I think they are two sides of the same coin. Time-rate of change of momentum is force and Newton's 3rd law is a direct outcome from laws of conservation of momentum. I would suggest something deeper and conceptual for students! The question should be, how did Newton derived the Newton's laws of motion and laws of gravitation? And perhaps the only book where you can find the answer in "easier" language is Feynman's last lecture! Other source could obviously be principia of mathematica but tough to comprehend.

It is true that Newton came first, and Lagrange refined many aspects of mechanics. Nevertheless,  in my opinion Newton's laws and rational mechanics have quite different origins and have different aims.

I would suggest that Newton's (and Leibniz') approach is a way of coming about Zeno's paradox of Achilles and the tortoise. According to Newton both, force and mass are defined as F=ma, and the distinction between Absolute and relative space requires insights.

Rational mechanics draws from statics and from the principle of virtual work instead. Force can be defined by means of the dynamometer, which is more akin to Aristotle's force law, whereas the representations of mechanics get at algebraic geometry.

To me, Newton's approach seems to address dynamics at a more fundamental level, whereas conservation principles are more insightful when studying the motion of gears and mechanisms.

I think it is important to teach Newton's Laws before relativity and quantum mechanics, QM.

The former consists of three fundamental laws: the force law, the momentum law and the energy law. In relativity they become incompatible.

The conservation laws are profoundly important in quantum mechanics, but special care has to be exercised, when extending from non-relativistic to relativistic QM. 

Hello,

I would like to stir the pot, so to say.

We may wish to acknowledge that it is hard to teach Newton's three laws today and keep a straight face. The  so-called "three" Newton laws are actually one, that we call the "second". The other two laws are just a corollary. And the second law comes out of nowhere, while it can come naturally from conservation of momentum, which comes naturally from Noether's theorem. 

It seems to work better for students to leapfrog to the present, using conservation laws to describe Nature, and then go back just to explain any concept that is still valid,  while abandoning the flogistic and other lore. The students have less lost time this way, and avoid misconceptions, such that every force would have an equal and oposite reaction, which is simply false.

Otherwise,  we would be teaching history. We may as well not use zero or negative numbers!

Cheers, Ed Gerck 

I agree with dr. Gerck on the fact that there are priorities in science as elsewhere.

On the one hand, a teacher is expected to motivate those priorities, and to provide his students with the implied knowledge. On the other hand, science itself possibly doesn't just consist of techniques and doctrines, and looks more like a human endeavor.

Now, there is a famous sentence (https://en.wikipedia.org/wiki/The_Prince): “The end justifies the means”. I don't think that this sentence is acceptable in science, too, and that there is a final goal or a reach in science distinct from the means to attain scientific knowledge. Thus, if I were a teacher, I would not completely dispose of its roots.

I am not sure what is meant by the statement: We may wish to acknowledge that it is hard to teach Newton's three laws today and keep a straight face.

Returning to Newton's law(s), it is a typical deductive theory based on four well-known fundamental assumptions. Are there any other priorities in science than proceeding by deductive reasoning?

Christian,

This is an excellent demonstration of the integrity phenomenon. All Newton's concepts are coming in the interconnection. And in another way you would not be able to get them. For the question chronology of appearance of concepts is interesting. I think that this is the natural way of their assimilation, which contributes to a correct understanding of the phenomena themselves. It makes sense to study not only concepts, but also their transformations over history.

Although I do not think I would have thought about it when I studied it in school.

Christian,

Yes, my statement is not undisputed. All that we have - is the actual historical sequence of understanding the phenomena. It is only assumed to be a most probable.

"Some of my professors had an almost aggressively arrogant attitude." - is a familiar pattern too. This (sometimes) is characterized mainly for pure lecturers. Routine turns it to cramming process, thus lost sense of the difference between the level of lecturer (from year to year repeats the same thing) and the student (who sees it for the first time).

One thing is clear that some of our teachers have been arrogant, incompetent and what not, however, is there an alternative to teach science without employing a deductive approach.  

For instance in the case of Newton dynamics, which is a typical deductive theory, it relates privileged reference systems in classical physics with the four axioms containing "undefined quantities" like the concepts of force, mass etc.! 

If there is a better way please inform.

Christian, Erkki and all,

When we apply deductive reasoning, it is critical that we reject any unfounded input. It is better to reject ten truths than to accept one falsity. For a truth that we reject today can be used tomorrow, while a falsity that we were to accept today would poison tomorrow. Newton's laws (even if just the second law) have conceptual and application pitfalls.

Considering something even as simple as non-relativistic rocket dynamics  (where mass is not constant and F=ma is not valid), would not a student of physics be justified to feel frustration? Unnecessarily, though, if conservation of momentum would be taught first.

I think that whatever students learn "should have legs". A main part of student’s' dfficulty with math, which paves the way  to give up math, can be easily seen in any classroom -- being taught and graded in using a wrong or impotent method, and feeling cheated intellectually because it does not make sense.  Don't we see the same in physics?  It is possible that students are giving up in science NOT because they are "too dumb" for science but because they are actually too smart!  

