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?

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    $\begingroup$ 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. $\endgroup$ Aug 17 '16 at 14:31
  • $\begingroup$ I think this question may be well-placed in the maths educators SE. $\endgroup$
    – lemon
    Aug 17 '16 at 14:34
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    $\begingroup$ 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". $\endgroup$
    – ACuriousMind
    Aug 17 '16 at 14:35
  • $\begingroup$ 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. $\endgroup$
    – garyp
    Aug 17 '16 at 14:36
  • $\begingroup$ @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? $\endgroup$
    – docscience
    Aug 17 '16 at 15:43