
#19
Feb413, 08:22 AM

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P: 14,477

Andrew, I see from your profile that you're a lawyer by profession, which is a field where going back to original sources (precedence) is very important. Going all the way back to Newton to understand Newtonian mechanics is not a particularly good idea. Going all the way back to any original writing in the sciences is in general not the best way to gain understanding of that topic. This is one of the key differences between science and liberal arts. Those original writings almost inevitably are obtuse and verbose, and are occasionally mistaken. They are not viewed as authoritative in the sciences.
Newton was no different. He intentionally conflated force and impulse, and he intentionally avoided using algebra and calculus in his Principia. He didn't use vectors. (How could he have? Vectors came 200 years after Newton wrote his Principia.) You're much better off using a modern formulation of Newtonian mechanics. As far as the primacy of Newton's third law versus the conservation laws, yes, one can derive conservation of momentum from Newton's third law. However, one can also derive Newton's third law from the conservation laws with the additional assumptions that forces act instantaneously and can be attributed to pairs of objects. What if forces those assumptions are violated  forces that don't act instantaneously (e.g., electromagnetism) or forces that cannot be isolated to pairs (e.g., the chiral three body forces in ^{3}He nuclei)? You don't get Newton's third law. The conservation laws are now seen as more the basic concept (and Noether's theorems being even more basic), with Newton's third law being a special case where those limiting assumptions are valid. 



#20
Feb413, 09:46 AM

Sci Advisor
PF Gold
P: 11,396

There is surely another point to be considered here. A charge (or mass) in a field will be distorting and affecting that field. You can't pick which of two charges is going to be 'the charge' with the other one the 'field provider', without a bit of a risk. I know that's what is done when we talk in terms of fields but aren't there some questions to be asked about this?
If we acknowledge the conservation of momentum then shouldn't we be bending this 'particle in a field' treatment to include it  rather than the other way round, and trying to demonstrate that momentum isn't always conserved? I realise it's all only a model but if we can discard momentum conservation in a trivial example like two electrons going past each other, then we may as well forget about the principle altogether. Newton may have been a massive, grumpy ego but I'm sure he wouldn't have been too surprised to be told that, hundreds of years later, his very simple laws may not be adequate for all cases. 



#21
Feb413, 10:08 AM

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P: 16,485




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