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In the comments for the question Falsification in Math vs Science, a dispute around the question of "Have Newtonian Mechanics been falsified?"

That's a bit of a vague question, so attempting to narrow it a bit:

  1. Are any of Newton's three laws considered to be 'falsified theories' by any 'working physicists'? If so, what evidence do they have that they believe falsifies those three theories?

  2. If the three laws are still unfalsified, are there any other concepts that form a part of "Newtonian Mechanics" that we consider to be falsified?

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"Falsified" is more philosophical than scientific distinction. Newton laws have been falsified somehow, but we still use them, since usually they are a good approximation, and are easier to use than relativity or quantum mechanics.

The "action at distance" of Newton potentials has been falsified (finite speed of light...) but again, we use it every day.

So, in practical terms, no, Newton laws are still not falsified, in the sense that are not totally discredited in the scientific community. Classical mechanics is still in the curriculum of all universities, in a form more or less identical that 200 years ago (Before Relativity, quantum mechanics, field theory).

Most concept in physics fit more in the category of "methods" rather than "paradigms", so can be used over and over again. And all current methods and laws fails and give "false" results, when used outside their range of applicability.

The typical example of "falsified" theory is the Ptolemaic system of Sun & planets rotating around the Earth. However, philosopher usually omits the facts that:

  • Ptolemaic system was experimentally pretty good at calculating planet motions
  • Most mathematical and experimental methods of the new Heliocentric paradigm are the same of the old Ptolemaic

So the falsification was more on the point of view, rather than in the methods.

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    $\begingroup$ Well, we can measure that the Earth is rotating, against Ptolemaic system. But yes, we can still write ( with a lot of patience) all physics from our rotating system, with a lot of "fictitious" forces. $\endgroup$ – patta Apr 12 at 9:30
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    $\begingroup$ Note that both general mechanics and quantum mechanics are just as false as Newtonian mechanics, in a certain sense. QM fails to predict gravitational lensing, and GR fails to predict interference patterns in the double slit experiment. Both fail to explain how black holes preserve information. (one says they don't, the other says they don't exist) $\endgroup$ – John Dvorak Apr 12 at 10:04
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    $\begingroup$ @piet.t That's a common misconception. Ptolemy's model actually makes physically different predictions. Note that Venus is always between the Earth and the Sun in the Ptolemaic model, but not in reality. Galileo's observation of the phases of Venus, showing Venus fully illuminated by the sun, falsified the Ptolemaic model. $\endgroup$ – Denziloe Apr 12 at 11:08
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    $\begingroup$ 99 c = 1 \$ $\pm$ 2% $\endgroup$ – patta Apr 12 at 18:41
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    $\begingroup$ @piet.t, the Ptolemaic system predicts that the fixed stars remain in the same relative locations at all times. Heliocentric models predict that they'll show annual variations in their positions relative to each other. High-precision observations of stellar positions show both parallax and aberration of light, which rather falsifies the Ptolemaic system (and almost all other geocentric systems). $\endgroup$ – Mark Apr 12 at 20:47
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Newtonian Physics is accurate in the specific domain it was designed for

Physics is not about identifying the "truth" of the world around us. It's about creating mathematical models that allow us to accurately predict the behavior of the world.

Nobody is trying to create a perfect model, because the complexity of such a model would be infinite. Instead, we look for the boundaries of a model's accuracy - under what conditions it produces reasonable results, and the precision of the results it produces under those conditions.

You can see this more clearly with other physics models, such as the Ideal Gas Law. The Ideal Gas Law models a hugely complex system of particle collisions as a simple formula of ratios. It breaks down relatively quickly at high or low values of any of its quantities, but because we understand when and how the law breaks down, it is still useful.

At extremely large quantities (large speeds, large masses, high energies), the Newtonian model starts to break down, and we need to use a Relativistic model in order to get accurate results. But that doesn't mean that the Newtonian model is false, it just means that it is inapplicable for those conditions.

Obviously, Newton wasn't aware of the limitations to his laws when he described them. He was trying to create a universally applicable set of relations. In that sense you could argue that he failed. But I would consider the modern understanding a refinement of his laws, rather than a falsification.

