Blackbodies and Black Bodies

Alas for Michael Jackson. Talented musician, deeply broken human being. Most of my knowledge of him was through cultural osmosis rather than his actual music, and I'm young enough so that I can't really remember the time before he was a punchline about changing skin color, disastrous plastic surgery, and child molestation. Well, de mortuis nil nisi bonum.

His death reminds me of my undergrad thermodynamics book, of all things. As you know, an object at a particular temperature will radiate light with a particular spectrum depending on the material. Heat something up enough, and it will glow red, then orange, then white, and so on. Cooler objects radiate in the infrared and lower wavelengths, and extremely hot objects like plasmas can radiate into the ultraviolet and x-rays. All other things being equal this radiation will follow Planck's law and emit light of certain frequencies in certain proportions. All other things are generally not equal, but Planck's law describes a very frequently encountered type of emission called blackbody radiation. A blackbody is an object that absorbs all light hitting it, without reflection.

The book gave a problem about calculating the blackbody radiation emitted by a human being. This immediately raises a question: are people blackbodies? Does it depend on what color the skin is? The fact that the term is essentially "black body" and thus somewhat evocative of race makes the problem scenario more awkward-sounding than it might have otherwise been. Had the author been a crass 8th-grader instead of a classy and professional physicist it would have been a good opportunity for a Michael Jackson joke.

I don't have the book handy and so I can't tell you the exact way the book gamely but slightly self-conscious way phrases the answer. But there is an answer, and it's pretty easy.

The visible light we see has energies on the order of an electron-volt. This is a very typical sort of number for the energy gaps between the different energy levels of electrons in atoms and molecules. Light might hit an atom, bounce the electron up a level, and be re-emitted as the electron falls back down to its previous position. We see this all the time in phenomena like fluorescence. But this isn't thermal energy. You might have guessed something from the fact that things have to be really hot before they start glowing visibly: an electron-volt is much more energetic than the energy being transferred by the random thermal motions of atoms as they jiggle around. The mechanisms of visible light emission and thermal light emission at human body temperatures are completely different.

Skin color is a product of melanin content - a visible light phenomenon of electron levels. More melanin affects those incoming visible photons and results in the different shades of human skin that we see. But thermally that melanin matters not a whit, as it's just another molecule vibrating and jostling thermally throughout our bulk. As a result, human skin of all races has effectively identical thermal emission characteristics. And those characteristics happen to be pretty much those of an ideal blackbody for that far-infrared light resulting from thermal radiation. Pretty much everything is a blackbody at those wavelengths, and humans are no exception.

"We all look the same under a FLIR scan" is not likely to be the next anti-racism PSA. But maybe it should be. There's not enough statistical mechanics in public service announcements these days...