Talk:Newton's laws of motion

Is the so-called "modern form" of Newton's second law compatible with Newton's authentic law?

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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The article introduces the second law in the modern form F = ma. Newton's authentic law, however, reads that the force F is not "equal" but proportional to its effect on the motion of the body on which it is impressed. Provided that this effect should be correctly measured ma, the authentic law of Newton would read F ~ ma, or, algebraically, F = ma times constant of proportionality. As this constant is missing in the "modern form", it must be inferred that this form is not compatible with Newton's authentic law, in other words: it is not Newton's law, and "classical" mechanics, which is undoubtedly based on F = ma, is not Newtonian mechanics. This should be mentioned, to say the least. 2003:D2:9724:5375:5978:EDD7:4D63:85CD (talk) 16:32, 17 October 2024 (UTC)

If you have a source to support this claim, post it. Otherwise I will go on assuming that mass is defined as the proportionality constant implied by Newton. Johnjbarton (talk) 16:44, 17 October 2024 (UTC)

We agree that there is "a proportionality constant implied by Newton", as you put it. Now, there are two terms, F and (ma), which are said to be "proportional" to each other. "Mass" m is a part of the term (ma) that is said to be proportional to F. Therefore, by basic mathematical reasoning, m is not available as "proportionality constant" between F and (ma). Note, please, that the proportion reads F ~ (ma), not F ~ a, and, algebraically written, not F/a = m, but F/ma = c = constant. This can also clearly be seen if one writes (dp/dt) instead of (ma). If F ~ (dp/dt), and F/(dp/dt) = c = constant, it is evident that the constant cannot be m. Right? 2003:D2:9724:5357:95E5:D83:52F7:AC49 (talk) 07:52, 26 October 2024 (UTC)

The term "Newtonian mechanics" is ubiquitously used as a catch-all that includes many ideas not introduced by Newton himself, e.g., the principle of inertia, and the concepts of work and energy. There's nothing that Wikipedia can or should do to change this terminology. Moreover, the article as it stands already explains this. XOR'easter (talk) 20:20, 17 October 2024 (UTC)

Of course Wikipedia can and should do something. It is not required to "change the terminology", if only here and there Wikipedia would point to the fact (here admitted) that "Newtonian mechanics" is NOT Newton's mechanics, and that the famous "second law of motion", F = ma, is NOT Newton's law but Leonhard Euler's: See L. Euler, Découverte d'un nouveau principe de Mécanique, Mem. Acad. Roy. Sci. Berlin, vol. 6, 1750 (1752), pp. 185-217. I take this reference from Giulio Maltese, La Storia di 'F = ma', Firenze (Olschki), 1992, p. 218. 2003:D2:9724:5357:95E5:D83:52F7:AC49 (talk) 08:02, 26 October 2024 (UTC)

The Maltese reference seems to be in Italian. Here is another more recent book chapter by Maltese on the same subject:

• Maltese, G. (2003). The Ancients’ Inferno: The Slow and Tortuous Development of ‘Newtonian’ Principles of Motion in the Eighteenth Century. In: Becchi, A., Corradi, M., Foce, F., Pedemonte, O. (eds) Essays on the History of Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8091-6_9

Contrary to your claim, the essential message of the Maltese work is that the modern form of the physical model attributed to Newton was developed over many years by many people. (This is a very common story line in the history of science). This is inline with the History section of the article. As always, these sections can be improved but no radical change is needed. For that purpose this reference is probably better:

• Coelho, R.L. On the Concept of Force: How Understanding its History can Improve Physics Teaching. Sci & Educ 19, 91–113 (2010). https://doi.org/10.1007/s11191-008-9183-1

Johnjbarton (talk) 14:41, 26 October 2024 (UTC)

