Sometimes (like now) when I wake up at night and can’t get back to sleep, I go to arxiv.org and browse through recent physics papers. Topics that interest me include dark energy, the physical basis (if any) of free will (if it exists), and alternatives to the the Copenhagen interpretation of quantum mechanics (I never grasped how a wave function “collapses”). Don’t worry, keep reading — I’ll keep it simple, and there’s no test at the end of the page.
What is odd is that I am not particularly adept in physics, or more specifically, the math used in college physics and beyond. They lost me at Hamiltonians, probably even earlier:
At left is the Hamiltonian. That triangle is called nabla.
Physics wasn’t this complicated in high school. In high school, I recall that we were taught Newton’s Laws; how things tend to expand when heated; how to calculate the horsepower we generated running up a flight of stairs; how “particles” of light that are absorbed by the fins of a radiometer make it spin; and maybe something about electric and magnetic fields, I don’t know. Mostly I remember how our teacher, Ron Noel, would take thirty-minute smoke breaks in the second period of the class, during which I would help my wife-to-be with her shorthand (yes, shorthand!) assignments.
As my wife relates it, Mr. Noel told her that if she were to remember only one thing from physics class, just remember F = ma. And she did. And that is basically what I remember about high school physics too: a world of laws and formulas, where you plug some numbers into an equation and you get an answer, and that’s that.
But things fell apart in college, when they started teaching us how the world really works. I found out electrons don’t really “orbit” the nucleus of an atom, but instead the energy of an electron is more like a cloud around the nucleus. I found out space is not an invisible three-dimensional stage on which the universe’s events take place, but more like a fabric that itself curves and stretches due to the mass and rotation of stars and planets. And I found out there is no “master clock” ticking away the seconds as Newton thought, but instead… well, the phenomenon we call time is still a matter of debate in physics!
I submit that much of my stone-headedness comprehending modern physics has to do with having been taught classical (Newtonian) physics in high school — a primitive view of the universe became wired into my brain, and once it took hold, it was hard to displace.
In first grade, we learned 2 x 2 = 4. Luckily, 2 x 2 remains 4 the rest of our lives. We don’t have to rethink 2 x 2 or find a better approximation to 2 x 2 as we learn advanced math. But the subject of physics is treated differently. Our kids are taught only an approximation of reality, things they will need to unlearn before they discover the truth about nature (if they ever do have that opportunity).
Why don’t we trust our high school children with the messy truth-in-progress that is modern physics? Why don’t we teach them from the start how space is like a fabric and how the flow of time may be an illusion? Is there no way to teach high school physics without using simplistic concepts like grids and universal clocks? I would like to see the imaginative leaps students could make, if their minds were not imprinted with the world views of four centuries ago.
We would do our children a greater service by teaching them physics without the tests, without the grades. Do lots of classroom experiments. Don’t ask them to plug numbers into formulas. Talk about time and space, forget F = ma.
We live in an incredibly fascinating universe, about which we (by we, I mean physicists) have an incredible amount to learn. I can see the challenge, how to introduce high school physics students to the intricate workings of our universe without overwhelming them. Unfortunately, I don’t see much effort to that end. Look at the online Physics Classroom. It is so Newton! It is still all about F = ma — nothing at all about the shape of the cosmos that Einstein helped reveal 100 years ago.
High-school physics curriculum needs a complete overhaul. If Einstein isn’t mentioned until the last week of class, something beside F = ma is fundamentally wrong.
Craig, you certainly write about some interesting topics (for some people anyway). I read and think about a lot of these things too. I was in Florence last weekend and saw some of Galileo’s mummified fingers (yuck!) and am now reading a book you might enjoy called “Galileo’s Finger” (The ten great ideas of science, by Peter Atkins). You make some good points, but I think you need to give a little more respect to Galileo and Newton as well as to Einstein. Einstein and the rest of modern physics seems to be a more accurate iteration on deconstructing and describing the universe. It is fascinating and even useful (as in quantum mechanics and semi-conductors, for example). As Atkins points out, increasing levels of abstraction have led to deeper understanding of how this whole universe thing works. But just because Einstein and Schrodinger are closer to “the truth” doesn’t mean that Newton should move to the back of the bus. We live in a largely Newtonian world. Even JPL spacecraft trajectory engineers essentially use F=ma to get a spacecraft within a few meters of a desired spot near Mars (there are some minor relativistic corrections). I have dabbled in oribital mechanics, mainly through the free Orbiter spaceflight simulator, which is a great (Newtonian) physics playground. High school physics labs can’t easily suspend friction and provide massive rockets and the whole solar system as a playground, but Orbiter can.
