On the teaching of introductory physics

[mov]

I am a junior in high school enrolled in an AP Physics B course, and as you are probably aware the curriculum consists exclusively "classical physics". I understand the value of easy calculation in teaching physics without calculus, but I am concerned as to whether or not an education in classical physics would actually aid one, or serve as a prerequisite to modern quantum mechanics. Perhaps my notions are fundamentally in error, but it seems counter productive to entice students such as myself to "understand" something which is accepted as wrong. I have learned some purely qualitative concepts of quantum theory which seem to point me in this direction as well. I would really appreciate if some teachers (perhaps even AP Physics B teachers) could shine some light on this.

Thanks,
Carter

 

[AlephZero]

Classical physics may be "wrong" in a philosophical sense, but it's still very useful. For example high school students heading towards engineering rather than physics might never use anything else in their whole working lives. Even electronics engineers using semiconductor components (diodes, transistors, etc) which need quantum mechanics to explain how they work, mostly don't use quantum mechanics to use those components to design practical circuits.

Classical physics is a very good approximation to "reality" except in extreme situations, like the behavior of sub-atomic particles, or for objects traveling close to the speed of light.

I'm not a teacher, but I would say it's much better to get a solid understanding of something you can "understand" with the math tools you have available (especially if they don't include calculus) rather than pick up a lot of "pop science facts" without the math. You can't begin to study say quantum mechanics properly unless you know calculus, linear algebra, differential equations, etc.

 

[mov]

Classical physics may be "wrong" in a philosophical sense, but it's still very useful. For example high school students heading towards engineering rather than physics might never use anything else in their whole working lives. Even electronics engineers using semiconductor components (diodes, transistors, etc) which need quantum mechanics to explain how they work, mostly don't use quantum mechanics to use those components to design practical circuits.

Classical physics is a very good approximation to "reality" except in extreme situations, like the behavior of sub-atomic particles, or for objects traveling close to the speed of light.

I'm not a teacher, but I would say it's much better to get a solid understanding of something you can "understand" with the math tools you have available (especially if they don't include calculus) rather than pick up a lot of "pop science facts" without the math. You can't begin to study say quantum mechanics properly unless you know calculus, linear algebra, differential equations, etc.

I guess I didn't put it in perspective, in terms of usefulness, I certainly acknowledge the value of a classical physics education. However, in education I think that students should not be taught contradictory information for the sake of usefullness. I recall that in chemistry we learned information which seems in direct contradiction with what we are being taught in our physics classroom. The other issue that seems problematic is the idea of understanding. We are told in rote that the purpose of the class is not to get the right answer, but to understand the concept.
If this does not seem problematic, allow me to propose a hypothetical example:
Pi ≈ 3.14159 so in classroom across the nation teachers teach that Pi=3.14159, until they reach calculus and can form a numerical understanding of it. The teachers come up with tricks to "understand" that pi=3.14159, and students are expected to recite and self assert these mnemonic devices. In the past, these students learned of regular polygons (we learned conversely of quantum theory in chemistry), but they began to resent those teachers for decieving them so.

 

[phinds]

... something which is accepted as wrong.

What is it you think is "wrong"

For example, there is a pedantic point of view that legitimately says that Newtonian gravity is "wrong" but do you really think people build bridges using General Relativity?

 

[D H]

Perhaps my notions are fundamentally in error, but it seems counter productive to entice students such as myself to "understand" something which is accepted as wrong.

Your notions are fundamentally in error. Classical physics is still valid, just not universally so. It falls apart in the realms of the extremely fast (the domain of special relativity), extremely large (the domain of general relativity), or extremely small (the domain of quantum mechanics). In our everyday world -- classical mechanics works quite well. If classical physics was "wrong", a whole lot of engineering practice would be invalid because much of engineering is applied classical physics. That engineering physics works just fine because the deviations between what a more precise physics would indicate is so small as to be meaningless -- and that's assuming that quantum mechanics or general relativity could even be employed. QM, for example, becomes pretty much intractable in the face of 10³⁰ particles or more.

