We can ask ourselves what the subject ‘looks like’, at the single-particle level, of polarized light. We know that at the level of wave-mechanics, both plane-polarized and circularly-polarized light are easy to understand: Either way, the dipole-moments are at right angles to the direction of propagation, all the time, even if randomly so. But there also needs to be a particle / photon -based explanation for all the properties of light, in order to satisfy the demands of Quantum Mechanics.
And so a key question could be phrased as, ‘If we pass randomly-polarized light through a simple linear polarizer, which consists of a gel-block, and which absorbs EM vibrations along one disfavored axis, maybe because it has been made ohmic along that axis, why is the maximum intensity of plane-polarized light that comes out, in fact so close to 50% of the intensity, of the randomly-polarized beam that went in?’ Using wave-mechanics, the answer is easy to see, but using particle-physics, the answer is not so obvious.
And one reason fw the answer may not be obvious, is because we might be visualizing each photon, as being plane-polarized at an angle unique to itself. In that case, if the polarizer only transmits light, which is polarized to an extremely pure degree, the number of photons whose plane of polarization lines up with the favored angle perfectly, should be few-to-none. Each photon could then have an angle of polarization, which is not exactly lined up with the axis which the polarizer favors, and would thus be filtered out. And yet, the strength of the electric dipole-moment which comes out of the polarizer, along the disfavored axis, could be close to zero, while the total amount of light that comes out, could be close to 50% of how much light came in.
If each incident photon had been plane-polarized in one random direction, then surely fewer than 50% of them, would have been polarized, in one exact direction.
(Updated 04/10/2018 … )