In 1966-1969 I was active in an experimental particle physics group at Caltech and taught intro physics using the Feynman Lectures on Physics as the textbook, which was a fantastic experience. I often saw Feynman at lunch in the Caltech cafeteria but only once had a substantive discussion with him, which had a long-lasting influence on my physics teaching.
I found myself puzzled about blackbody radiation, a topic in the course. One common way of talking about blackbody radiation is to imagine an oven with a small hole from which radiation escapes, and to imagine the oven walls to be made of material with evenly spaced energy levels that emit similarly quantized photons. But no solid material has such an energy level scheme (the Einstein solid is such a material but is just a highly simplified though useful model), so what’s going on? (The proper approach is to quantize the electromagnetic field, not the emitters.)
I decided to make an appointment to talk with Feynman about this. I was acutely aware that my question was likely to sound hopelessly confused and naive, so I overprepared for the meeting and spoke really fast to try to show that there was an issue. As I expected, initially his face darkened as he wondered why this idiot had been allowed on campus, let alone teaching the curriculum he had created. But by continuing to talk really fast I got far enough to get him intrigued, and he could see that there was an interesting question, and we had an interesting and substantive conversation.
We considered together an astronomically large cloud of atomic hydrogen with some initial energy in the form of atomic excitation. This cloud will emit a line spectrum, not blackbody radiation, yet thermodynamics tells us that eventually the cloud (together with the radiation) will reach thermal equilibrium and the energy distribution of the radiation will be the blackbody continuum. How does the cloud and radiation get from the initial state to this equilibrium state? (It’s not quite an equilibrium state because energy is being radiated away.)
We could see that various processes would alter the initial line spectrum, including doppler effect (from recoil associated with emission) and collisional broadening. So there’s no mystery in the fact that we don’t expect a clean line spectrum to persist. The details of the transient that gets us from initial state to final state may be quite complex, and hard to calculate in detail, but just recognizing that there must be a transient gives a sense of mechanism that is lacking if the final state is presented with no preamble.
Next Feynman supposed that somewhere in the cloud is a speck of dust. (I can no longer remember whether this was special magic dust with evenly spaced energy levels.) Thermodynamics assures us that eventually the hydrogen atoms must come into thermal equilibrium with that speck of dust. Thermodynamics has great power in this respect, but using it alone tends to remove all sense of mechanism.
I believe that this was my first experience of the sense of mechanism that comes from discussing the transient that leads to establishing an equilibrium state or a steady state. In retrospect I think that as a student I was somewhat puzzled by how certain states came into being, but as far as I can remember there was no talk of the transients. Another person who influenced my thinking on this was Mel Steinberg, the creator of the CASTLE electricity curriculum. In the late 1980s I took an AAPT (American Association of Physics Teachers) workshop from him that included desktop experiments with half-farad capacitors (“supercaps”). One of the things he stressed was that the several-second time constant for charging or discharging could be usefully thought of as an observable transient leading to an equilibrium state. This viewpoint in turn influenced the emphasis in Matter & Interactions on the transient that leads to the steady state in DC circuits.
Another influence on both Ruth Chabay and me was doing numerical integrations with a computer, where you gain the strong sense of things happening step by step, not just described in terms of an analytical solution that is a known function of time, which gives little sense of the time evolution of the process.
All of this has had a big effect on the Matter & Interactions curriculum, plus Ruth Chabay’s insight that computational modeling must be a part of introductory physics. Thinking Iteratively is a 30-minute video of a talk we gave at the summer 2014 AAPT meeting that includes examples of these issues.
Bruce Sherwood