It seems that students today can more easily see through this game, and that's why I  commented that t it is hard to teach Newton's three laws today and keep a straight face. The same applies to teaching magnetism independently from electrostatics and frame transformation, using different units for electric and magnetic fields, or teaching about vector cross-products. All fiction, rightly suspicious to the skeptical mind, and ugly. The beauty, the common underlying principles, the important insights for today and the unknown future, that can awe and sustain the student's interest through grueling work, where are they?

Cheers, Ed Gerck 

Ed and Christian,

You did not answer my question.

Ed,

Your offer will lead to the exposition the confusing mathematical formulas without understanding the physics of the phenomenon. It can be seen in some modern textbooks.

You can not build walls without building a foundation... It is not possible to step to the next stair without step on the previous one... This is the meaning of the deductive reasoning (in the most general sense).

Yes, there are things that are beginning to work just together. At the same time, you can really study some of their components in a random order. But this does not give the whole understanding of such concept. It only determines the absolute sequence of causes and final effect. For example, Newtonian mechanics is a system with its own set of axioms as Erkki said above.

The initial assumptions of deduction is an axiom or a hypothesis. They have the character of general ("common") statements. The end theorems ("private") are consequence of the assumptions. If assumptions are true - true also consequences.

Erkki,

Your question (if I have the right one, is "If there is a better way please inform") is answered as follows: teach what is actually used more often and widely, conservation  laws first. See this answer,  for example, in the explanation I gave when presenting the thread question,  also in my previous reply:

Considering something even as simple as non-relativistic rocket dynamics  (where mass is not constant and F=ma is not valid), would not a student of physics be justified to feel frustration? Unnecessarily, though, if conservation of momentum would be taught first.

The thread question itself also includes it as the first option. Would it be more insightful for students to learn conservation of momentum laws before Newton's laws?  

Cheers, Ed Gerck 

Christian, 

Of course I agree, since deductive reasoning should be based on deliberate experiments and accurate observations.

Ed,

When mass depends on motion you will find that the force law breaks down at the gravitational radius. To teach the students the deeper reasons why gravitational interactions cause incompatibility between the energy- force- and momentum laws are important to give fundamental insights of the importance of physical principles. 

Of course continuing to wave propagation, wave mechanics, EM waves and QM naturally lead to belabouring symmetries and conservation laws.

In fact, the example of the reactive motion is incorrect. It does not violate the laws of Newton.

The laws themselves (at least in the training program in my country) is considered much earlier (at secondary school) then appear Hamiltonian or Lagrangian term. Reactive motion, by the way, is also considered a little later. So, in high school the order is not principled.

It also reminds me the difference in the consideration of the motion of a continuous medium in the concept of Lagrange and Euler. As a rule they are given in a pair of consecutive lectures, or just one.

I agree with Charles, "Vectors are a much more useful".

Vasily and Charles,

It is not disputable in physics today that when mass changes during motion you cannot apply Newton's 2nd law of F=ma for that motion. However, you can apply momentum conservation. Momentum conservation applies both where Newtons' laws apply and where they do not.

The assertion that "Vectors are a much more useful" is hard to place. More useful compared to what?  Rather, I'd say that life is movement and movement generates a vector, so vectors are more natural than numbers, which are static.

Cheers, Ed Gerck

Erkki, Christian and all,

Erkki timely wrote, "Of course continuing [from newtonian mechanics] to wave propagation, wave mechanics, EM waves and QM naturally lead to belabouring symmetries and conservation laws." 

Erkki and Christian also mentioned  the central use of deductive logic in physics, and we all talked about "first principles".

But, in physics, when we talk about "first principles" what are we talking about?  Are we talking about Newton's laws in the context of Erkki's quote above (what came first), or are we talking about what we now know to be fundamental principles?

Evidently, in history it would be the former (what came first), but not in deductive logic as used and taught  throughout physics. Conservation laws provide a fuller description of Nature and are the "first principles" we use in physics today.

That is why I am suggesting that physics in undergraduate and high-school levels should wake up to this realization, which is more than one hundred and fifty years old in post-graduate terms [Crowell 1]:

"In many subfields of physics these days, it is possible to read an entire issue of a journal without ever encountering an equation involving force or a reference to Newton's laws of motion. In the last hundred and fifty years, an entirely different framework has been developed for physics, based on conservation laws.

The new approach is not just preferred because it is in fashion. It applies inside an atom or near a black hole, where Newton's laws do not. Even in everyday situations the new approach can be superior. We have already seen how perpetual motion machines could be designed that were too complex to be easily debunked by Newton's laws. The beauty of conservation laws is that they tell us something must remain the same, regardless of the complexity of the process."

Further, it is useful to realize that we must teach conservation laws first if we want to follow an axiomatic description that is based on deductive logic. This will not be relevant if we want to teach the history of physics although, there too, it will be useful for the student to know that all ends well when facts are proven wrong. After all, especially for a physicist, a fact is what once was believed to be true [2].

Conservation laws have the further benefit, critical in deductive logic terms, that since Noether they no longer have to postulated, arbitrarily.  Conservation laws follow directly from Noether's theorems -- as well as the conservation laws' validity regions. With Noether, conservation laws depend on fundamental ideas that are easy to grasp and verify, such as the isotropy of space. Noether's theorems can be mentioned early on, intuitively, and then rigorously explored later by the student (after calculus is learned).

