I’m putting together slides for a TED audition talk in a couple of weeks, about how the history of quantum mechanics is like a crossword puzzle. This involves talking about black-body radiation, which is the problem that kicked off QM– to explain the spectrum of light emitted by hot objects, Max Planck had to resort to a mathematical trick: he assumed that the objects were composed of “oscillators” that emitted light in discrete amounts, with the energy of the emitted light proportional to the frequency of the light. This was a desperation move, and made him a little crazy:

(Not really, but that picture (from here) is so unlike the old-bald-dude-with-glasses image that is the default Planck picture that I love sharing it. I also like this 1878 picture of Planck quite a bit…)

Anyway, Planck’s formula kicked off the quantum revolution. Five years later (or so), Einstein ran with the idea of light quanta, and eight years after that Bohr proposed his model of hydrogen, with atoms absorbing and emitting light in discrete chunks with the frequency determined by Planck’s rule. Planck was never all that happy with the trick, but as the famous cartoon says, it works brilliantly.

Thinking about this, coupled with my usual desire to procrastinate, got me wondering about something I’ve never entirely understood, though. And while I could probably Google up an explanation somewhere, it’s probably worth a blog post to explain what I managed to distract myself with.

So, the issue is this: since the 1850’s, we’ve known that atoms absorb and emit light at discrete frequency. Bohr provided the conceptual framework for understanding this in 1913 and Schödinger, Heisenberg, and Dirac provided the mathematical machinery for predicting the characteristic frequencies of a particular atom. We understand where these frequencies come from, and can predict them to very high precision.

Meanwhile, Planck’s formula gives a broad, continuous spectrum, which again we can predict to exceptional precision, and this matches reality. The problem I have is understanding how to connect these two. That is, the objects emitting a broad spectrum of thermal radiation in keeping with Planck’s formula are made up of atoms, which we know emit light at discrete frequencies. So, how does the narrow emission of atoms get turned into the broad emission of objects?

If you’re talking about things like the filament of an incandescent bulb, one of the canonical examples of black-body radiation used in popular discussions, I’m usually okay with writing this off as one of those black-magic effects you get when you start combining excessive numbers of atoms– the solid lattice offers a crystal structure that can soak up energy, so you get inelastic processes where you absorb one frequency and emit another, and wave hands madly, broad spectrum output.

But then there’s the Sun, which is pretty close to a black-body emitter (see the spectrum in the “featured image” up top, which I got from here). The Sun isn’t a solid– like the song says, it’s a mass of incandescent gas, without a lattice structure to do black-magic things. But there again, there’s an out– it’s not really a mass of incandescent gas, it’s mostly a miasma of light-emitting plasma, with lots of free charges running around, so again, wave hands madly, broad spectrum output.

But, of course, actual neutral clouds of gas also emit thermal radiation, and people can and do use this to monitor the temeprature of gases emitted from power plants and that sort of thing. And there, you don’t really have any outs. You don’t have a solid lattice or free charges to do black magic, just a bunch of atoms that want to absorb and emit light in specific, very narrow spectral lines, and yet the end result of all this is a broad thermal spectrum of light. And I’ve never really understood how that works out at a microscopic level.

I assume that the answer is inelastic light scattering– that is, while the most direct form of interaction with radiation that AMO people like myself like to think about involves the absorption and emission of well-defined frequencies, there’s also a probability of off-resonant scattering. This is completely negligible compared to the resonant scattering that we deal with when we start blasting things with lasers, but in the absence of light deliberately tuned to resonance, it’s the only game in town. So an atom that really wants to absorb some narrow line still has a tiny probability of an absorb-and-emit interaction with photons that are way, way off that resonance, and sometimes that process will transfer energy between atoms and light. A moving atom exposed to incoming photons at one frequency will send out photons of a slightly lower frequency, speeding up a tiny bit to account for the energy difference. The probability of this happening is tiny, for any given atom, but when you start thinking about molar quantities of gas, that still adds up to a whole lot of scattering. And enough of this will eventually give you a thermal distribution.

I think that’s really the only thing that can be going on, but I’m really just guessing, here. I’ve never seen the details worked out, though I assume somebody must have thought carefully about this at some point. Anyway, I thought I’d throw this out there, on the off chance that any of my wise and worldly readers know of a great explanation of this floating around somewhere.

(Also, while the academic politics stuff has been great for blog traffic, I feel a little guilty about the lack of front-page physics content, and this fixes that problem…)