My claim concerns the true meaning of Newton's second law. I do not doubt "that the modern form of the physical model attributed to Newton was developed over many years by many people". - My question is what Newton's authentic second law says if expressed in mathematical symbols. Newton's central message is the "proportionality" between impressed force and change in motion. Proportionality is a mathematical term. It stems from Euclid, Elements, Book V, Definitions. Euclid defines "ratios" (logos) between quantities of a same kind, and "proportions" (ana-logos) between quantities of a different kind. Newton rightly understands "force" and "change in motion" as quantities of a different kind (cf. Principia 1713, Book I, Scholium after Lemma X). Thereforce he puts them proportional, not equal, as it is mistakenly done in nearly all the papers on this subject through 300 years, beginning perhaps with the Principia edition of Thomas Leseur and Francois Jacquier, Rome 1739. Newton's law evidently requires a "proportionality constant". This is shown in my paper "Die Newtonische Konstante" (Philos. Nat. 22 nr. 3/1985, p. 400), followed in a way by I. B. Cohen's and Anne Whitman's Principia edition Berkeley 1999. The "Newtonian constant" (as I termed it) has been suppressed and dismissed from the beginning by writers who, ignorant of the meaning of "proportions", in the footsteps of Newton's antipode G. W. Leibniz (!!) have put "force" and "change in motion" equal, F = (ma), or F = (dp/dt). What I want to say, regarding the historical truth, is that this law F = (ma), in whatever a form it is expressed, is NOT "Newton's second law", contrary to the article and to all textbooks over the world. It is evident, by the way, that everything in theoretical physics, and that the whole modern world view, would change if the physicists would erect their science on the true foundation laid by Galileo Galilei and Isaac Newton more than 300 years ago. 2003:D2:9724:5371:95E5:D83:52F7:AC49 (talk) 09:17, 27 October 2024 (UTC)

"...contrary to the article and to all textbooks over the world." When the textbooks change we can change the article, even it that means stumbling along in ignorance for another 300 years. Johnjbarton (talk) 15:18, 27 October 2024 (UTC)

This means that he who wants to understand Newton's laws of motion should not read Newton but a modern physics textbook instead, which tells him, for example, that Newton's second law of motion reads F = ma; right? In other words: If Newton's teaching does not correspond to modern textbooks, so much worse for Newton. What is truth? Oh my God ... 2003:D2:9724:5371:95E5:D83:52F7:AC49 (talk) 22:35, 27 October 2024 (UTC)

Wikipedia does not claim to present "truth", nor is there any practical way for it to do so. Rather it claims to summarize knowledge as represented in reliable sources, a practical though still challenging goal. That is why I requested reliable sources in my first reply. Johnjbarton (talk) 22:48, 27 October 2024 (UTC)

The "reliable source" to answer the question "what are Newton's laws of motion" - isn't it Newton's Principia? What if this source contradicts all textbooks, as it is evidently the case? Should the reader then rely on the textbooks? Really? 2003:D2:9724:5381:95E5:D83:52F7:AC49 (talk) 10:02, 28 October 2024 (UTC)

Wikipedia policy is to rely on secondary sources, so no Newton's Principia, as a primary source, is not considered the best choice. In this case it would be a bad choice because language and science changes over the centuries. There are many excellent historical analyses for Newton. Textbooks are excellent sources for concepts because they are typically very well reviewed and designed to explain concepts.

This article isn't about Newton's historical words but rather about the physics taught today which is traced back to Newton's work. So yes, "so much the worse for Newton" if the modern differs in some detail from his words. We have an entire long article on Philosophiæ Naturalis Principia Mathematica and a sad little article on History of classical mechanics about historical issues. Johnjbarton (talk) 15:39, 28 October 2024 (UTC)

With all due respect: No, Sir. This article of course claims to truly represent Newton's historical words! Under the headline "Newton's laws of motion" it claims that Newton's second law would read F = dp/dt = ma! Which, however, is not true if one reads Newton's Principia! Therefore I accuse Wikipedia of telling the reader not the truth but a myth. Nowhere does the article inform the reader that the modern reading F = dp/dt = ma differs from Newton's words "because language and science changes over the centuries", or, because "the modern form of the physical model attributed to Newton was developed over many years by many people", as you put it in your first reply. Once again: So long as Wikipedia does not change the article it is evident that this encyclopedia contrary to truth represents not Newton's laws of motion but something different; fiction instead of science. 79.198.227.190 (talk) 18:21, 28 October 2024 (UTC)