Cheers, Ed Gerck

[1] Benjamin Crowell, Light and Matter, chapter 14, retrieved from

http://lightandmatter.com/html_books/lm/ch14/ch14.html

[2] Facts are not static, history is not static. History changes, and history books evidence that. New facts, wrong facts, and new interpretations need to be taken into account when we want to find "first principles", not just in physics but also in history itself.

This is just an example of what I said :)

I can not imagine studying Netёr theorem in secondary school (the action functional, partial derivatives ...).

Charles and Vasily,

I think you understand each other well, and there is merit in Newton's laws for that. I am sure that both of you have read in my posts what everyone already knows, that Newton's laws fail even in non-SR cases, and fail absolutely in SR, but conservation laws keep going, with no existing example otherwise. Denying this may be fun, but is not physics.

I have met many students just like Charles humbly reported for himself, who think that they were doing well in secondary school, but when they go to university they do not do well and are told that "something is missing", which they can not quite figure out. Then, those students enter the first stage of acceptance of a novel idea: denial. But that something "missing" is most often just a broader understanding that they were ignorant of while kept within an outdated formalism, which was served as the "end-all, be-all"... while it is just quite old history.  BTW, I see this happening not just in physics and math, but also in writing essays and term papers. That is why many universities offer remedial courses for first-year students.

But it does not have to be so. Let's fix it before? How? Looking for a more inclusive and extensive understanding starting in high-school. Conservation laws have long replaced Newton's laws in post-grad work for achieving that broader understanding. My point is that it is surely time after 150 years that this should creep into undergraduate and high-school work as well.

I say by experience that Noether's theorems can be well understood intuitively by current high-school students with just two years of integrated algebra-geometry. But, even if such students cannot even grasp it, as Vasily fears, this is irrelevant in terms of knowing the simple fact that conservation laws have earned a basic underpinning in how Nature works, which is all to be more fully understood as the students grow up.

I suggest you read the reference I cited, the physics book by B. Crowell, and give it a shot. It is 100% free and online (I do not know Dr. Crowell, but I think he wrote well and used undisputed facts). I am sure that there are other references as well, highlighting the now 150-year use of conservation laws over Newton's laws.

Too often, Vasily and Charles, the student has been the party at fault -- and suffered for it, suffered by not knowing what the "big dogs" are tired in long knowing. Psychology says that ignorance is bliss. However, more than 150 years old is not tolerable to ignore any more, in the Internet age and in physics, unless we are not concerned in educating a generation of intellectual dwarfs.

Cheers, Ed Gerck

Charles,

In my phrase, I wrote and meant that students who may be doing well in secondary school (as you humbly reported you did), may not do well in the university and be told that "something is missing". There was no other meaning, I do not know what you were told.

I liked when you wrote, "The question as set, though, was not what is the most fundamental treatment, but what is the best way to start with students."

Exactly. And the best way to start with students is to not risk losing their trust later on, including the trust that they are learning and being graded for something that they will use later.

You also wrote, "I continue to see nothing wrong with starting with Newton's laws, provided that one rapidly proves conservation principles and points out that conservation principles are more fundamental."

The word "rapidly" seems to indicate the logical frailty of the process. The word "proves" indicates its impossibility. Conservation laws cannot be proven from something less fundamental than themselves, where, as you wrote, "conservation laws are more fundamental" than Newton's laws.

So, what what will happen, in what you suggest as "nothing wrong"?  When students see, after all that effort, that they would have had a more logical and faster route in physics had they started with conservation laws?

Cheers, Ed Gerck

Charles and all,

You ask, "Ed, Why do you think conservation principles are not proven from Newton's laws?"

I quote yourself,  some 8 hours ago, "I [Charles] have already said that conservation laws are more fundamental than Newton's laws."

I agree with you and, therefore, conservations laws, being more fundamental, cannot be proven ftom Newton's laws. Further, the validity domain of Newton's laws is smaller than the validity domain of conservation  of momentum, so the former is impotent to lead to the latter. 

I do not agree with Christian's comment on its face, that "Newton's first law is a conservation law", but I am not sure what he intended to say with that.  I explained before that N1, N2, and N3 are not independent from each other. N1 and N3 are a corollary of N2, which is not a conservation law, and not a law at all. N2 is a definition of force, restricted to a validity domain that is smaller than the validity domain of conservation laws.

Cheers, Ed Gerck 

Christian,

I should note that we are talking, after all, about learning. The universal pattern can be detected only after studying at least a few phenomena where it manifests itself. This is detected post factum and, at a minimum, requires an appropriate level of abstraction.

At the beginning learning of physics can not be operated in such a level of abstraction and formalism. All should begin from something. Physics begins with mechanics.

Christian, for me a qualitative understanding of the phenomena is more important than memorization of techniques quantify a particular value. Example with rocket motion clearly shows the importance of this.

The most "versatile" way does not mean "absolute" way. Some things kill critical thinking. I do like not everything in the way physics is taught, but I think this is the other problems. In addition, I believe that different people need a different approach to the study of physics (and not only). The result of this education will also be different. The result in either case is different for everyone.

Ed,

Fundamental principles and conservation laws go hand in hand and you cannot talk about one without the other. In particular a mathematical continuous symmetry manifests itself in a conservation law and vice versa.