I'll close with some words by Isaac Asimov:

"When people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together."​

 

[mov]

What is it you think is "wrong"

For example, there is a pedantic point of view that legitimately says that Newtonian gravity is "wrong" but do you really think people build bridges using General Relativity?

This is what I am saying. However, I strongly disagree that this view is pedantic given that students are asked if they "understand" why an approximation is true, when it is inherently false by its own label of "approximation". Is this so minute a detail when explanation is at hand? I have no trouble self-affirming formulas and truths which give me a near perfect answer, but there is something in this which seems very unscientific. When it comes time to learn Newtonian gravity, we are not told this is approximately how gravity works, we are told this is how gravity works. My peers and I did not sign up for a course in physics calculation or in bridge building; we signed up for a course which would teach us the underlying principles of physics, regardless of how inconveniently complex our current understanding of those principles may be.

Allow me to finish with a quote from Bertrand Russell:

When you are studying any matter, or considering any philosophy, ask yourself only: What are the facts, and what is the truth that the facts bear out. Never let yourself be diverted, either by what you wish to believe, or what you think could have beneficent social effects if it were believed; but look only and solely at what are the facts.

And to address D H:
Given y=x/(10^999)
Using your logic, we might state that y<1, since it only begins to break down when x>=10^999 (a very big number). While y<1 may be a practical range when a mundane value is inputted, stating that y<1 is unscientific and does not reflect or permit a conceptual understanding of the equation.

 

[D H]

What is it you think is "wrong"

For example, there is a pedantic point of view that legitimately says that Newtonian gravity is "wrong" but do you really think people build bridges using General Relativity?

This is what I am saying.

I'll be very blunt. You're wrong. People do not build bridges using general relativity. They use Newtonian mechanics. NASA sent people to the Moon and brought them back without using one iota of general relativity.

You are mistaken in a couple of other regards. One is that physicists almost universally do not view general relativity and quantum mechanics as the ultimate truth. One of the biggest pushes in theoretical physics is to find a way to meld these two currently incompatible topics. If and when that happens, it will inevitably involve a hitherto unknown flaw in both general relativity and quantum mechanics that this new physics fixes.

The other regard in which you are wrong is that you do not have the mathematical background to understand general relativity or quantum mechanics. You will learn that background by first studying Newtonian physics, and first in its Newtonian form. You can start that journey now because some of the underlying mathematics is accessible even without calculus. You'll learn Newtonian physics again with calculus. If you stick with physics, you will learn classical physics yet again, this time in terms of the Hamiltonian reformulation of Newtonian mechanics. This learning and relearning will happen again and again. You will learn and relearn special relativity. You will learn and relearn and relearn electricity and magnetism. You will learn and relearn and relearn and relearn quantum mechanics. Those first steps are absolutely essential to understanding physics and in developing the mathematical understanding needed to take those subsequent steps.

 

[SteamKing]

Instead of teaching kids to count in kindergarten, they should all be thrown in the deep end of the pool and start learning calculus immediately. The same results would apply if you took even the brightest high school physics students and threw them into studying QM and SR without first introducing them to basic physical concepts developed in classical mechanics.

The scientists who developed relativity and QM all had a deep understanding of classical mechanics. Einstein and Planck wrestled with their respective theories before publishing them because they knew that a giant break in interpreting the physical world would result. It's not recorded that they felt any resentment toward their training in classical physics because it did not and could not explain everything. Even Newton declined to provide an answer on how gravity could work apparently instantaneously across great distances on various bodies.

 

[Andy Resnick]

<snip>you do not have the mathematical background to understand general relativity or quantum mechanics. <snip>

I agree with everyone's responses, I just wanted to tweak this sentence a bit.

Yes, the mathematics of GR and QM are (often) more sophisticated than classical mechanics (although GR is a classical field theory). More to the point, the *physics* of QM is incomprehensible without the context of classical mechanics that assigns physical properties to mathematical objects.

A simple example is 'velocity'. This physical concept is easily defined in classical mechanics but not so in QM. The same holds true for other foundational concepts such as conservation laws, stress and strain, heat and dissipation, pressure, etc. etc.