I don't see where this discussion is going. How would adding a (linear?) proportionality constant (now 1) to each and every force equation change physics? This F is only a middleman; a program, as Feynman (I believe) called it. Take one F formula for causes, take another F formula for the effects, forget about F. The ideas are Newtons', so is the mechanics. Just like the equations are Heaviside's, but the grand idea is Maxwell's. Ponor (talk) 19:54, 28 October 2024 (UTC)

The article already gives the quotation from Newton. It already says that $\mathbf {F} ={\dot {\mathbf {p} }}=m\mathbf {a}$ is the "modern form" of Newton's second law. It already says that expressing the law as $\mathbf {F} =m\mathbf {a}$ was Euler's idea. There is literally nothing we need to do here. XOR'easter (talk) 20:53, 28 October 2024 (UTC)

The article does NOT give "the quotation from Newton" which reads (main part): "Mutationem motus proportionalem esse vi motrici impressae". Sorry that this is Latin. It is Newton's language. It says that a force impressed on a body ("vis motrix impressa") is proportional - NOT EQUAL! - to the generated change in the body's motion ("mutatio motus"). No "acceleration"! By no means can Newton's formulation be identified with F = ma, which should be Newton's law according to the article! Never did Euler express Newton's law as F = ma! Quite to the contrary, in 1750 in Berlin, when he introduced F = ma to the public, he explicitly and rightly claimed that this was "a new (!) principle of mechanics" which he (HE!) had discovered ("decouverte")! No mentioning of Newton! Note that nobody has ever accused Euler of plagiarism! - Why is it so difficult to simply admit the evident fact that F = ma (F = dp/dt) is not Newton's second law?? 2003:D2:9724:5381:95E5:D83:52F7:AC49 (talk) 22:13, 28 October 2024 (UTC)

Wikipedia re-publishes information that is already published in reliable sources, but does so without plagiarism. At Wikipedia:Verifiability it says If reliable sources disagree with each other, then maintain a neutral point of view and present what the various sources say, giving each side its due weight.

Wikipedia does not arbitrate on which source is correct, and which is incorrect. Dolphin (t) 23:17, 28 October 2024 (UTC)

Obviously Wikipedia arbitrates on which source is "reliable" and which is not. According to Wiki reliable is what modern textbooks say about Newton's laws; what Newton himself says is not reliable. Really? 2003:D2:9724:5317:9C9E:E62D:57C8:D9A7 (talk) 08:03, 29 October 2024 (UTC)

Wikipedia is not the place to argue that every physics book is wrong.

Wikipedia is not the place to argue that all physicists should change what they mean by "Newton's laws".

Wikipedia is not the place to invent controversies that do not exist. XOR'easter (talk) 01:01, 29 October 2024 (UTC)

1) Wikipedia tells the reader about Newton's (!) laws something that is not true. I'm trying to correct that. Isn't this a most normal case? Or is Wikipedia always true, never to be corrected?

2) Wikipedia is certainly the place to inform physicists and others of "what are Newton's laws"; Newton's! not Euler's, and not what modern textbooks say. This exaxtly, namely to show what Newton's laws are saying, is what Wiki does in the article; but wrongly, alas.

3) That Wikipedia is wrong here is easily demonstrated by the fact that those who aim at defending the article rightly argue that the "second law" as shown in the article is a product of centuries-long evolution. I agree; so this evolutionary product is certainly not "Newton's law" as one finds it in the Principia of 1687. To which source Wikipedia, however, mistakenly and misleadingly refers, even by illustrating the article with a copy of that outdated (?) source's title page! 2003:D2:9724:5317:9C9E:E62D:57C8:D9A7 (talk) 08:36, 29 October 2024 (UTC)

Ponor on 28 Oct asked "how would adding a proportionality constant to each and every force equation change physics?" This question doesn't belong to the subject of this discussion. Nonetheless it is an important one. The answer is given with the identification of the "Newtonian constant", that is, the proportionality constant c between "Force" F and "change in motion", delta p. F/delta p = c = constant. This constant c bears dimensions, not just "1" but "element of space, s, over element of time, t": c [s/t], as it follows from a careful study of Newton's principles. So the "Newtonian constant" coincides with the "c" of modern science. If added according to F/delta p = c it guarantees that the force F will generate a change im motion delta p NOT instantaneously (which absurdity F/delta p = 1, of F = delta p insinuates), but in space and time, in full accordance with natural experience for the first time. 2003:D2:9724:5317:9C9E:E62D:57C8:D9A7 (talk) 17:57, 29 October 2024 (UTC)