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    $\begingroup$ Avoids answering the question... $\endgroup$ – Rob Jeffries Apr 13 at 16:53
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    $\begingroup$ This is the modern understanding, but I don't think it is true to say that Newton's laws were designed (by Newton, at least) for slow speeds and mild gravitational curvatures. $\endgroup$ – Rococo Apr 13 at 19:36
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    $\begingroup$ This answer would probably make more sense if "designed for" was replaced with "conceptualised within". $\endgroup$ – Ian Kemp Apr 13 at 22:37
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    $\begingroup$ @IanKemp I would've awarded a bounty on this comment if it were a feature! I mean, of course, Newtonian mechanics was designed for everything. It was just conceptualized within a certain regime of experiments. And it is not in the spirit of science to actually design a theory for the regime in which the experimental results are already known. A scientific theory has to make predictions and that means that it necessarily has to go beyond the domain from which it takes empirical inspiration. $\endgroup$ – Dvij Mankad Apr 13 at 23:33
  • $\begingroup$ When Newton was studying Kepler's work, he probably wasn't wondering if he could apply it to the $1s$ orbital of the hydrogen atom. $\endgroup$ – Cinaed Simson Apr 15 at 20:16
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One of the problems of Newton's law of universal gravitation, $$F_\text{Grav} = G \frac{m_1m_2}{r^2},$$ is that it does not correctly describe the precession of Mercury's orbit. Mercury behaves slightly different than predicted by Newton's law and general relativity does a better job.

See also the corresponding Wikipedia article.

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    $\begingroup$ When you say "Newton's Laws", which do you mean exactly? There are laws for inertial motion, action/reaction, force as dp/dt, and gravity. I believe only the last one could be seen as needing modification by General Relativity. $\endgroup$ – Jens Apr 13 at 10:55
  • $\begingroup$ Indeed Mercury's elliptical orbit slowly rotates by a tiny amount extra than what Newton's gravity predicts. However people generally underemphasise other precession effects: 5000 "/c [seconds of arc per century] from precession of the equinoxes, and 530 "/c from other planets, compared with the observed 43 "/c extra that general relativity (and other gravity theories) explains. So Newtonian gravity is correct to within less than 1% error, in explaining the precession of Mercury's orbit. $\endgroup$ – Colin MacLaurin Apr 17 at 1:50
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Relativity is an extension of Newtonian physics, not either a replacement or correction. As such, relativity does not "falsify" Newtonian physics. For velocities far smaller than the speed of light (approaching zero), relativity simplifies back to the Newtonian model. For everyday use, and for everyday engineering problems, Newtonian physics is more than accurate enough. It's only when you get into more "interesting" situations that Newtonian physics fails to provide adequate solutions. The orbit of Mercury is a famous one. It's only because of Mercury's proximity to the Sun that its orbit defies accurate modeling in purely Newtonian terms. Similarly, without an understanding of relativity and relativistic effects on orbiting spacecraft, the GPS system could not work (the onboard timekeeping of the GPS satellites must be extremely precise and the very small relativisitic effects on their clocks must be accounted for). These are not everyday situations, and the relativistic effects are small, but the position of Mercury can be very precisely measured and GPS signals are timed with very high precision (light/radio travels about a foot or about 30cm in a nanosecond).

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  • $\begingroup$ This answer seems to flip between two contradictory viewpoints. You say relativity is an "extension" of Newtonian physics, not a replacement or correction; but then proceed to talk about Newtonian physics "failing to provide adequate solutions" unless relativity is accounted for. Wouldn't that make it a "correction" to Newtonian physics in most senses of the term? I wouldn't consider new information that makes all prior information slightly inaccurate an "extension"; I would specifically call it a correction; because it corrects the errors in Newtonian physics. $\endgroup$ – JMac Apr 15 at 16:08
  • $\begingroup$ @JMac I stand by my core point that relativity is an extension not a correction because of the way the relativistic terms cancel out (leaving the simplified Newtonian forms) as velocity approaches zero (or the comparable terms which relate to curvature of spacetime due to mass). $\endgroup$ – Anthony X Apr 15 at 23:37
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First of all no scientific theory can possibly be falsified. Popper was wrong. See the Quine-Duhem thesis which says that instead of rejecting the theory when a seemingly falsifying experiment occurs, one can always instead reject some underlying "auxiliary hypothesis". The perfect example of this is how when experiments came out seeming to indicate neutrinos were moving faster than light no serious scientists actually believed the neutrinos moved faster than light, rather, all the scientists rightly believed that there must have been something wrong with the experiment.

