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What is the absolute Logical origin of Newtons three axioms? Have physicists worked out what is the fundamental reason for actio = reactio and other things?

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    $\begingroup$ There is no "logical origin" for axioms of physical theories. After all, physics is still an experimental science. $\endgroup$ – ACuriousMind Feb 24 '16 at 18:14
  • $\begingroup$ and because it is experimental we have still to assume that These laws of mechanics come from god? $\endgroup$ – kryomaxim Feb 24 '16 at 18:16
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    $\begingroup$ You can easily find papers and texts written on the topic of axiomatic mechanics; one random example that you may find interesting is arxiv.org/abs/1205.2326, "Foundations of Newtonian Dynamics: An Axiomatic Approach for the Thinking Student." No branch of physics is truly axiomatic, for it is all founded on experiment, and our "physical laws" are almost certainly approximations. $\endgroup$ – Peter Diehr Feb 24 '16 at 18:31
  • $\begingroup$ Newton's laws aren't axioms. They are short hand notation for a large class of observations, but curiously you can't even make those observations here on Earth. To find a place where Newton's laws hold, you need, at least, a vomit comet or, better, a spacecraft in low Earth orbit. $\endgroup$ – CuriousOne Feb 24 '16 at 20:40
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As pointed out in the comments, there is no known absolute logical ground from which all the three of the Newton's Laws come. All the three of them are completely Experimental. Although there is certainly a great and absolutely brilliant theoretical work done by Newton in order to express the experimental facts expressed in them. But we certainly don't have to assume that they come from God. That is what Physics is about - we keep on finding and finding and finding. We find more and more fundamental and underlying laws and replace the old ones with these new ones. Maybe one day we can come up with an absolutely logical ground from which all of the Physics flows naturally. But we don't know for sure that it will happen or it has to happen.

FYI: Action Reaction law has not a logical requirement of any tautology or something. Proof: It is an invalid law for so many electromagnetic system.

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Newton did in fact have theoretical reasons to believe his first two laws were correct. They implement what we call the principle of relativity, which is really the deepest physical axiom of them all. Roughly speaking, the principle is about coordinate systems that we call inertial reference frames. The principle states that the laws of physics should be the same for any observer/experimenter, regardless of the inertial reference frame he happens to be in.

Without going into too much detail, Newton's first law tells us how to decide when we are actually in an inertial reference frame (This is the case if objects keep constant velocity if no net force is applied to them). The second law tells us what happens when we try to compare experimental results by two observers who are in different inertial reference frames. (e.g. the forces don't change because they are proportional to acceleration and the acceleration is the same in all the inertial reference frames. Therefore $F=ma$ holds good in every inertial frame.)

I have yet to meet a physicist who doubts the validity of the principle of relativity. There is, however, more than one way to implement the principle of relativity (Einstein's special relativity is one such example). The experiments to check if Newton's laws hold are therefore essential. So, even though Newton had the principle of relativity on his side to guide his arguments, the experiments ultimately decide what is correct and what is not.

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