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The way I have seen in presented, Newton's First Law is an empirical observation. Therefore, it seems plausible that it is not true in all cases. Have there been any attempts to seek out violations and/or is there some reason no attempts have been made?

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  • $\begingroup$ It depends on what you mean by "violation". Strictly speaking gravity violates Newton's first law because there is no measurable force on a body in free fall in a gravitational field and yet that body does not move in a straight line. Is Newton's theory wrong? Yes. That's why we had to invent general relativity to deal with gravity. $\endgroup$ Oct 18, 2022 at 15:49
  • $\begingroup$ @FlatterMann What does "measurable force" mean here? Newton himself (approximately) measured gravitational forces, no? $\endgroup$
    – user37344
    Oct 18, 2022 at 16:04
  • $\begingroup$ @FlatterMann, Newton probably is remembered best for how his "laws of motion" explained both the motion of things on Earth, as well as the motions of heavenly bodies (i.e., His laws explained the orbits of planets and their moons in the Solar System.) Gravity is regarded as a force in Newton's system. Einstein's system, which does not regard gravity as a force, gives slightly more accurate predictions, but the difference, as it affects bodies like Mercury within our own Solar System, is so small that it took years before the scientific community accepted that Einsten's really was better. $\endgroup$ Oct 18, 2022 at 16:11
  • $\begingroup$ All physical laws are based on empirical observation. A physical law is a mathematical description of how things seem to behave which, sometimes within some specific conditions such as, within an inertial coordinate system, has always proven to be true. $\endgroup$ Oct 18, 2022 at 16:16
  • $\begingroup$ There is no measurable force of gravity on a body in freefall. The sun does not exert a force on Earth's center of mass. That is exactly the problem with the Newtonian description of gravity. We can measure a force between us and the floor that keeps accelerating us upwards at 1g, but that is not the force of gravity. That is the force of the floor that keeps us from falling freely. I know, it's confusing to live in a non-inertial system. $\endgroup$ Oct 18, 2022 at 19:51

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Newton's first law is most commonly violated in non-inertial reference frames. Often, rather than considering the law to be an empirical observation, people instead consider it to be the definition of an inertial frame.

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  • $\begingroup$ Two questions: (1) When you say mostly, am I to infer that it can be violated within an inertial reference frame? (2) I'm struggling to re-frame my question under this definition, but there must be an empirical finding for this reasoning to not be circular. Maybe the question is "why do we believe there are inertial frames at all" or something like that? I'm not sure, but it either reflects some aspect of physical reality or it doesn't. $\endgroup$
    – user37344
    Oct 18, 2022 at 16:03
  • $\begingroup$ @user37344 by "most commonly violated" I meant that in non-inertial frames there are sometimes specific locations in the frame where Newton's first law is not violated. For example, a point particle along the axis of a rotating frame. I cannot help with your (2) since I don't see circularity as a big deal. I will take circular reasoning which is consistent with observation over non-circular reasoning which is inconsistent with observation any day. Circular reasoning also has the benefit of being self consistent $\endgroup$
    – Dale
    Oct 18, 2022 at 16:08
  • $\begingroup$ I guess my point is that the term "consistent" with observation is meaningless if your claim is circular. Hook's law: ma = -kx is a testable claim. Whereas a circular statement like ma = ma can't be tested against anything. It's true by construction. $\endgroup$
    – user37344
    Oct 18, 2022 at 16:13
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    $\begingroup$ @user37344 That is not necessarily the case. It is quite possible to come up with circular reasoning that is not consistent with observation. I can say the earth is flat therefore horizontal distances on the surface of the earth are given by $ds^2=dx^2+dy^2$ therefore the earth is flat. That is circular reasoning that is inconsistent with observation. But you are right that definitions cannot be tested, they are true by definition/construction. In any case, I don't mean to derail your question with a tangent in comments. I just won't be able to help with the circularity thing as I said $\endgroup$
    – Dale
    Oct 18, 2022 at 16:52
  • $\begingroup$ @Dale, Your contrasting circular reasoning, and inconsistency with observation is a false alternative. In Physics we need both: i) noncircular reasoning and ii) agreement with experiments. Missing ii) we are not speaking about our world. But missing i) we lose contact with what we are discussing. The consequence in Physics is that we do not know how and what we have to measure to ensure ii). $\endgroup$ Oct 19, 2022 at 13:46
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Scientific explanations operate, roughly, in two separate levels of understanding: the framework and the model.

Newton's first two laws are best understood as trying to provide an explanatory framework. Frameworks are the playgrounds in which models play. Without phrasing a model within a framework, that framework makes no predictions about the world. In turn the explanatory framework is compatible with all manner of observations, and cannot be disproved by observation.