I see what you mean. He definitely says "Force" ~ Δ(mv). However:

In his Scholium after Corollary VI he says: When a body is falling, the uniform force of its gravity acting equally, impresses, in equal particles of time, equal impulses upon that body, and therefore generates equal velocities. (there are other similar examples; his way of thinking is discrete, geometrical)

To us, that sounds about right, no? The only thing is that Newton didn't use the word impulses but forces. But if the force of its gravity is uniform and acting equally, why would he have to say "in equal particles of time"? With our definition of the word "force", his statement would have to be "force of its gravity impresses in equal and different particles of time equal forces upon that body". Total force does not depend on time, impulse does. So Newton's force is most likely our impulse, though probably not consistently throughout the book: "Newton's Force" = F Δt ~ Δ(mv) → F ~ ma.

Anyway, this is not something we should discuss here. You're free to propose changes, with good sources. I haven't read the article and can't say what should be said differently. We should, perhaps, rely on our modern understanding of the words, not Newton's, and not quote him literally mixed with our modern formulas. Ponor (talk) 01:05, 30 October 2024 (UTC)

Thank you, Ponor. Indeed, as you say, Newton's way of thinking is discrete, geometrical. Accordingly, in the Scholium after Corollary VI he DISTINGUISHES between "the uniform force of gravity" and the discrete "impressed forces" (not "impulses"), as he also does it in Def. 4. Here the uniform force of gravity, called "centripetal force" (synonymously), is described as a "source of" discretely impressed forces. Therefore, "the total impressed (!) force DOES depend on time, it is "the sum over time" of discretely and successively impressed forces. The "total force" is NOT "the uniform of gravity" and it is NOT our "impulse", but it is "proportional to" the impulse: F ~ delta(mv), which is in algebraic form: F/delta(mv) = c = constant. c is the "Newtonian constant". May I refer you to my paper "Inertia, the innate force of matter", in P. B. Scheurer and G. Debrock (eds.), Newton's Scientific and Philosophical Legacy, Kluver (1988), pp. 227-237 (a "reliable source"??), with further readings. Thank you in advance for reading me.

Ed Dellian, Berlin, Germany. 2003:D2:9724:5305:51E3:FFE1:2229:7E99 (talk) 08:12, 30 October 2024 (UTC)

We are entering Wp:NOTFORUM territory now. Multiple editors have listened and concluded that no change to the article needs to be made. Thanks for the suggestions. Johnjbarton (talk) 01:38, 30 October 2024 (UTC)

It is o. k. to show the user of Wikipedia the modern form F = ma as the foundation of "classical mechanics". It is NOT o. k. to call this form "Newton's law". If at all, then it is Euler's law. This to find in a revised version of the article was my only aim from the beginning. 2003:D2:9724:5305:51E3:FFE1:2229:7E99 (talk) 08:43, 30 October 2024 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

The following should be added to the history part

https://drive.google.com/file/d/1G52qRjxXpj0VLtNrWIHqKJlcJ7vu4art/view?usp=drivesdk https://drive.google.com/file/d/1G0UligaThs--uidrJWyiDpgDNedxYA86/view?usp=drivesdk These are some research that can be added to the history part of the wikipedia's law of motion. 2409:40C4:3B:4EC:8000:0:0:0 (talk) 17:51, 13 November 2024 (UTC)

Those links don't work. And anyway, the contents of an individual's Google Drive isn't suitable for use as a source on Wikipedia. AntiDionysius (talk) 17:57, 13 November 2024 (UTC)

https://www.researchgate.net/publication/378857007_Title_Comparative_Analysis_of_Kanada's_Laws_of_Motion_and_Newton's_Laws_of_Motion

https://www.ajer.org/papers/Vol-9-issue-7/K09078792.pdf analysis_of_Kanada's_Laws_of_Motion_and_Newton's_Laws_of_Motion

Given by to institute the American journal and research gate. 2409:40C4:346:F311:8000:0:0:0 (talk) 06:49, 16 November 2024 (UTC)

Thanks. However these sources are essentially student essays and would not be considered reliable sources. I think we could add something to the History section based on the first 4 references in the AJER paper. Unfortunately, based on that paper, the first four refs do not discuss physics. Maybe some of the references in history of physics or other articles would include discussion of Kanada's work?

