The above also explains what happens when light meets a filter on an angle. A filter at an angle to the polarization plane of light reduces the light that gets through but still lets some photons through entirely. A filter at bigger angle to the light polarization lets fewer photons through, e.g. a filter at 81º to the polarization plane lets only 10% of the photons through but again some still get through entirely. How can a photon pass entirely through a filter that mostly blocks it? The answer proposed now is spin.
To recap, spin involves a:
a. Rotation axis. Around which the spin occurs that doesn’t change with the spin.
b. Rotation plane. In which the spin occurs whose dimensions swap values as the structure spins.
Imagine a spinning propeller that rotates round an axis into the rotation plane that we see from the front. From the front the blades swap vertical and horizontal extents but the axis is just a point. From the side we see the axis but one propeller blade “disappears” as it spins into an unseen horizontal dimension.
Now spin in four dimensions works like spin in three but with more options. If a photon spins on its movement axis, as a bullet from a gun does, it spins into all the planes that cut its movement axis (Figure 3.19). This allows it to pass through a filter on an angle to its polarization plane. But as it spins, its quantum amplitude direction doesn’t change because it isn’t on the rotation plane so when a vertically polarized photon spins into the horizontal plane it disappears entirely, like a piece of paper on edge that can’t be seen. As a photon spins on its movement axis, its amplitude varies according to angle. The quantum amplitude of a spinning photon appears and disappears like a propeller seen from the side. That this amplitude projects into the planes that cut its movement axis according to angle explains the percentage of light that gets through a filter on an angle.
How then do photons get entirely through a filter on an angle? Again it is because measurement is an all-or-nothing affair. The filter reduces the probability that instances get through a filter but if one does and is detected, the entire photon restarts at the point. The entire photon gets through a filter for the same reason that a screen registers an entire photon. A physical event always delivers “the photon”.
PS. If Q is the quantum amplitude it reduces as Q.Cos(θ°) as it spins, where θ° is the angle from in the polarization plane. So at a 90° angle it has no value as Cos (90°) = 0.