# Physics education is 60+ years out of date

• Will Flannery
Will Flannery
<Mentor’s note: this thread is closed as a duplicate of https://www.physicsforums.com/threads/the-coming-revolution-in-physics-education.954664/ >

In the March 2024 issue of Nature Physics 'Computing in Physics Education' (https://www.nature.com/articles/s41567-023-02371-2) we read:
"In the USA the undergraduate physics curriculum - that is, the standard set of coursework and activities in an accredited physics major – looks much the same as it did 60 years ago."

In that 60 years the computer has completely transformed how physics is used to analyze the real world, specifically:
#1 Classical physics is based on the analysis of differential equation models of physical systems.
#2 The differential equation models of most physical systems are analytically unsolvable (this is the University's little secret). This is why physics education is so difficult, and why so few physical systems are analyzed.
#3 The computer and computational calculus, i.e. numerical methods for solving differential equations, made it possible to to analyze unsolvable models of physical systems.
#4 Computers and computational calculus quickly became the norm for analyzing systems outside the classroom in science and engineering.

Clearly this transformation has not been incorporated into physics education.

The first step would be to incorporate computers and computational calculus into the curriculum. Fortunately, computational calculus, unlike analytic calculus, is simple, intuitively transparent, and the powerful basic method can be taught to high school science students with no previous exposure to calculus in a single one-hour lecture.

Now, what else needs to be taught? Newton's law of gravity and 2nd law of motion are already being taught in high school.

I've taught such an introductory class, and written it up in 'The Coming Revolution in Physics Education' (https://pubs.aip.org/aapt/pte/article/57/7/493/1016338/The-Coming-Revolution-in-Physics-Education) and described the extension to the university here 'A Revolution in Physics Education was forecast in 1989, why hasn't it happened? What will it take?' (https://pubs.aip.org/aapt/ajp/artic...volution-in-physics-education-was-forecast-in)

Just as computers and computational calculus will transform introductory courses, they will transform all courses in the classical physics curriculum, introductory to advanced.

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jbergman, weirdoguy and Bystander

topsquark and Bystander
Will Flannery said:
In the March 2024 issue of Nature Physics 'Computing in Physics Education' (https://www.nature.com/articles/s41567-023-02371-2) we read:
After a Mentor discussion, this new article adds enough to the discussion that we can let this thread go on (as opposed to trying to merge it into the old thread on this subject from a couple years ago). Thanks for your patience.

Note that the main distinction between this post and the previous thread is the recent Nature Physics article. Please focus on discussing that. If we start rehashing the old thread then we will close this one as it would be redundant.

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berkeman
Will Flannery said:
In the March 2024 issue of Nature Physics 'Computing in Physics Education' (https://www.nature.com/articles/s41567-023-02371-2) we read
I don’t have access to the full article. In the abstract the authors claim “Computing is central to the enterprise of physics but few undergraduate physics courses include it in their curricula”. Do they provide any evidence to support that claim? I remember doing a double pendulum numerical computation in undergraduate in the 90’s. So I am skeptical of that claim

Klystron and PhDeezNutz
I'm skeptical of the article's claims, especially with respect to lower division physics classes.

In those classes, the idea is to establish the basic concepts of the laws of physics at the classical level, informed by calculus, generally including special relativity, but with little or no treatment of quantum mechanics and general relativity. Students in those classes are usually either taking calculus at the same time or took it in their junior and/or senior year of high school.

Many high schools don't offer physics at all, or offer only a watered down, non-calculus based physics presentation, so the college curriculum needs to establish a baseline of the basics of calculus based mechanics, electromagnetism, and thermodynamics.

As such, there isn't much need for computers in lower division classes, and it is important to be sure that the students understand the underlying calculations that computer programs would use. As they say in football, you have to run to establish the pass.

