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Before you close this has a duplicate !

I've read some the related posts on this - but I have slightly different question.

A lot of posts on stack exchange have demonstrated that Newton's laws can be derived / or proved

(A couple of posts have shown that you could derive the 3rd law and potentially the first from the 2nd).

But the 2nd is almost always referred to as an axiomiatic law - i.e. something that is believed to be true - on who's foundation Newtonian mechanics is built.

I'm aware that it has been experimentally proved - in school laboratories countless times (at small scales) etc,.

But - do we have any understanding of WHY this law holds? Is this something fundamental about the universe that it tells us or is the best explanation that it is an approximation of relativistic mechancics at sub-speed of light time frames.

So my question is:

"Why are Newton's Laws true - what does it tell us about space, time and matter - and is there any way to develop any more fundamental "laws" that are grounded in more "lower level" axioms. For example - Euclidean Geometry is built on a relatively small set - 5 of axioms - that most of us would intuitively believe to hold true on a plane http://en.wikipedia.org/wiki/Euclidean_geometry#Axioms " - are there any similar axioms that could underpin Newtonian (or indeed Lagrangian / Hamiltonian) Dynamics.

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    $\begingroup$ Why they are true is probably more Philosophy than Physics, which can only simply observe that they do hold (in their appropriate cases). $\endgroup$ – Kyle Kanos Jan 10 '17 at 19:00
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    $\begingroup$ Laws in physics are the necessary "axioms" that connect observations with a predictive mathematical model, in this case classical kinematics $\endgroup$ – anna v Jan 10 '17 at 19:01
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    $\begingroup$ Suggest migrating to god.stackexchage.com $\endgroup$ – garyp Jan 10 '17 at 19:20
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    $\begingroup$ What if you thought about $F = ma$, not as a "Law" that nature must obey, but instead as a definition of 'force'? $\endgroup$ – DilithiumMatrix Jan 10 '17 at 21:02
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    $\begingroup$ Euclids "axioms" for geometry are not at all rigorous. Almost every proof in the Elements involves looking at a diagram and making "common-sense" deductions that are not covered by the axioms. See Hilbert's "Foundations of Geometry" archive.org/details/abr1237.0180.001.umich.edu for a more rigorous version using 21 axioms, not 5. $\endgroup$ – alephzero Jan 11 '17 at 1:18
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Physical "laws" are mathematical models intended to reproduce, to some level of accuracy, the quantitative and/or qualitative behavior of a real system or systems.

But physical "laws" are just models. The rules underpinning the model are chosen specifically to reproduce the desired behavior. Other rules are rejected because they do not reproduce the desired behavior in the model.

As it happens we use mathematics to do the modeling. As it happens that has worked so far and we have refined our theories as best we can using this approach.

In a sense Newton's laws are true in that they reproduce the behavior of many real world systems to within a reasonable accuracy.

In a sense they are also not true, because they do not reproduce behaviors of real world objects accurately enough in all situations.

Similar statements could be made for all the current theoretical models we use. It would be nice to think that there is a single model of the way everything in the universe operates that has unlimited accuracy. But we don't know of such a model and we have no guarantee that such a model is possible.

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  • $\begingroup$ I will repeat my comment at the question level, :Laws in physics are the necessary "axioms" that connect observations with a predictive mathematical model, in this case classical kinematics $\endgroup$ – anna v Jan 10 '17 at 19:03
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A law is "true" if it can be used universally to predict the outcome of experiments (within reason).

Along the way, the causal relationships between quantities that are expressed in a law acquire interpretation that says more about how our brain works than how the universe works.

Newton's laws were successful in predicting the motion of celestial and earthly objects by unifying the formulation of mechanics and gravity. But it is all a facade in some ways because when looking at sub-atomic particles, or at galactic scales or at high energy situations (or high gravity situations) the laws don't work anymore universally.

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  • $\begingroup$ PS. Personally I think a grand unified theory doesn't exist. $\endgroup$ – John Alexiou Jan 10 '17 at 20:12
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    $\begingroup$ Comment to your PS: There are plenty of grand unified theories. They clearly "exist". What you don't believe to exist is one that works on the phenomenological level. We have tons of GUTs, but none of them works properly. $\endgroup$ – AccidentalFourierTransform Jan 10 '17 at 20:18
  • $\begingroup$ @AccidentalFourierTransform thank you for the clarification. $\endgroup$ – John Alexiou Jan 10 '17 at 20:22

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