Every year I am assigned to teach the "general interest" class in wave matter to non-science majors. I don't mind this assignment, as the material is interesting despite the facile treatment given in the class. We cover general wave phenomena (wave creation, propagation aspects, Doppler shift, bow waves) and then move on to talk in detail about sound and light.
It's light that's got me in a bind. When I was first tasked with explaining such things as why the sky is blue, why water looks blue (from inside it), refraction, dispersion in rainbows and prisms, absorption, and stimulated emission, I really didn't think much of it. The 'explanation' is just a list of facts and analogies:
- Higher frequency light (shorter wavelength) scatters more from gas molecules (hence blue photons scatter during the day in all directions)
- ... on the other hand, blue light scatters less from liquid molecules
- light refracts (bends at an interface between two media) due to velocity change in concordance with Fermat's principle (alternatively, and somewhat more satisfactorily, from Huygen's principle)
- Dispersive media have frequency-dependent velocities, making red refract more
- light is absorbed by an atom whose electron orbitals have the same energy difference as the photon's energy E=hf
- Stimulated emission is likely to occur with excited atoms in the presence of another photon of the same energy
With each passing year, I started to internally inquire why the hell any of these things really happens. Nitrogen molecules have a higher scattering cross-section for blue photons than red. How come? Light takes the path of least time. Why the hell would that be, particularly when a ray of light is viewed as a stream of photons? Photons in a laser cavity stimulate emission of identical photons (statistically) because they are bosons, but by what mechanism do they do that?
Now, I don't feel like such a fool. I'm going to reckon that a large number of physicists do not know the answers to these questions, not in the least because they are actually rather difficult to ascertain, and aren't covered in undergrad or graduate courses. But this doesn't absolve me, because the answers are knowable.
The first clue, and I suspect the last, lies with good ol' Feynman. While his fairly enjoyable lecture series at Cornell was recently put up online by Bill Gates, of much more interest is a series of lectures given at the University of Auckland about quantum electrodynamics. QED, as it's unfortunately abbreviated, can answer the questions of which way the photons go in optical experiments, how photons interact with electrons, how electrons interact with other particles, and such. These are the answers I sought, but the QED lectures are for a general audience, and just left me hungry for the real theory. His explanation about the probability amplitudes as vectors in the complex plane that obey certain rules of addition and multiplication was all well and good, but he never says how to calculate these amplitudes.
So, going into my fourth time teaching a class about why the sky is blue, I actually do not know the answer. I know only the proximate cause: blue light scatters more from air than red light does. But this is not the ultimate cause, and it's odd that it took me this long to be really curious about it.
By the end of the term, I must answer the following questions:
- How does Fermat's principle come from a quantum theory of photons?
- What determines the scattering cross-section of a photon with matter?
- What is the quantum mechanical explanation of an electron confined in an atom? How does the presence of a (non-virtual) photon influence the probability of spontaneous emission of such an electron?
- What determines the effective wavespeed of light in a medium, such that a dispersion relation v=v(f) arises?
And finally...
- WHY THE HELL DO I HAVE TO THINK ABOUT THESE THINGS?