• Yale’s Physics 200: Less Dismal Science

    Economics is not physics, and that bothers some people. Such physics envy seems odd to me. It isn’t the fault of practitioners that economics models don’t correspond to reality with the same fidelity as physics models. A system of humans and human institutions is just fundamentally harder to model. It’s not time invariant. People are not particles. In some respects physics is easier.

    In Fundamentals of Physics, freely available as part of the Open Yale Courses program, Ramamurti Shankar masterfully reveals just how easy and fun it can be. My prior knowledge of Shankar is through his excellent quantum mechanics book, which I read as a Cornell undergraduate majoring in Applied and Engineering Physics. So, I’ve taken a lot of physics courses and enjoyed nearly all of them, but few as much as Shankar’s. What makes it so good is that he develops all concepts presented from first principles yet finds astonishingly short and simple–but correct–paths to results.

    For instance, he patiently led his students toward the correct interpretation of Newton’s F=ma and each variable in the equation. How does one measure acceleration? What about force? What does each side of the equation mean? Why is it not tautological? How would you find the mass of an object? (The answer is not, “Put it on a scale.”) When one really ponders these questions seriously, as Shankar insists, one finds they’re surprisingly deep. Yet the answers are simple, once you understand what you’re after. Then you’ve learned something!

    Shankar is also very funny, both in class and on his website where he lists the following among his accomplishments:

    Discovered a small parameter that justifies most calculations performed in physics: 1/ego, where ego is the author’s ego.

    Identified a new dangerously irrelevant variable: Sarah Palin.

    Beyond just explaining physics well, Shankar brings the subject to life by relating some of its history. For instance in the seventh lecture, on Kepler’s Laws Shankar says,

    By the way, Newton took a long time to publish this Law of Gravitation. Does anybody know why he was holding back for a long time? …

    [O]riginally Newton had a law of gravitation between two point objects, namely point-like. The distance between them is unambiguously the distance between the points, and he got this law. But in the end, he wants to apply it to the Earth and the apple; they are close enough for you. You cannot pretend the Earth looks like a point from where I am. It looks like a big, fat thing. You cannot say it’s point-like. So, what you really should do is divide the Earth into tiny pieces, each one of which is point-like, find the force on each from each chunk of the Earth, using this law, and add it up. And if you’re lucky, it will look as if all the pull is coming from one point at the center, carrying the entire mass of the Earth. So, what branch of mathematics do you have to use to get that result? …

    [H]e had to then invent integral calculus also. So, if he felt that no one around him was doing any work, it was probably justified because they just dumped the whole thing on this kid and said, why don’t you do [integral calculus too]? That’s why it took him a long time to verify, using integrals, that the sphere behaves like a point particle at the center. … [T]hat’s what held back a publication.

    As with this bit of history, most of the material of the course was familiar to me, though Shankar’s novel presentation style made it fresh. Some of the details of Special Relativity were new to me, however. Somehow, in my education, I missed (or completely fail to recall) the packaging of variables (time and space; energy and momentum) into four-vectors and how doing so facilitates manipulation and solution of problems. Seeing (hearing, really, as I “took” the course aurally by iPod) that topic presented in this fashion cleared away much of the confusing clutter of Special Relativity and let me focus on some of its wonders.

    For example, I found myself marveling at the photon. Why does it get to be so special? It gets to travel at the same speed for all observers. It gets momentum and energy without mass. It just doesn’t seem to belong in the same model as other particles. In fact, it’s the wave nature of light that shows up in the four-momentum for photons. In the class, the form of the photon’s four-momentum is just asserted. I could almost feel Shankar restraining himself to explain that further when he covered waves.

    Likely he’s saving it for the next class, in which he covers electricity and magnetism and quantum mechanics. But that class is not available via Open Yale Courses right now, sadly. The class I listened to covers classical and relativistic mechanics, including brief introductions to waves, fluid mechanics, and thermodynamics. If/when Yale posts Shankar’s next class I’ll listen eagerly.

    (See also my review of Yale’s Astro 160.)