The Nobel Laureate P: W. Anderson stated in "More is Different" that "it is only slightly overstating the case to say that physics is the study of symmetry". Maybe this is overstating a bit, like saying that physics is the study of conservation laws.

Of course we probably agree in general, but I still, like Francis, give my vote to fundamental principles. 

Erkki,

Please point me to where I did not link fundamental principles and conservation laws. Charles even mildly complained more than once that I did that, as he said that this tread is about how to best teach students.  But, as you can read in my comments,  physics fundamentals and teaching are not in conflict in this case.

Further, as known in physics literature for more than 150 years, Newton's laws are less fundamental than conservation laws, contrarians notwithstanding. This issue is no longer debatable in physics. What is debatable is the teaching, whether students should still learn the old way, with Newton's laws first. The penalty for teaching it the old way is not just that it is less powerful but also less insightful, and that the student will be forced to unlearn the old way in order to make progress.

There is also more beauty in introducing conservation laws before Newton's laws. And I can do it with a straight face. Or, can one keep oneself from laughing when "deriving" conservation laws from Newton's laws? 

Cheers,  Ed Gerck 

Charles,

There are at least seven misconceptions in what I am quoting below. In the spirit of mining the gold of truth through public and fair discussions, I  do not think that those misconceptions are debatable in physics. If you think otherwise, you can reach me by private message and this may help clear out the air. 

This is the quote, with at least seven misconceptions:

In Newtonian dynamics it is simple to prove conservation laws from Newton's laws. It is sufficiently simple that, if you can't prove it, I doubt you even know enough to discuss it sensibly.

N1 is not a corollary of N2. N2 is a definition of force. Without first stating N1, N2 would not even make sense. N3 is not a corollary of N2. Taken together with N2 it is equivalent to conservation of momentum.

Perhaps more relevant, in mechanics the domain of validity of Newton's laws is actually much greater than conservation laws. As I have pointed out, conservation laws do not apply to non-conservative systems or to non-inertial reference frames. Newton's laws do apply. Your suggestion would mean that students with no prior experience would have to learn how to fix these issues, requiring a much deeper level of understanding, whereas Newton's laws can be directly related to daily experience, and form a much better introductory point.

End of quote.

Cheers,  Ed Gerck 

Charles,

It is known in physics that one cannot deductively go from Newton's laws to conservation laws, but the reverse is possible. It is OK to debate this, though, with  students if they still need to learn the difference between deduction and inference.

This difference is out of scope in this thread, and today's secondary school students  learn it already in first year of algebra.

Cheers, Ed Gerck 

For my part, I believe that classical mechanics, and then leading on the QM, should be taught from a Lagrangian/Hamiltonian view point.  That is, you teach it from the point of view of a minimisation/maximisation principle.  It is clear that in optics, the minimisation principle gives nice solutions to ray tracing and this can then lead on to the more mathematically challenging motions of particles and systems through the Lagrangian, then formulate as a Hamiltonian and then lead on to QM.  A nice logical system, from which, at the beginning, equations like F=ma can be derived, but we can also treat circular motion and Eigen systems just as well.  I guess this is a task for me later, and would need a good text book to lead it.

Charles Francis.  Lots of science can be observed and therefore taught from a Lagrangian point of view,  by that I mean minimising/maximising some functions of the object being observed.  Take a sop bubble as an example.  Can you explain why it is "round", without invoking some kind of minimisation principle.  Of course you can but the answer is much more difficult than saying the sphere minimises the area whilst maintaining the volume as a constant.  Simple principle, which does not go into surface tension, pressures etc.  Why does a free particle describe a parabolic arc when projected into a constant gravitational field rather than an ellipse or some more complex curve, minimisation of an action variable.  Then this can also describe elliptical orbits in 1/r potential fields.  Do you really know what a "force:" is when referring to circular motion.  Whilst force generates motion through F=Ma, motion also generates "force", such as centrifugal "force", which is a "pseudo" or inertial force.  lt comes out simple if you used Lagrangian methods.  Just Google teaching Lagrangian Physics at High School to see what other people have done.  The usual way of teaching mechanics, confines the learning to a rote system without understanding, in my view.

In my opinion, in teaching one should distinguish between calculative issues and basic understanding. Perhaps, the viewpoint on Newton's laws should be actualized, and not simply stated as is, without mentioning that his laws have been scrutinized afterwards, for example by Mach. This holds true also for conservation principles, since at the beginning force was conflated with kinetic energy more often than not.

As dr. Gerck knows German, if he has the opportunity, I would like to suggest a nice book on mechanics and its principles, written by Istvan Szabo, a mechanical engineer: Geschichte der Mechanischen Prinzipien und ihrer wichtigsten Anwendungen

(http://link.springer.com/book/10.1007%2F978-3-0348-9288-9). I think that there are similar historical books in other languages, too.

Lagrangian formalism and other fancy tools are very good, but much has been left in the way.  The lagrangian formalism can't describe non holonom systems, we need the Hamiltonian formalism, which itself can't describe non conservative forces.