Typically, a physics or engineering major wouldn't learn differential equations, and wouldn't be taking physics classes where they could be applied and used with numerical methods, until sophomore or junior year of their undergraduate education. And, at that level, I share Dale's skepticism in post #5 that computers aren't being used.

When I was in college as a math major taking lots of physics courses in the early 1990s we were using computers to do numerical approximations of differential equations. Similarly, my sister-in-law was a physics major in the early 1990s, and her first job out of college was in IT rather than physics, a shift facilitated by the heavy use of computers by physics majors in her program.

When my children were in high school in the twenty-teens (an "inner city" public school no less, complete with lock downs for shootouts near the high school campus), they had to turn in assignments written with LaTex on a computer which often integrated computer made charts and graphs illustrating whatever they were dealing with in their assignments. Graphing calculators (which also do numerical calculations) were required as well. Their high school didn't offer calculus based physics. Incidentally, both of them went on to graduate from highly selective colleges with STEM majors (although neither of them was a physics major).

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CalcNerd, DeBangis21, PhDeezNutz and 2 others
Dale: "Do they provide any evidence to support that claim? "
One of the authors, Caballero, is a one of the top honchos at PICUP, and he wrote a paper on the subject a few years ago ... "Prevalence and nature of computational instruction in undergraduate physics programs across the United States" (https://journals.aps.org/prper/abstract/10.1103/PhysRevPhysEducRes.14.020129)

Also there is a AAPT/APS report - Phys21: Preparing Physics Students for 21st Century Careers (https://www.compadre.org/JTUPP/report.cfm) where we read

Despite the emergence of new disciplinary sub-areas such as computational physics, biophysics, and materials physics, the undergraduate physics curriculum has changed little over the last 50 years.

ohwilleke:
Think of it this way - Today (as I recall) students in high school study Newton's law of gravity, and 2nd law of motion. From these laws they derive (by dividing) an equation for the acceleration of a falling object. An equation for acceleration is a differential equation. However this differential equation does not have a closed form solution, Lagrange derived an infinite series solution in the 1700s, you can see one version here - wiki Free Fall (https://en.wikipedia.org/wiki/Free_fall). This is beyond not only high school calculus but also university calculus. So, in high school they simplify the to A(r) = -9.8 m/sec2, and give a heuristic solution and are able to study projectile motion near earth.

The only reason differential equations are not studied earlier than the 3rd or 4th semester at the U is because they are difficult to solve. In mechanics, a differential equation is just an equation for velocity or acceleration, i.e. there is absolutely nothing difficult about it, unless you try to solve it.

And, given that computational calculus calculus is trivially easy and intuitively transparent, in the new curriculum students can begin analyzing orbits and rocket trajectories in high school! All the details are in the paper linked in my 1st post. Thus, we have high school students analyzing systems that are beyond the scope of university physics.

Note: there is a general feeling that numerical analyses are inferior to analytic analyses. And while analytic solutions are elegant and do have some features that numerical solutions, the hard reality is that most systems can only be analyzed (i.e. their performance predicted) using computation.

All this was written up in 1989! See ... Using Computers in Teaching Physics (https://pubs.aip.org/physicstoday/a...ng-Computers-in-Teaching-PhysicsComputers-can) where we read ...
Computers can revolutionize not only the way we teach physics, but also what physics we teach’

The computer has revolutionized the way we do physics, but surprisingly, it has not significantly altered the way we teach physics. Talks and papers on teaching with computers fill the meetings and journals of the American Association of Physics Teachers, and workshops on the topic abound, yet the real impact of computers in the classroom is slight.

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Will Flannery said:
"Prevalence and nature of computational instruction in undergraduate physics programs across the United States" (https://journals.aps.org/prper/abstract/10.1103/PhysRevPhysEducRes.14.020129)
Interesting. That data doesn’t seem particularly dire to me. From the paper

"We find that a majority of faculty respondents report some experience teaching computation to undergraduate students and that a majority of departments have a simple majority of faculty reporting having such experience (Fig. 2). "

So, most professors at most universities have personal experience teaching using computational methods as part of their course. The actual question of interest is if students gain such experience during their coursework. And if most of the faculty in most of the universities are doing that, then almost all of the students will necessarily gain such experience over their degree. This seems like very positive data.