Note that the AJER paper points out that the scientific work of the Kanada era died out due to multiple societal forces. I am confident that there were many brilliant people in that era but sadly their important work was lost. This could be notable for the history of India or for historical analysis of cultures but work that disappears before having an impact on modern science isn't really notable for the history of modern science except as a tale of parallel discovery. Johnjbarton (talk) 16:36, 16 November 2024 (UTC)

The American Journal of Engineering Research is on Beall's List. It's not a real journal. (Any claims about the history of Indian mathematics and science have to be evaluated very carefully, because garbage sources go way overboard for nationalistic reasons [1].) XOR'easter (talk) 21:28, 16 November 2024 (UTC)

The Introduction

In the introduction is a list of areas which require improvements in Newton's formulation. It mis-characterizes the changes for special relativity and general relativity as being for high speeds and for very massive; but the reason for both of their discoveries are the allied reasons that the speed of transmission of information is finite and is still observer independent. And quantum mechanics should be characterized as being increased understanding of what constitutes information. In other words, special relativity is true at all speeds, general relativity is true at the level of an apple pip, and quanntum mechanics is true at the level of the universe writ large. YouRang? (talk) 16:49, 26 November 2024 (UTC)

Here is the entire sentence from the current introduction:

• Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (special relativity), are very massive (general relativity), or are very small (quantum mechanics).

The sentence accurately summarizes part of the section "Relation to other physical theories". That is all it needs to do. The sentence is not here to characterize relativity or quantum mechanics. Johnjbarton (talk) 17:24, 26 November 2024 (UTC)

Singularities

After discussion "Flying off to infinity in a finite time" on the Science Reference Desk I have reworded the section. Other interested parties Malypaet, Baseball Bugs, jpgordon, Trovatore, PiusImpavidus and Wrongfilter were invited to comment here.

Previous text:

Singularities

It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time. This unphysical behavior, known as a "noncollision singularity", depends upon the masses being pointlike and able to approach one another arbitrarily closely, as well as the lack of a relativistic speed limit in Newtonian physics.

changed to:

Singularities

Mathematicians have investigated the behaviour of collections of point masses that may approach one another arbitrarily closely, possibly collide together, and move in accord with Newton's laws. In studies that assume no relatavistic speed limit, singularities of unphysical behavior are predicted. For example, a particle velocity can accumulate through successive near-collisions to the extent of theoretically departing the system to infinity in a finite time. Philvoids (talk) 14:32, 13 January 2025 (UTC)

I prefer the old version. Starts with the unnecessary personalisation ("mathematicians") and continues with the "prediction" (predicted for what? Nobody expects these things to be observable) and the assumption of no relativistic (sic!) speed limit — these considerations are fully within Newtonian theory, which quite simply has no speed limit. I see these studies as investigations of the mathematical structure of the theory, not of the physics that the theory is supposed to describe; the old version states that more clearly. --Wrongfilter (talk) 15:33, 13 January 2025 (UTC)

I think it would be helpful if you summarized the issues you have with the existing content. Johnjbarton (talk) 15:54, 13 January 2025 (UTC)

I think this paragraph belongs in the Multibody section. Here is a different suggested paragraph based on the sources:

• The stability of a system of multiple point point masses was introduced as a mathematical problem by Paul Painlevé and Henri Poincaré. Against intuition, systems with at least 5 point masses exhibit "non-collisional singularities" in which a particle may be launched to infinity in finite time. In the 5 particle case, a light particle oscillates between two pairs of heavy particles, each in a binary orbit; in every cycle the binary orbits shrink and the two pairs move further apart in a way that grows out of control. This problem is related to other mathematical singularities in physical models like Zeno's paradox, self-energy, and the center of a black hole.