 

[mov]

Just to post for the benefit of others who might be asking themselves similar questions:
My thoughts:
I am not a physicist, and if I understood or was able to apply general relativity, then I would not be in this dilemma in the first place.
I see the reasoning behind your comments, and I wish to acknowledge your valid points.
I now understand that approximations are often a necessary part of necessary part of general relativity, while in some situations an exact solution is in order.

The community here has put forth the resounding opinion that the notion that Newtonian is not fundamentally wrong and I accepted this as fact for several weeks, until I began to research more deeply and happened upon an introduction to special relativity which struck a chord with me:
"Beginners often believe that special relativity is only about objects that are moving at high velocities. This is a mistake. Special relativity applies at all velocities but at low velocity the predictions of special relativity are almost identical to those of the Newtonian empirical formulae. As an object increases its velocity the predictions of relativity gradually diverge from Newtonian Mechanics." - Instructors Guide to teaching special relativity <http://upload.wikimedia.org/wikipedia/commons/7/74/Special_Relativity_V2.11.pdf>
This seemed to me to contradict an assertion made very clearly by D H:

Your notions are fundamentally in error. Classical physics is still valid, just not universally so. It falls apart in the realms of the extremely fast (the domain of special relativity), extremely large (the domain of general relativity), or extremely small (the domain of quantum mechanics).

At I first thought that the book's assertion must be invalid. I decided to make one last search on my quest for truth, and I found that others shared my, and the book's view on the validity of Newtonian physics:
My resources:
* - http://arxiv.org/ftp/physics/papers/0207/0207109.pdf
* - http://www.feynmanlectures.caltech.edu/I_39.html

To address a point made D H:
"One is that physicists almost universally do not view general relativity and quantum mechanics as the ultimate truth."
I never stated that it was ultimate truth, but no science is apodictic, so the word true or truth means the best we have- that is, if true is to have any meaning at all.
My rational is the same as that which argues against the teaching of Aristotelian physics. If I have learned anything from my basic understanding of relativity and cosmology it is that the Earth does not hold a privileged frame of reference. We have no right to assert that the conditions we experience on a day to day basis are, when all's said and done, the only conditions which high school children should be taught about.

As I do more and more research, I find increasingly belittled by your ostensible (albeit, well intended) deception (and I certainly do not mean to say that you don't understand what you are talking about, only that you feel it is not necessary to provide a proof for your disputed assertion).
I am puzzled at this most unscientific expectation in a bastion of science; I hope that I will not be so credulous as to believe in someone's undemonstrated assertion merely because they are an authority figure.

Perhaps I am utterly lost and have misconstrued every word I have read in my research, but I will leave you with a video which tackles the matter in simplistic format which even I can claim to fully understand:


Good bye for now,
Carter

" If we are not able to ask skeptical questions, to interrogate those who tell us that something is true, to be skeptical of those in authority, then we’re up for grabs for the next charlatan, political or religious, who comes ambling along."
- Carl Sagan

 

[D H]

Instead of teaching kids to count in kindergarten, they should all be thrown in the deep end of the pool and start learning calculus immediately.

That's not the deep end of the pool! Learning calculus is close to the shallow end of the pool. The deep end of the pool contains Hilbert space, non-Euclidean geometry, differential geometry, Lie groups, and group theory.

Just to post for the benefit of others who might be asking themselves similar questions:
My thoughts:
I am not a physicist, and if I understood or was able to apply general relativity, then I would not be in this dilemma in the first place.

That you are not a physicist means you are not qualified to judge how physics is taught or used. As a high school student, I am 99.9% sure (or higher) that you do not have the mathematical skills to learn general relativity. That top 0.1% or less who do have those skills: They learned Newtonian mechanics along the way. It is an essential part of physics education.

Continuing, emphasis mine:

"Beginners often believe that special relativity is only about objects that are moving at high velocities. This is a mistake. Special relativity applies at all velocities but at low velocity the predictions of special relativity are almost identical to those of the Newtonian empirical formulae. As an object increases its velocity the predictions of relativity gradually diverge from Newtonian Mechanics." - Instructors Guide to teaching special relativity

It is an even bigger mistake to think that this means Newtonian mechanics is wrong. It is "wronger than wrong."

