Decoherence as projection discusses photon polarization as a phenomenon that can only be explained quantum mechanically even at the macroscopic level –

“All right,” you say, “that just seems weird.” You pause. “So it’s probably something quantum.” Indeed it is.

Not so quick I think. It is true that if you do this experiment at the microscopic level with single photons you’ll have no classical explanation for it – erm classical physics doesn’t know about photons to begin with.

At the macroscopic level though, oscillating E and B fields is adequate to explain it. A polarizer projects the vectors along it’s polarization. So in the “3 filters at 45 degrees” case you get two projections. The fields are oscillating in a specific direction after passing through the first filter, say with amplitude E. When it hits the second filter, the projected component is simply E cos 45. This projected vector is now oscillating along the second polarizer’s direction. When this hits the third filter this gets projected again and becomes E cos 45 cos 45. So the final amplitude has an energy that is pow(cos 45, 4) which is ¼. That is exactly what the quantum explanation gives.

What macroscopic aspect of plane polarization does the above explanation not cover?