Will Flannery said:
All this was written up in 1989!
Let's stick with the new stuff. The old stuff was exhaustively covered in the other thread and does not need to be rehashed here. If you insist on doing so, then this will be a short thread. This is not an opportunity to re-air your old complaints. This is an opportunity to discuss the new data.

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Klystron
There are 2 things to consider, are the Nature Physics quote and the APS/AAPT quote authoritative, i.e. correct, and, if they are correct, are they important?

To answer these questions it’s necessary to understand the context. There is the academic context – for 20-30 years there have been major efforts to improve physics education. And there is also the physics and engineering practical context, i.e. how have computers changed physics.

First, the academic context. In 1989 a revolution in physics education was forecast in Using Computers in Teaching Physics. It is subtitled ‘Computers can revolutionize not only the way we teach physics, but also what physics we teach’, and begins:

"The computer has revolutionized the way we do physics, but surprisingly, it has not significantly altered the way we teach physics. Talks and papers on teaching with computers fill the meetings and journals of the American Association of Physics Teachers, and workshops on the topic abound, yet the real impact of computers in the classroom is slight."

In the 30+ years since then physics education research (PER) has become a recognized academic field and there are 80+ PER centers in the US. Physics professors formed the partnership for incorporation of computation in undergraduate physics (PICUP), and it now has 1500+ members.

In addition, NSF spent \$200 million funding the STEM-C program to improve science, technology, engineering, and mathematics instruction, with a major emphasis on the use of computers.

Yet, we have the APS/AAPT quote below. Note that one of the authors, P. Heron, of APS/AAPT report is an editor for Physical Review Physics Education Research, so one would assume the quote is authoritative.

"Despite the emergence of new disciplinary sub-areas such as computational physics, biophysics, and materials physics, the undergraduate physics curriculum has changed little over the last 50 years."

I submitted a AJP letter to the editor ‘A Revolution in physics education was forecast in 1989, why hasn’t it happened?’ that included the APS/AAPT quote. The letter went through 3 rounds of reviews(!) and there was considerable pushback against the quote. I also tried this quote from the earlier Caballero article:

"A majority of faculty do report using computation on homework and in projects, but few report using computation with interactive engagement methods in the classroom or on exams."

But that too was a no go. Finally the editor agreed to publish the letter if I removed the quote, which I did.

Two months after my letter was published the AJP published a letter from the dean of PER, E. Redish, titled ‘The computer revolution in physics education, it’s here!’ Quoting –

"Want to include more computing in your class? Try Chabay and Sherwood’s Matter & Interactions, wrapped around a core of VPython programming."

The 1989 paper, by Wilson, Redish(!), had kicked off a real effort to incorporate computation into physics education. B. Sherwood had worked with them and Matter & Interactions is an introductory physics text that incorporates some computational calculus into mechanics. It is in use in several universities today. I think it’s the one exception to the APS/AAPT and Nature Physics quotes above. Read about it here https://brucesherwood.net/?p=87

So, I think the quotes are accurate, with possibly an asterisk for Matter & Interactions.

Even though I got pushback on the APS/AAPT quote, The Nature Physics quote below is so categorical, I assumed it would be taken as authoritative. Wrong again!

"In the USA the undergraduate physics curriculum - that is, the standard set of coursework and activities in an accredited physics major – looks much the same as it did 60 years ago."

In order to understand why the both quotes are authoritative and important, it’s necessary to understand not only the academic context, but also the physics and engineering practical context.