D'Alembert who was at the origin of rational mechanics avoided to speak about forces because the concept was very muddy at his time, and used only motion, which was rather awkward.  There is a reason why science developed as it did.  Teaching first momentum conservation will yield confusion in the mind of the students about the concept of force, while they will ultimately encounter the four fundamental interactions that can't be thought of without it, because they have a very specific form and first principles of their own.  A force as derived from a potential is essential to understand them, and it is introduced through the idea of conservative force.  It is also important to explain what is a non conservative force in the framework of thermodynamics, because otherwise it would be confusing with respect to energy conservation.

In general, teaching from first principles isn't a good idea, because the mind isn't prepared to deal with such abstractions.  It is a long and winding road, no stage should be skipped. The beginning is the study of all the many facts on which the theories are based, and then gradually making sense of them through progressive abstraction. Of course, for a working physicist is it better to think with emcompassing concepts. But alas, we observe that outside of their domain of expertise, muddiness is rather the rule.

Ed,

I really do not understand your aversion to Newton's laws. It is true that his first axiom is redundant since it can be derived from the second one. In retrospect one can understand this "omission" since at the time it was believed that a force was necessary to keep a body in motion.

Its most genial part is of course axiom 4, expressing the gravitational law and later to the equivalence between gravitational and inertial mass. It is notable that Newton's laws include the three fundamental laws of mechanics, including  the momentum- and the energy law.

In fact the latter shows, when the mass depends on the velocity, that dE=d(mc2), which demonstrates that the kinetic energy writes E=mc2 and furthermore that the total energy is a constant of motion even in the special theory of relativity. The latter is true for ordinary potentials but not for the gravitational potential.

To go the way via Newton's theory is the most pedagogical way to understand why e.g. GR is needed. This narrative combines fundamental principles, conservation laws and deductive thinking. To me it is impossible to teach physics without conveying the basic understanding of Newton's laws.

Hello,

I just had a great deal of fun by re-reading the entire thread of answers, and thank you for the book / paper recommendations.

Of course, we are all indebted to England for Newton's laws. I have no aversion to them, but physics has changed since Newton, because of Newton. There is a "new" post-Newton way of thinking (not just language) in physics.

As Crowell (op. cit. in the thread), wrote, "In many subfields of physics these days, it is possible to read an entire issue of a journal without ever encountering an equation involving force or a reference to Newton's laws of motion. In the last hundred and fifty years, an entirely different framework has been developed for physics, based on conservation laws."

In the last 150 years, physics has thus moved away from coordinate-based and force-based descriptions. We now use much more frequently physics models with less calculations and more insight, based on symmetry, stationary or least action, and conservation laws including conservation of momentum. Of course, as I mentioned before, force did not disappear  but is now caculated as F = dp/dt, where where p, the momentum vector, is well defined, and conserved for a system.

The greatest challenge that physics teachers and professors face today, without a doubt, is that  students are already way ahead of them in many ways, following fast social and technological changes motivated by the Internet. We can contrast this challenge with the observation that most students are already familiar with the "new" post-Newton way of thinking in physics.

The cat is out of the bag, and this is exciting. As Feynman commented:

“When I was in high school, my physics teacher—whose name was Mr. Bader—called me down one day after physics class and said, ‘You look bored; I want to tell you something interesting.’ Then he told me something which I found absolutely fascinating, and have, since then, always found fascinating. Every time the subject comes up, I work on it. In fact, when I began to prepare this lecture I found myself making more analyses on the thing. Instead of worrying about the lecture, I got involved in a new problem. The subject is this—the principle of least action."

Hestenes credits Herman Grassman at least equal to Clifford in the development of Geometric Algebra. We are also indebted to England for the development of Geometric Algebra, that students can google easily and use to code graphical games, 3D rotations, and solve a problem known as "gimbal lock" -- all in high-school.

Finally, starting in high-school, students can do away with "pseudo" vectors, "polar" vectors, "axial" vectors, "pseudo" scalars, which violate symmetry principles in physics and the closure principle in algebra, as well as "pseudo" or "virtual" forces such as the Coriolis force  (which violates all three Newton laws)

The challenge is, then, how to teach physics to students (high-school and undergraduate) who are already way ahead of the teacher, in many ways?

But, as a thought-experiment, let's forget all the above and try the Newton approach:

1. The three laws are introduced by the teacher. Although the first law can be derived from the second, the teacher can save face here and the student can be told that Newton's justification in stating the first law is historical, and that it can be seen today as a definition of inertial frames of reference, used by the second and third laws.

2. (big limitation) This means that Newton's laws are only valid in inertial frames of reference. Students learned enough logic and social thinking to know that if the teacher derives what could be called a "conservation law" from Newton's laws, the teacher cannot spin it to be valid outside of Newton's laws domain. Yet and most importantly, conservation laws are not limited to inertial frames of reference and will be violated (well, not actually) if that is not taken into account. So, the derived "conservation law" is some sort of "pseudo" conservation, students can be told.

Both students and teacher should laugh at this point, using this hardship as a motivation to change course, introducing symmetry, stationary or least action, and conservation laws, and face any hard but useful work that may be needed to do so.