Newton's explanatory framework is, roughly, to say “In the past, it seemed obvious that whenever something was moving there was a force which explained its motion, and you might therefore have defined $\sum_i F_i = mv$ or so. However after the work of Galileo it seems like a ball set in motion will roll across a level floor indefinitely, and I choose not to explain this tendency in terms of a ‘force’ anymore, but just take it as the natural state from which all deviations must be explained. Instead of a force being a disposition to move, I define a force as a disposition to accelerate, $\sum_i F_i = m~ \mathrm dv/\mathrm dt.$ When things are moving with a constant speed in a straight line, that requires no explanation other than the forces are balanced, when things deviate from the straight line that is where we speak of forces causing them to deviate.”

Now, what falsifies an explanatory framework like this? That is more subtle. Frameworks get falsified, as they get clumsier to use. So for example, one thing that would have made this very hard to use is if you could not use vector summation to analyze multiple forces acting on a single particle. The two laws would not care: you would say that “you have force A, and force B, but oh, whenever you have both of those forces there is the nonlinear coupling force AB which must also be considered in the resulting sum.” But in practice this would be very tedious to work with and people would try to find a simpler way to describe the world.

Or, let's take the things that actually falsified it. Quantum mechanics, to start: the above framework says you should understand the phenomenon of Heisenberg uncertainty as “as you confine a particle to a smaller and smaller box it increasingly feels a random-looking interaction with whatever box-walls-forces you are imposing. However do not be fooled as the interaction seems to have many correlations with a global-hidden-variable reality which prevents it, for example, from violating conservation of energy in the long run, even as over short times we find particles escaping their potential wells that should have confined them.”

Heisenberg chose to try and preserve Newton's laws by instead promoting all of these vector components—force in the x direction, momentum in the y direction, x-coordinate of position, etc.—to be matrices over an unknown vector space using complex numbers. This allowed him to understand Heisenberg uncertainty as $x~p_x\ne p_x ~x$, for the usual real numbers order does not matter, but for these physical observables maybe it does. He made a very good attempt! We still use it to understand real systems, it is a working restatement of the core of the Schrödinger equation. But you can see in $x~p_x\ne p_x ~x$ the sort of thing which eventually falsified Newton’s first two laws. (That and special relativity.)

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  • $\begingroup$ Would it be more correct to say that Newton’s laws/framework is sometime “unusable” rather than “wrong?” $\endgroup$
    – user37344
    Oct 20, 2022 at 14:45
  • $\begingroup$ Yes, “wrong”/“falsified” becomes a poor choice for scientific theory. For example the Copernican revolution is a wash: you can, in Newtonian mechanics, put the Earth at the center of the universe. It requires what we'd call a “fictitious force” from the “non-inertial” character of the reference frame, but you can just take that force as “real” and be happy. And “epicycles” are just a Fourier transform, which you can always do. It's not even “unusable,” you can use it just fine, it just takes a lot more effort than the easiest way. $\endgroup$
    – CR Drost
    Oct 20, 2022 at 16:11
  • $\begingroup$ An even better analogy than “unusable,” would be that theories are in competition with each other, and reproduce by facilitating the publication of scientific papers—so a biological metaphor for theory-choice. In philosophy of science these ideas are associated with Imre Lakatos’ “methodology of research programs.” $\endgroup$
    – CR Drost
    Oct 20, 2022 at 16:18
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Principles in Physics are not always a compact summary of direct experiments. It is perfectly valid to introduce as a principle (law) some statement not directly amenable to direct measurements but such that its consequences are. It is enough to think of the case of Maxwell's equations, the laws of electromagnetism. Nobody checks or has checked them by measuring directly the $div$ or the $curl$ of vector fields but rather by extracting the measurable consequences of the equations for the fields on the motion of charged particles.

In a similar way, the validity (or violation) of Newton's laws as principles of dynamics is verified every time we compare predictions about the motion from knowledge of forces and initial conditions and experimental values of real motions.

Newton's laws have no unconstrained validity. Each of them, in a sense, is violated in specific conditions. However, in order to identify the cases of violation, one needs to start with an explicit statement of each law. This is an important step because there is more than one version of "Newton's laws."

In particular, with reference to the First Law,

  • if it is stated as Newton did as a body on which no net force is acting moves uniformly, we need to clarify what definition of force we are using. If we state that forces are only due to interactions with other bodies, @Dale's example is enough.
  • if it is stated (as in Landau&Lifshitz textbook on Mechanics) as a statement about homogeneity and isotropy of the configuration space of an isolated body, we need to verify such symmetries;
  • if it is stated as a claim on the existence of special reference systems, we have to characterize them, and we need to verify, on the basis of measurements, how inertial is a specific reference frame.

It should be evident that the final answer to the original question depends on the exact wording of the First Law.

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