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?