Suppose this does not happen, and the teacher continues with Newton's laws exposition. This is what likely comes next:

3. Students realize that not even your desk is an inertial frame of reference. Voila, when Newton's laws are transformed to a rotating frame of reference such as the student's desk, the Coriolis force and centrifugal force appear. The student is told by the teacher that these are  (various names may be used here) "pseudo", "fictitious", or "inertial" forces but they have "real" effects. This is awkward, not insightful, metaphysical, and ... it gets worse! The student is then told that the Coriolis force has no reaction whatsoever, that it directly violates Newton's third law, while the rotating frame of reference had already violated the first law. The students are then asked, nonetheless, to use what is in violation of the use. And someone may still dare to call this physics...

How should I put it kindly?  Physics education has been outdated by well-known facts, already in high-school. Students are moving on. Today, the greatest challenge is faced by physics teachers and professors. BTW, a similar situation happens today in math, biology, and English [1, 2], and the challenge is mostly generational [3].

Cheers, Ed Gerck

References are given below to similar cases in English and Internet use, physics is not alone in hyper anachronicity, all ultimately powered by the exponential Moore's law and globalization in the last ~40 years. Change is coming faster after 150 years, and physicists can appreciate well that an exponential driver eventually  dominates the solution.

1. Crystal, David. “The Biggest Challenges for Teachers.” Web video. Available: https://www.youtube.com/watch?v=ItODnX5geCM

2. Crystal, David. The Calm Before the Storm Before the Calm. The English Teacher's Yearbook, 2004-5, 14-16. MToseland, editor. Available: http://www.davidcrystal.com/?id=4260

3. Negroponte, Nicholas. “Being Digital.” (New York: Vintage Books, 1995)

Ed, all human behavior is subject to the principle of least action. It Freud understood. However, it is not easy explain to physicists even now.

I also want to remind that differential calculus came with Newton's laws at the same time, however it introduction even now occurs later. Roughly speaking, this makes impossible to introduce not only a functional concept in secondary school. At the same time, at the moment of admission to high school student is already familiar with classical Newtonian mechanics. A single person evolved approximately at the same vein as the whole mankind. IMHO

Ed,

You stated: "In the last 150 years ......", which is far from correct! If you look at published work in cosmology, solid state physics, thermodynamics, chemical physics, quantum chemistry, molecular dynamics, high energy physics, acceleration physics, calculations, simulations, ab initio many body computations, sub dynamics, super conductivity, superfluidity, non-equilibrium statistics, etc. etc. you will encounter fundamental concepts based on Maxwell's equations, Newton's laws, Einstein's laws, forces, constants of motion, coordinate transformations, operator representations, linear algebra, eigenvalue problems, Fourier transformations, background dependence, differential geometry, separation of variables, reaction coordinates ...etc. etc.

I do not see that your selected readings carry any weight as regards how to teach physics!

Erkki,

The original quote is "In the last hundred and fifty years, an entirely different framework has been developed for physics [bold was added], based on conservation laws." It is not mine, it's Crowell's (op. cit.).

The last references I gave were for similar cases in English and Internet use, physics is not alone in today's hyper anachronicity, all ultimately powered by the exponential Moore's law and globalization in the last ~40 years. Change is coming faster after 150 years, and physicists can appreciate well that an exponential driver eventually  dominates the solution. I am adding this note to that posting, to help the context. Thank you.

Cheers,  Ed Gerck 

Charles,

Have no angst. As I mentioned before, force did not disappear but is now caculated as F = dp/dt, where p, the momentum vector, is well defined, and conserved for a system. Students can re-create all Newton's laws, even better. They are able to describe rocket motion, for example, using F = dp/dt, not F= m*a.

Metaphysics has actually been reduced. Coriolis and centrifugal pseudo forces are no longer metaphysical or "pseudo", as "defined" when using Newton's laws. The motions are real but those forces are not real, they are artifacts of using Newton's laws where they are not valid. 

Let me give an example. Consider a stone going around in exact circles, held tightly by a rope tied to your hand at the center, and you talk about a radial centrifugal force on the stone, and you say you can feel it.  When someone cuts the cord, the stone never moves radially, showing that the radial centrifugal force was an artifact. It was literally created by an impotent use of Newton's laws, and reinforced mentally by your sensorial lag. By using conservation laws, we are able to easily see what is inconsistent in this case.  Although we could also have seen that by noting that Newton's laws (valid for inertial reference frames)  were being applied to a non-inertial reference frame, the radial centrifugal force would still seem as really radial as in the James Bond's Moonraker movie.

Cheers,  Ed Gerck 

Charles Francis, We adhere to different philosophical principles/language.  I take physics as  being the manifestation of some basic principles, such as minimisation / maximisation  of some property of the system/object you are trying to describe.  You seem to take physics as obedience to some equation like F=ma or to descriptions based on microscopic interactions, like surface tensions or atomic interactions.  In terms of universality of application, I think that my philosophy is better, but physics is a broad "church" and can accommodate more than one philosophical viewpoint.

Will someone derive the shape of a soap bubble using F=ma?

Charles, Your explanation seems as intuitive as my philosophical position as far as mechanics is concerned, and minimising an action principle in a Lagrangian sense.