Finally, we’re getting to the crux of the matter. What effect did computers have on physics? I’m a big fan of Bing AI, so let’s ask it - ‘How did the computer revolutionize physics?’ This is one section of the response:

"#2 Numerical Simulations and Modeling: Computers enabled physicists to perform complex numerical simulations and model physical phenomena. From simulating fluid dynamics to predicting particle interactions, computers allowed researchers to explore scenarios that were previously impossible or time-consuming. For example, chaos theory in non-linear systems saw renewed interest due to computational capabilities."

I believe this accurately reflects the opinion of most academic physicists, but it is both wrong and misleading.

First, it’s wrong, the computer did not enable physicists to model physical phenomena. The differential equation models of physical systems in all branches of classical physics existed before 1900. The problem for physics was that the differential equation models were unsolvable, so the performance of the system could not be predicted. The computer and computational calculus made it possible to calculate solutions to analytically unsolvable differential equations and hence predict the performance of analytically unsolvable systems.

Second, it is wildly misleading, it states that the computer made it possible to analyze previously impossible (or time-consuming?) systems, which is correct, but instead of noting that almost all systems in classical physics are analytically unsolvable (i.e. impossible) it gives chaotic non-linear systems as an example, i.e. tangential systems that are of very limited interest.

This is the crux of the matter, and it is an invisible elephant in the physics classroom: the differential equation models of most physical systems are analytically unsolvable.

Link to a photo of the elephant in the physics classroom - https://i.ibb.co/DG9spnt/elephantintheroom.jpg

Is the elephant really invisible? A search of past and present issues of the AJP, Physics Today, Nature Physics, Physical Review Physics Education Research, and the PICUP web site, for ‘unsolvable differential equation’ yields only one hit, my AJP letter to the editor.

Unsolvable systems
Central force motion - Orbits: the two-body problem doesn’t have a closed form solution, the Lagrange solution (see wiki Free Fall) is beyond the scope of university mathematics. The three-body problem is unsolvable.

Electric circuit analysis - Electric circuit analysis is taught in the university without non-linear elements, and analyzed in advanced classes using the Laplace transform. If a circuit contains a non-linear element the Laplace transform can’t be used and the circuit is analytically unsolvable. In the real world circuits are analyzed with programs like SPICE (Simulation Program with Integrated Circuit Emphasis).

Rigid-body dynamics – from Classical Mechanics, J. Taylor:
"The three Euler equations determine the motion of a spinning body as seen in a frame fixed in the body. In general, they are difficult to use because the components Γ1, Γ2, Γ3 of the applied torque as seen in the rotating body frame are complicated (and unknown) functions of time. In fact, the main use of Euler’s equations is in the case that the applied torque is zero**… however there are a few other cases where the torque is simple enough that we can get useful information from Euler’s equations.”
(**otherwise the equations are unsolvable, ed.)

Heat transfer - From Heat and Mass Transfer, Y. Cengel, A. Ghajar:
"Analytical solution methods are limited to highly simplified problems in simple geometries. The geometry must be such that its entire surface can be described mathematically in a coordinate system by setting the variables equal to constants.
… Even minor complications in geometry can make an analytical solution impossible.
... Even in simple geometries, heat transfer problems cannot be solved analytically if the thermal conditions are not sufficiently simple."

Fluid dynamics - From Fundamentals of Fluid Mechanics, P. Gerhart, A. Gerhart, J. Hochstein:
"Unfortunately, because of the general complexity of the Navier–Stokes equations (they are nonlinear, second-order, partial differential equations), they are not amenable to exact mathematical solutions except in a few instances.”

Maxwell’s equations – From, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropics, K. Yee
"Solutions to the time-dependent Maxwell’s equations in general form are unknown except for a few special cases."

The graphs below show the results of computational analyses of unsolvable systems spanning the range of classical physics. They are all far beyond the scope of the current university physics curriculum.
Link to graphs of results of analyses of unsolvable systems: https://i.ibb.co/FXyqcBX/Graphs.jpg

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I was very clear about not rehashing the old stuff. This thread is closed.

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