It was a far greater leap from Aristotle’s ox-cart physics to Galileo’s understanding of intertia to Newton’s many insights than it was from Newton and Maxwell to Einstein’s special and general relativity. I agree that students should be helped to appreciate that there are many layers to this onion and that there are such things as space-time and quantum mechanics for which Newtonian physics is only an approximation. But if you give those very abstract approaches precedence, it’s a little like telling a driver ed student that she must be able to re-assemble a carburetor before she can learn to drive a car. Good to know that an engine converts the energy in gasoline to mechanical energy to propel the car, and that brakes use friction to slow it, but more detail here won’t help her learn to drive any better. Newtonian physics (for those few students who ever study it) is still a good and worthy framework, methinks.
Hi Bruce, as always thanks for your comments! I respect your viewpoint, and I certainly am in no position to dis Galileo or Newton (or you) but I don’t think we need to teach physics in the same order that humanity learned it. I suspect that high school students (esp. those who might take physics) are capable of thinking greater thoughts than the ones I was taught. It appears to me that h.s. physics is being taught the same old way, in spite of the knowledge acquired in the last 40 years: black holes, dark energy, qubits, etc. I think a h.s. physics class would be successful if it left the student with a feeling of awe. I’d pass kids for showing up!
You took a picture of all my books!
Don’t get me started on education reform in the U.S. It’s a sad state indeed when teachers are only motivated by attaining tenure, and their only task is to get students to barely pass some god-awful standardized test.
There are many things that should be overhauled in the Math curriculum, as well. For example, teaching set theory, group theory, and abstract algebra *before* teaching about polynomials or trigonometry. Or, once and for all, redefining π to be 6.283… (twice the present definition), which would simplify things enormously.
However, echoing Bruce’s statement, I don’t immediately see how physics can be taught without a firm Newtonian foundation. I hardly think that the equations of GR and QM (or their maddeningly counterintuitive implications) are any *simpler* than the Newtonian equations to which they converge.
Your proposition seems to be that, if we teach high school kids a cursory overview of modern physics, one of them might make some kind of Einsteinian leap to an as-yet-undiscovered theory. I doubt that would be the result.
It’s not really useful to tell a high school class that “spacetime is curved due to the presence of energy” or that “a particle is also a wave” without also introducing them to the mathematical underpinnings of these statements, which are orders of magnitude more advanced. If anything, they would walk away more confused, or worse, with misconceptions about these theories.
Personally, I don’t think we should reform the physics curriculum until we unite GR with QM. Until we have a master equation that unifies all the forces, we shouldn’t burden the minds of young kids with concepts that the world’s foremost physicists can’t reconcile themselves yet. When that day comes, we’ll be able to adjust the physics and math curriculum simultaneously to accommodate learning the master theory from the ground up.
That being said, I do think that Newtonian physics should be taught with frequent reminders that it’s only an *approximation* of what happens at high speeds or small scales, and that our five senses are very limited and give us a extremely narrow view of the real world. And I wholeheartedly agree that students should never be taught to just “plug numbers into formulas,” but instead to truly understand what the formulas mean.
I think the broader point here is that the curriculum should be supplemented with “teaser” materials that demonstrate what’s to come, should a student choose to pursue a career in physics (i.e. black holes, expanding universe, Higgs boson, etc). This has everything to do with the engagement of the teacher in the classroom, and the parents at home.
Excellent comment, db, one that I will not counter. Except! Except to say that I think we could introduce h.s. students to the concepts of curved space and thermodynamic (?) time without exposing them to the math. Yes, we would have to abandon the idea of teaching to the test. When the objective is to plant a seed, what kind of test (if any) would fit the situation? Based on Bruce’s challenge, I have in fact been thinking, how would I personally teach the course that I envision? It would make for an interesting pilot program, if I could assemble a coherent course and then teach it, and compare the results (whatever the “results” might be) to a control group taught the traditional way. Thank you for adding to this discussion.
One last thing (something I just told my wife)… To me, it’s like h.s. physics is taught as if there is Santa Claus (Euclid and Newton) and then later you find out there’s no Santa Claus (Einstein, Dirac, etc.). I’m thinking of emailing Lee Smolin, to see what he thinks.
You were always good at math.