Thursday, May 24, 2007

"Modern" physics

It's that time of year.

Wave-particle duality isn't the easiest concept to convey to high school freshmen (or to anyone. for that matter), but I think I have found a successful analogy that plays on a sort of complementarity that the students have already been using in physics class (and life).

Earlier in the year, when we did projectile motion or force problems, we treated the surface of Earth as if it is flat. Later on, when we looked at gravity and considered Earth orbiting the sun, we treated Earth as if it is a point.

So which is it? Is Earth a plane, or is it a point??? Well, of course, it's neither -- it's (approximately) a sphere. But spheres are difficult to deal with. And when you're really close to a sphere, it looks like a flat plane, and when you're really far from it, it looks like a point. So each of these models is appropriate under certain circumstances.

Likewise, when we observe diffraction or interference or polarization, we treat light as if it is a wave, and when we observe the photoelectric effect, we treat light as if it is a particle. So which is it? Neither -- it's something outside our everyday experience. But the wave model and the particle model are each appropriate under certain circumstances.


  1. pshhhhhhhhh! I like it!

    -sarah m

  2. Please share your thoughts on why Freshmen should take physics @

  3. I've heard this used as an analogy for the uses of different ways of understanding G-d. When you're in the middle of a prayer, we use the model of a personal confidante; when we're considering something global like human rights, we abstract G-d to something much less personal but more conceptual about the dignity of human beings. Both models work in the settings in which they're invoked; neither is completely "right."

  4. My elevator pitch about freshman physics:

    Physics-chemistry-biology is a much more logical order, because students can use physics concepts in chemistry, and can use chemistry in biology. (My colleagues who teach chemistry report that they can predict how well a student will do in chemistry by whether s/he has taken physics.) Yet biology-chemistry-physics is more common, primarily because the standard high school physics course requires more math (algebra and basic trig) than many students have had by the beginning of high school, so physics is put off until they've had more math.

    There are two ways to deal with this:
    1) An increasingly popular option is to teach a "conceptual physics" course freshman year, to provide a foundation of physics concepts without much math, then students can take chemistry and biology, then take another physics course (with math) senior year.
    2) At my school, freshmen take Regents physics; i.e., the same curriculum that the juniors take. I don't recommend this for everyone, but this is a self-selected population within a selective public high school (incoming freshmen have a choice between physics and biology, and about 1/3 of the freshman class is taking physics), so most of the students come in with the math they need. Even though it's the same material that the juniors are learning, the freshmen are segregated into their own sections, so we can spend more time developing mathematical techniques that they may be less experienced with (e.g. vectors). The freshmen taking physics tend to do better than the juniors. Of course, a part of this is that it's a self-selected population. But it's also because freshmen are more motivated about school, and aren't overburdened with a thousand AP classes and extracurriculars, so they have the time and energy to devote to physics.

  5. That's actually a pretty poor model for how physics works. The earth as a sphere/point/plane works to explain stuff like Newtonian vs. Einsteinian physics. But the point of the wave/particle thing is that electromagnetic energy is both a particle and a wave. Really. Think of the photoelectric effect.

    @w brown - everyone should take physics. The world is made out of physics (yes, okay, I'm a physicist. But still!)

    @bz - reductionist much? Anyway, I believe that in a better world, physics and math would be taught as one subject

  6. That's actually a pretty poor model for how physics works. The earth as a sphere/point/plane works to explain stuff like Newtonian vs. Einsteinian physics. But the point of the wave/particle thing is that electromagnetic energy is both a particle and a wave. Really.

    What do you mean by "is" and by "really"? The classical wave and the classical particle are models that predict how something behaves. To the extent that these models successfully predict what something does, we might say that that thing "is" a wave or a particle. But nothing perfectly obeys either of these models, just like there is no such thing as a rigid body or an ideal gas or an ideal blackbody; these are just idealized approximations that work well under the appropriate circumstances.

    Light sometimes exhibits wavelike behavior and sometimes exhibits particlelike behavior. But it doesn't correspond completely to either the classical wave or the classical particle. If it's at radio frequencies, then the photon energy is so small that it might as well be a wave; you're not going to observe the photoelectric effect with radio waves. If it's at gamma frequencies, then the wavelength is so small that it might as well be a particle; you're not going to observe interference patterns with gamma rays. With visible light (in between), it depends.

    But if you don't believe me, you can ask Feynman (Feynman Lectures, volume I, chapter 2):

    "[T]hings that we used to consider as waves also behave like particles, and particles behave like waves; in fact everything behaves the same way. There is no distinction between a wave and a particle. So quantum mechanics unifies the idea of the field and its waves, and the particles, all into one. Now it is true that when the frequency is low, the field aspect of the phenomenon is more evident, or more useful as an approximate description in terms of everyday experiences. But as the frequency increases, the particle aspects of the phenomenon become more evident with the equipment with which we usually make the measurements."

    And in chapter 38:
    "[N]either the wave viewpoint nor the particle viewpoint is correct. ... [W]hen we try to talk about the wave picture or the particle picture, both are approximate ... [A]ll our experiences are with waves and with particles, and so it is rather handy to use the wave and particle ideas to get some understanding of what happens in given circumstances."

    Think of the photoelectric effect.

    Already covered it in the main post. (And what is the photoelectric effect if not "Einsteinian"?)

    yes, okay, I'm a physicist.

    What kind?

    reductionist much?

    To what are you referring?