Now to answer your questions.

  1. Are any of Newton's three laws considered to be 'falsified theories' by any 'working physicists'? If so, what evidence do they have that they believe falsifies those three theories?

Despite what I said above the answer to your question is yes. This is because 'working physicists' are generally not good philosophers of science and many 'working physicists' incorrectly think Poppers program of falsification is correct. Working physicists aren't good philosophers of science because philosophy of science doesn't really help them do their job better and they simply may not find it that interesting, so if they hold misconceptions about philosophy of science it doesn't cause any problem whatsoever in their daily work.

  1. If the three laws are still unfalsified, are there any other concepts that form a part of "Newtonian Mechanics" that we consider to be falsified?

No. As I said above no physical theory can be falsified.

Here's some information about Imre Lakatos who has a better philosophy of science in my opinion than Popper.

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    $\begingroup$ I carry no water for Popper, but a statement like "no scientific theory is ever falsified" does not seem to me to be an actual description of what scientists think and do (as you have noted), and I question a theory of science that says that most scientists don't do science. $\endgroup$ – Rococo Apr 13 at 19:40
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    $\begingroup$ @Rococo I won't make any claim as to what percentage of scientists will say falsification is how science works because I've never done or seen a survey. I will point out that one can be a productive scientists regardless of ones opinions about philosophy of science. I would argue that all good scientists (even those who believe in falsification) do not actually do their science by trying to falsify things. Instead they do what all good scientists do: $\endgroup$ – jgerber Apr 13 at 21:37
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    $\begingroup$ They mess around with their theories and experiments seeing which theories work under which conditions, they try to figure out why and when theories break down, they generate new theories if necessary. The question is: does this theory explain what I am seeing? Why? Why not? What does it mean if this other theory also describes what I am seeing? $\endgroup$ – jgerber Apr 13 at 21:40
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    $\begingroup$ No where did I say that most scientists don't do science. All I said was that many scientists have misconceptions about philosophy of science but I was careful to point out that a scientists thoughts on philosophy of science have very little bearing on his or her aptitude as a scientist. $\endgroup$ – jgerber Apr 13 at 21:42
  • $\begingroup$ I apologize for mischaracterizing your position. Nonetheless, I am not personally convinced that, for example, 'all good scientists (even those who believe in falsification) do not actually do their science by trying to falsify things.' To be clear, I would neither make the extreme opposing claim that science is all about falsifying theories. $\endgroup$ – Rococo Apr 13 at 22:56
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No, they are not considered falsified. They are still a valid low energy approximation, which is all they ever were claimed to be. Or, if you must, they have been falsified at very high energies only.

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    $\begingroup$ Did Newton claim his laws were a low energy approximation? I doubt it. $\endgroup$ – user253751 Apr 15 at 5:49
  • $\begingroup$ @immibis he claimed his laws explained the solar system. That claim has not been falsified apart from extremely tiny deviations. $\endgroup$ – my2cts Apr 15 at 6:36
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    $\begingroup$ @my2cts Newtonian mechanics wasn't created to work "apart from extremely tiny derivations". It was created and applied to work at all scales. That's why we had to develop beyond classical/Newtonian mechanics when the model was no longer accurate. They were not as widely applicable as was originally thought. $\endgroup$ – JMac Apr 15 at 16:13
  • $\begingroup$ @JMac "as originally thought" Can you tell where in "Opticks" speeds of the order of 300.000 km/s are considered? Where an accuracy of 43 arcsec per century was claimed? $\endgroup$ – my2cts Apr 16 at 19:40
  • $\begingroup$ @my2cts Can you show where he mentions that it's only exact when velocity is zero? I don't believe he states anywhere the assumptions that this doesn't apply at particular scales, or anything of the sort. All the evidence suggests that the physical laws he derived were to apply at all scales and velocities, and none of what he wrote that I'm aware of ever tried to mention that it was only an approximation for low energy. $\endgroup$ – JMac Apr 16 at 19:46

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