Charles Francis.  My position is that you must get the philosophy right first, then you can start to describe observations in terms of rules, laws and symmetries.  By the way, conserved quantities come from the observations of symmetries.  Nother's theorem tells you that.  So conservation of linear momentum comes from the symmetries under linear transformation, conservation of angular momentum by the symmetries under rotation.  So certain things ARE conserved in non-inertial frames such as rotating frames.  Observe symmetries and derive conservation laws from them, not the reverse.   On the theme of F=ma, this is a self referential definition of force in terms of mass and acceleration, but being self referential is at least consistent.  I still prefer the minimisation principles encompassed in the Lagrangian formulations.  Neat, intuitive, complete and lead to much deeper results.  But don't get tied to one methodology, different problem solving for different situations.  You can derive/define F=ma from Lagrangian mechanics.

 Charles,

You wrote, "Ed, the senselessness in the discussion has been generated by your own claims, and the derisory tone is a reflection of your own attitude, as reflected in you long derisory post of page 7, and the snide remarks you have made throughout, about "students not doing very well", other peoples "misconceptions" when actually the misconceptions were your own,"

I accept your derisive tone, and I have met many friends this way, people who react strongly against a new vision but then find out that they also benefit from it. Leibniz has my deep appreciation (also in life philosophy) and I just regret what Newton did on that one, although Newton did benefit from the higher mathematics and better notation (still used today) in Leibniz formulation. We seem to be at a similar cross-road in this discussion, let us take the high road.

I stand by what I said were misconceptions, no offense intended. Science is built on skepticism, so I welcome misconceptions and exploring them as a way to mine the gold of truth. In science, YES means "not yet false", not just in natural sciences such as physics but also in a formal science such as mathematics.

You continued, "and how students should laugh at being taught the meaning of an inertial frame, which is fundamental to all of physics"

I did not write this, or the rest you mentioned, or meant Crowell's book to be more than a reference to the discussion.

Best regards, Ed Gerck

Hello,

It has been a false question in this thread, whether one should use Newton's laws, Lagrange, Hamiltonian, the principle of least action, or whatever, first or ever.

The question for this thread is "Would it be more insightful for students to learn conservation of momentum laws before Newton's laws?"

The question is not about finding a way to reduce the importance of Newton's laws to the student (high-school or university), or to use anything else. The question is not about inertial or non-inertial reference frames, coordinate-free formulations, or what frame or calculative physics method is "best".

Rather, the question is about increasing the importance of the insight that certain things are conserved. The insight must be shown when working independently of the observer's reference frame or choice of calculative methodology, as physics must not depend on the observer's choice of reference frame or mindset.

Current secondary school math teaching has made it very easy to pursue this program. Much of algebra and geometry taught in high-school are now based on using transformations of translation, dilation (boost), rotation, and mirroring, and symmetries under these transformations. Math has, again, set the stage for physics.

Physics students just have to learn (using Noether's theorem according to their level, even if only intuitively), that empirically conserved physical quantities can be predicted from the observation of symmetries under transformations that students already know from math. Observation of nature directly leads to predicting the conservation of physical quantities.

From symmetry under translation, comes conservation of linear momentum. From symmetry under rotation, comes conservation of angular momentum.  From time translation symmetry comes  conservation of energy, and so on.

The insight is that certain things are conserved, from a symmetry transformation reason, and this insight indeed works independently of the observer's reference frame or calculative methodology used. Welcome Newton's laws, Lagrange, Hamiltonian, the principle of least action, or whatever comes!  The observer is free to choose, although some choices may be better than others, depending on the desired objectives.

The insight "has legs". It works for the classical mechanics of a point particle using Newton's laws, for classical field theory, and quantum field theory. It applies to theories described by a Lagrangian, a Hamiltonian, or both. Further, the insight is empirically supported by the principle of least action, which plays a central role in Noether's theorem [1-2].

Note that, although Noether's theorem can provide an insight into conservation laws and where they come from, the ultimate definition of conserved quantities such as momentum and energy remains an empirical process. This can be pursued using not only formulations such as Hamiltonian, Lagrangian, and the principle of least action, but also Newton's laws or whatever formulation and reference frame may work better [2].

Cheers, Ed Gerck

[1] The Hamiltonian, in most cases, is simply the kinetic energy plus the potential energy. The Lagrangian, in most cases, is simply the kinetic energy minus the potential energy. Noether's theorem applies to theories described by Hamiltonian or Lagrangian formulations, describing a correspondence between continuous symmetries and conserved quantities.  Since both Hamiltonian and Lagrangian formulations can use the principle of least action as a fundamental principle, the observable relation between symmetries and conservation laws provides empirical support to a central role played by the principle of least action in Noether's theorem.

[2] The principle of least action can also be used directly, solving difficulties in the Hamiltonian formulation going from classical to quantum mechanics. Since the Hamiltonian formulation of Noether's theorem is already stronger than the Lagrangian (in the sense that canonical transformations form a "larger" group than point transformations), this directly supports the principle of least action as  fundamental in physics. However, this is not a question in this thread, e.g., whether the principle of least action is fundamental, valid, or even useful, and its consideration is not needed to answer the thread question, "Would it be more insightful for students to learn conservation of momentum laws before Newton's laws?"

It is interesting to learn what Benjamin Crowell says about the center of mass

The center of mass, introduced on an intuitive basis in book 1 as the “balance point” of an object, can be generalized to any system containing any number of objects, and is defined mathematically as the weighted average of the positions of all the parts of all the objects...

