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PROFESSOR: Last time, we spoke about photons in the context of an interferometer. The Mach-Zehnder interferometer. And we saw the very unusual properties of photons and interference, and how relatively simple interference a effect can be used to produce a very surprising measurement. Today we're going to backtrack and go from the beginning, and think about photons as physicists did 100 years ago, and how, by thinking about photons, they pretty much came up with quantum mechanics. So we want to trace this back. And the best place to start, probably, is with a photoelectric effect. The photoelectric effect is an experiment done by Hertz in 1887, in which he irradiated plates. That means shine light, high energy beams of light, on metal plate, and he found that electrons were released. Those were called photo electrons. And therefore, you would get a photoelectric current from those electrons. So this is the effect we want to discuss now, is the photoelectric effect. And...

PROFESSOR: We spoke last time of the existence of symmetric states. And for that we were referring to states psi S that belonged to the M particle Hilbert space. And V is the vector space that applies to the states of the M particles. And we constructed some states. So within the construction, we postulated, there will be some states that [AUDIO OUT] that meant that any permutation of [AUDIO OUT] state will be for the symmetric state or all alpha. So that meant the state was symmetric. Whatever you apply to it, any permutation, the state would be invariant. So these are special states, if they exist, in VN. Then there would be anti-symmetric states. And we concluded that an anti-symmetric state-- with an A for anti-symmetric-- also stayed in this tensor product. That state would react differently to the permutation operators. It would change up to a sine epsilon alpha times psi A. It would be an eigen state of all those permutation operators. But with eigenvalue epsilon a...