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Most physics textbooks will introduce Newton's 2nd law as $$F = ma$$ or $$F = \frac{dp}{dt}$$ and I've seen educators that interpret this as "the product of mass and acceleration lead to a net force" or "the change in momentum leads to a net force". So they rather claim that more appropriate expressions of the 2nd law would be $$a=\frac{F}{m}$$ and $$\frac{dp}{dt}=F$$ thus implying a better sense of causality; that it's the force that comes first, and this is what leads to motion.

So my question is can the ordering of a physics mathematical model be such that it properly takes causality into account?

Or is there a more proper convention/notation to take causality into account?

docscience
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    How can this be anything other than a matter of opinion? FWIW my opinion is that Newton's first law is an experimental observation of correlation not causality. – John Rennie Aug 17 '16 at 14:31
  • I think this question may be well-placed in the maths educators SE. – lemon Aug 17 '16 at 14:34
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    I concur with JohnRennie that this is opinion-based, and also want to point out that physics doesn't have a formal notion of causation - all theories work perfectly well without ever once using the notions of "cause" and "effect". – ACuriousMind Aug 17 '16 at 14:35
  • Some have given a technical argument that $F=ma$ defines force. This would prefer the first form. Others point out what you point out: variables that describe the system on the right, the observed behavior on the left. I prefer this in introductory classes. Similarly I write Ohm's Law $I=V/R$ But I don't think there is a right way. – garyp Aug 17 '16 at 14:36
  • @lemon Mathematical equations know no order. Nature however does seem to have an order in which events occur. So how could you possibly refer this to a maths forum? – docscience Aug 17 '16 at 15:43
  • @JohnRennie you are probably right in saying the 2nd law is a correlation especially considering it's been superseded by Einstein. But interesting that I've never seen it taught in thee terms or written in the textbooks as a correlation. I wrestled with stating the question in terms of Does vs Should. Should is definitely opinion. Does can raise some arguments. Math is the language in which we describe the nature of physics, but by not considering cause and effect aren't we leaving out punctuation in the language? – docscience Aug 17 '16 at 15:52
  • @ACuriousMind Maybe as a pure physicist one may not be concerned about cause and effect. But engineers that apply the physics sure have to deal with it. Garyp's example: what comes first, current or potential? Well without potential you certainly won't have current. – docscience Aug 17 '16 at 15:54
  • @docscience Although we often talk about force 'causing' acceleration when we use the everyday sense of the word 'force', the equation F=ma does not capture causality. As this question appears to be locked I'll point you to my partial answer http://physicsfootnotes.com/force-does-not-cause-acceleration/, which may address your main concern. – Physics Footnotes Aug 17 '16 at 23:16
  • @PhysicsFootnotes I did read your foot note, and yes I agree in nature there are more equations to consider other than just inertia that make up the net force (compliance, friction, etc.) and so this constitutes a system. And you can categorize forces as either internal or external to the system. Can force cause motion? Yes. Can motion cause force? Yes. More fundamentally I suppose it's a matter of which direction the energy flows. And regardless of direction entropy increases. That's allot of physics, and not all captured by $F=ma$. So I guess in the end it just matters what part of the... – docscience Aug 18 '16 at 00:07
  • @PhysicsFootnotes ... physics one wants to be addressing. And that determines how many equations you write. – docscience Aug 18 '16 at 00:08
  • @docscience I think your question is important, and that's why I upvoted it. If the powers that be open your question for answers I have much more to say on the matter. Otherwise, the comments are not supposed to be for answering questions, so we'll see what they decide. – Physics Footnotes Aug 18 '16 at 00:33
  • @PhysicsFootnotes Thanks for the upvote. If your reputation is high enough, please also vote to reopen. – docscience Aug 18 '16 at 01:12

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