Johnjbarton (talk) 16:26, 13 January 2025 (UTC)

A paragraph on this could work in either place, I suppose, but I think it's a little better in its current spot, where it follows the discussion of unpredictability in the previous subsection, and can then segue into Navier–Stokes existence and smoothness. Mentioning who introduced what and when would blend the history in with the concepts, which isn't in principle a bad thing but is different from how the article is currently structured. The phrasing "This problem is related to other mathematical singularities..." feels a little vague. What's the relation, apart from them all being examples of mathematical singularities? XOR'easter (talk) 21:07, 13 January 2025 (UTC)

The refs are about math (mathematical physics perhaps) but the two other summaries focused on physics picked out of the sources. The content sounds like it it trying to explain away the non-intuitive result in an unsourced way (Baez says "the set of initial conditions for which two or more particles come arbitrarily close to each other within a finite time has ‘measure zero’.", that is, phase space is too big). The Painleve/Poincare sentence was intended to position the issue in math. We could start with something based on Saari/Xia's concluding sentence: "the Newtonian n-body problem serves as a source of intriguing mathematical problems".

Baez groups these as "problems that arise from assuming spacetime is a continuum", so we could just say as much. Johnjbarton (talk) 22:54, 13 January 2025 (UTC)

I don't see how the previous version tried "to explain away the non-intuitive result in an unsourced way". It seems a reasonable paraphrase of Saari and Xia's phrasing: It turns out that particles must approach other distant particles infinitely often and arbitrarily closely; First, the particles must shuttle among each other infinitely often causing arbitrarily close approaches. And Baez says, Of course this isn’t possible in the real world, but Newtonian physics has no ‘speed limit’, and we’re idealizing the particles as points. So, if two or more of them get arbitrarily close to each other, the potential energy they liberate can give some particles enough kinetic energy to zip off to infinity in a finite amount of time! After that time, the solution is undefined. The idea that the set of initial conditions leading to these outcomes has measure zero is conjectured, but unproven. XOR'easter (talk) 00:18, 14 January 2025 (UTC)

The lack of a relativistic speed limit in Newtonian physics doesn't cause or prevent the behavior. As far as I can tell no one has worked on the relativistic problem. So Baez is only saying this is a math problem.

Saari and Xia say for the 5 body problem, "Initial conditions leading to a Xia type example are in a set of Lebesgue measure zero;" and Saari's previous work eg (Improbability of Collisions in Newtonian Gravitational Systems Donald Gene Saari, Vol. 162 (Dec., 1971), pp. 267-271) suggests this a characteristic. The previous content "depends upon the masses being pointlike and able to approach one another arbitrarily closely" amounts to the same thing. This is Baez's overall point about the continuum. The infinity that is at work here isn't one flown-off-to so much as the one the model work within.

But on the scale of all Wikipedia paragraphs, the existing content is fine. I was just trying to suggest a way forward. Johnjbarton (talk) 01:56, 14 January 2025 (UTC)

I prefer the old version, which avoids the "mathematicians" (too specific — are you 100% sure none of the people who have studied this are physicists?) and "predicted" (it's not a prediction about any realistic system). The new version also includes awkward phrasing, like "to the extent of theoretically departing". XOR'easter (talk) 20:58, 13 January 2025 (UTC)

This is the old first sentence that was questioned at the Science ref. desk: "It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time." It is a poor lede if read isolated from the proviso "This behavior...depends..." as a general reader is liable to do. I cannot qualify whether people who have studied this are physicists or not but the study is a mathematical one. There was an objection to calling the studies "simulations" so I arrived at the term "predicted" qualified as (only) theoretical. I agree the new version phrasing is awkward. Philvoids (talk) 23:57, 13 January 2025 (UTC)

If this "general reader" is unable or unwilling to read all of two sentences, I don't know what we can do for them. XOR'easter (talk) 00:20, 14 January 2025 (UTC)

We could just reorder the content:

• It is mathematically possible for a collection of point masses, moving in accord with Newton's laws and able to approach one another arbitrarily closely, to exhibit unphysical behavior. Under certain contrived conditions they can interact to launch some of themselves away so forcefully that they fly off to infinity in a finite time. This unphysical behavior is known as a "noncollision singularity".

Johnjbarton (talk) 02:07, 14 January 2025 (UTC)

References