Rhetorical question: If Newtonian mechanics is flat out wrong (never valid), why do physics instructors still teach it? The answer is that Newtonian mechanics is still valid as the limiting behavior when velocities are small compared to the speed of light and densities are small compared to that needed to create a black hole. In our ordinary world of small velocities and small masses, the discrepancies between those predicted by Newtonian mechanics and relativity are immeasurably small.

 

[AlephZero]

" If we are not able to ask skeptical questions, to interrogate those who tell us that something is true, to be skeptical of those in authority, then we’re up for grabs for the next charlatan, political or religious, who comes ambling along."
- Carl Sagan

Any fool can ask skeptical question and challenge authority by claiming that the Earth is flat and the moon is made of green cheese. That's not skepticism or interrogation. It's stupidity.

You need to be able to ask the questions and interrogate the authorities rationally. If you can't do that (and it's unlikely you can do much of it, with a high school level of knowledge), its you who is posing as the charlatan.

 

[Jorriss]

If Newtonian mechanics is flat out wrong (never valid), why do physics instructors still teach it? The answer is that Newtonian mechanics is still valid as the limiting behavior when velocities are small compared to the speed of light and densities are small compared to that needed to create a black hole.

I would in addition add that I still believe classical mechanics to be the most appropriate avenue to learn about mechanical quantities such as momentum, energy, angular momentum, etc.

On another note, one often hears how 'chemistry was solved' once the Schrodinger equation was developed as quantum mechanics explains the whole of chemistry. It might be somewhat surprising to realize outside of a few (large) areas of chemistry just how much theoretical chemistry is dominated by classical mechanics (with some quantum corrections). Classical mechanics gives an exceedingly good picture of how molecules behave in bulk.

 

[chenleo]

A taste of classical physics would help you relate physics with daily lives. Science is a kind of attempt to understand the nature. So there would be some seemingly wrong first and then be filled with more accurate details.
My suggestion would be learn classical physics well first and then learn calculus and applied math, which would benefit you a lot when you further study physics.

 

[R136a1]

Feynman:

You might ask why we cannot teach physics by just giving the basic laws on page one and then showing how they work in all possible circumstances, as we do in Euclidean geometry, where we state the axioms and then make all sorts of deductions. We cannot do it in this way for two reasons. First, we do not yet KNOW all the basic laws: there is an expanding frontier of ignorance. Second, the correct statement of the laws of physics involve some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean. No, it is not possible to do it that way, we can only do it piece by piece.

Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth as far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again, or more likely, to be corrected.

...

Now, what should we teach first? Should we teach the correct but unfamiliar law with its strange and difficult conceptual ideas, for example, the theory of relativity, four dimensional space-time and so on? Or should we first teach the simple "constant mass" law, which is only approximate, but does not involve such difficult ideas?? The first is more exciting, more wonderful, and more fun, but the second is easier to get at first, and is a first step to real understanding of the second idea. This point arises again and again in teaching physics. At different times we shall have to resolve it in different ways, but at each stage it is worth learning what is now known, how accurate it is, how it fits into everything else and how it may be changed when we learn more.

 

[gmax137]

When I was in high school, physics appealed to me because I viewed it as study of the world/universe and how it really worked. By the time I graduated with a bachelor's in physics, I saw that this wasn't really true, at least not in the sense that I had believed. Science, it seems, is more about predicting the outcomes of measurements (readings on scales, rulers, and stopwatches; counting clicks from a detector, etc.). It is about "what" will happen, not so much "why" things happen. This was very disappointing to me. But, this realization frees you from the notion that you are learning "the truth" in any deep sense. So, it isn't correct to say teaching Newton's (or Hamilton's) mechanics is deceiving the student. Those disciplines are no less "true" than quantum mechanics, special relativity, or GR.

If there's anything different the teachers might be doing, it is to let the students know this. Classical mechanics is about "how to aim your cannon" - it is NOT about "how" the cannon ball "knows" what to do. But really, most high school freshman have enough to be confused about, there isn't really much point in going into this. The few who are smart enough to see it at that age (like the OP, maybe) will likely figure it out on their own.

