity to talk about.