In fact it follows trivially from Newton's second law (and one).

Charles Francis, I don't believe that Lagrangians are determined from a definition of Force and Acceleration in a formula like F=ma.  It is rather the other way around, Force, as concept is derived/defined by starting from a Lagrangian.  Circular arguments are not to be dismissed ad hoc; at least they will be self consistent.  I still prefer the Lagrangain/Hamiltonian structures as they include a wider range of phenomena which can be studied and solved, than the rather "mechanistic" F=ma paradigm.  Still for every problem, choose the method that gives the best and most satisfying result.  In many cases this is the integral formulation and minimisation of some property.  Some problems, especially in Electrodynamics, cannot be resolved by the F=ma paradigm and require different methods of solutions.  I cannot assign a greater relevance to Energy, over momentum or other variables of motion, as I think that they are all unified in a self-consistent whole.  The ones we choose at any time to describe "motion" depend on the circumstances which are often determined by boundary conditions and symmetries.

Nother's theorem, in my view is a much more satisfying principle that a demonstration that momentum is preserved, as in your formulaic derivation.

Astro/Galactic physics has, no doubt, a long way to go, but trying to resolve the interactions of billions of stars in a galaxy, using F(I)=m(I)a(I), seems an over-daunting task.  I would choose a minimisation method, which might resemble statistical thermodynamics, which itself is not an F=ma theory, but still gives very powerful results.

Charles Francis,  Just a further comment on the structure of galaxies and other systems which demonstrate apparent self-ordering.  There are theorems in non-linear dynamics, which demonstrate that non-linear systems can become self-ordering.  As galactic interactions (mainly gravity) are non-linear, it should not surprise that they show some structure which also shows up in some regularity of different galactic systems.  Another possible consequence of nonlinearity, is for systems to become stable and to counter the influences of external drivers which might otherwise change them.  You must be aware, of course, of consequences of such non-linear dynamics.

Hello,

By request, I added two comments at the end of my last posting, on the context use of Hamiltonian, Lagrangian, Noether's theorem, Newton's laws, and the principle of least action, and other updates.

Cheers, Ed Gerck

Charles Francis, but here are motions, particularly those associated with EM fields that are not described by Maxwell's equations in their differential form, which you indicate are associated with F=ma paradigm.  These problems are resolved if you use the integral forms and solve in terms of Lagrangian methodologies.  The "force laws" of EM do not work for the Betatron and the ideal transformer.  The acceleration is not given simply by v x B, in the Betatron.  This gives the radial "force", but not the tangential force which produces the orbital acceleration.  Furthermore, as a physicist, I cannot accept that the definition of an EM field is based on F=ma.  How does that explain the energy which resides in a static electrical or magnetic field?  I would claim that matter and motion have much less metaphysics about them than force does.  In physics you work from principles, one of which might be a minimisation principle of some function of a system, which is easily expressed in terms of mass and motion, then derive, if you like, a "force" which can in the simplest cases give you an easy way of doing calculations.  This does not detract from the first principle of finding a minimum of some property of the system.  This works in dynamics, statics, equilibrium, optics and many other areas, and so becomes a much more unifying and uniform principle than applying an empirical formula like F=ma.  Try doing quantum mechanics with F=ma or tracing optical paths through non-uniform media with an F=ma paradigm.  Dead ends.

Hello,

Conservation of momentum and Noether's theorem are like apples and speedboats. The former is an experimental fact, the latter is a human construct. The empirical utility and precedence of Noether's theorem is to provide an insight into conservation laws and where they come from. However, the ultimate definition of conserved quantities such as momentum and energy remains an empirical process.

Of course, this can be pursued using not only formulations such as Hamiltonian, Lagrangian, and the principle of least action, but also Newton's laws or whatever formulation and reference frame may work better.

However, the question whether one should use one or other formulation, or reference frame, is out of scope in this thread, and its consideration should not be needed to answer the thread question, "Would it be more insightful for students to learn conservation of momentum laws before Newton's laws?"

Cheers, Ed Gerck

Saying that the Noether theorem would somehow "explains" the conservation laws is rather an empty statement. It can be as well used to "explain" the symmetries, it is just some form of equivalence, or tautology in some kind of mathematical formalism.

In the scope of this thread, it seems useful to remind that mathematics are something different from the empirical science that is physics.  Newton's laws can be derived from momentum conservation, but the other way round too.  Physics is not about what should be derived from what, it is about how to relate the mathematical formalism to experiment.  A force is a tangible concept, while momentum conservation is not, and in a didactic context, that makes all the difference.

There are many types of "mechanics."  The mathematicians are more focused on analysis, limits and all that stuff, as well as putting down the physicists.  The engineer are more interested in materials and their properties, equilibrium, rigidity, efficiency etc. as well as putting down the physicists and the mathematicians.  There is also physical mechanics, and finally mechanical mechanics, which really works out everything for the mathematicians, the physicists, and the engineers.

Christian, putting aside that deeper and wider is rather empty parlance, it is precisely why momentum conservation should'n be taught first, since deepness and wideness are not natural and must be gained by first studying what is closer to everyday experiment.  The teacher must put himself in the shoes of the students, otherwise it would lead to massive drop out, the very thing he doesn't want.