 

[mal4mac]

When I was in high school, physics appealed to me because I viewed it as study of the world/universe and how it really worked. By the time I graduated with a bachelor's in physics, I saw that this wasn't really true, at least not in the sense that I had believed. Science, it seems, is more about predicting the outcomes of measurements (readings on scales, rulers, and stopwatches; counting clicks from a detector, etc.). It is about "what" will happen, not so much "why" things happen. This was very disappointing to me. But, this realization frees you from the notion that you are learning "the truth" in any deep sense. So, it isn't correct to say teaching Newton's (or Hamilton's) mechanics is deceiving the student. Those disciplines are no less "true" than quantum mechanics, special relativity, or GR.

If there's anything different the teachers might be doing, it is to let the students know this. Classical mechanics is about "how to aim your cannon" - it is NOT about "how" the cannon ball "knows" what to do. But really, most high school freshman have enough to be confused about, there isn't really much point in going into this. The few who are smart enough to see it at that age (like the OP, maybe) will likely figure it out on their own.

I agree with everything you say here, except for the last couple of sentences. I don't see why teenagers can't be introduced to this idea, and it's really something everyone should know, so it should be taught at school level. Hawking's latest book explains these ideas well for an audience at this level; even their parent might understand it:

http://en.wikipedia.org/wiki/Model-dependent_realism

 

[thegreenlaser]

I agree with most people here that GR and QM shouldn't be taught at a high school level. I do, however, feel that there is some benefit in teaching students physics by saying "here is a collection of models for predicting how the world works" rather than "this is how the world works." I don't think that it's that difficult of a concept for high school students, and by doing that you teach students two valuable lessons:
1) All of the answers physics gives us are only approximately correct. (At least so far)
2) Approximate answers can be extremely valuable, even if they aren't "right."

It also avoids any confusion caused by saying "here's how the universe works" and then later saying "okay, actually it doesn't work that way, it works this way." If you word things like that, how is a student not justified in saying that you lied to them?

Because I was taught physics as if it was the "truth" of how the world works (and I took that at face value) I had some serious misconceptions in this area when I was in high school, which I suspect the OP has as well. Those misconceptions quite often led me to confusion and frustration. Because I thought that physics could always give you the exact, correct answer, I didn't understand why you would ever want to make approximations, and I was frustrated whenever textbooks/teachers used approximations to solve a problem. I thought that more accuracy is always better, which led to a bad habit of immediately attacking problems with the most sophisticated model available rather than first gaining some intuition with simpler, approximate methods.

To the OP:
I hope you can learn the two lessons I listed above, and realize that your teachers are not "lying" to you, they might just be phrasing things poorly. As others here have said, physics is not trying to tell you how the world works, it's trying to give you some models (of varying degrees of accuracy) for predicting how the world works. As of yet, we have no perfectly correct models. We have some models which are more accurate than others, but they tend to be more difficult to use, which decreases their value in certain situations.

In the real world, there is huge value in approximate answers. When you run a simulation to see how an antenna will work, for example, there's usually a balance between accuracy and run-time. It might be a question of getting a 98% accurate answer with a simulation that takes a day to run vs. getting a 99% accurate answer with a simulation that takes a week to run. If the 98% answer is good enough, why would you spend the extra week getting a slightly better answer? The same thing goes for designing bridges. The amount of time and effort it would take to design a bridge using quantum mechanics and general relativity would be ludicrous, and the increase in accuracy probably wouldn't even be noticeable. That's why they teach you classical mechanics--even though it's more "wrong" than other models, it's still extremely valuable. For most problems, the classical model is far more valuable than the more correct models based on quantum mechanics and relativity.

 

[MalachiK]

Any fool can ask skeptical question and challenge authority by claiming that the Earth is flat and the moon is made of green cheese. That's not skepticism or interrogation. It's stupidity.

You need to be able to ask the questions and interrogate the authorities rationally. If you can't do that (and it's unlikely you can do much of it, with a high school level of knowledge), its you who is posing as the charlatan.

This is the most righteous text I've read on the internet all year! I may print off a copy and stick it up above the board in my classroom.