The Quantum Venn Diagram Paradox

Hold two polarizing filters between you and the light. As you rotate the second filter, the lamp will get lighter and darker. It should look darkest when the second filter is oriented 90 degrees off from the first. What you're observing is that the photons with polarization that allows them to pass through a filter along one axis have a much lower probability of passing through a second filter along a perpendicular axis - in principle 0%.

polarization black magic

But here's where things get quantum-ly bizarre. All these filters do is remove light - they "filter" it out. But if you take a third filter, orient it 45 degrees off from the first filter, and you put it between the two, the lamp will actually look brighter. This is not the middle filter generating more light - somehow introducing another filter actually lets more light through.

Here's what's happening.

We can interpret a diagonally polarized wave as a superposition of a horisontal and a vertical wave.
If you were to take a vertically oriented polarizing filter and shoot this diagonally polarized photon right at it what do you think would happen?
Classically the way you'd interpret the superposition is that the half of it's energy (in the horizontal direction) would be absorbed. But because energy comes in discrete packets (photons) it either has to pass through with all of it's energy or get absorbed entirely. And if you actually did this experiment, about half the time the photon goes through entirely and about half the time it gets absorbed entirely.

If it does pass through, forcing it to make a decision like this, actually changes it so that it's polarization is oriented along the filters direction.

This is analogous to the classic Schrodinger's cat setup. You have something that's in a superposition of two states, but once you make a measurement of that superposition forcing it to interract with an observer in a way where each of those two states would behave differently from the perspective of that observer this superposition collapses to be entirely in one state or entirely in another.

So 50% of photons passing that vertical filter will also pass through the diagonal filter, and once they do they're going to be changed to have a purely diagonal polarization and once they're in that state they have a 50% chance of passing through a filter oriented at 90 degrees.

Source: https://www.youtube.com/watch?v=zcqZHYo7ONs - Minutephysics https://www.youtube.com/watch?v=MzRCDLre1b4 - 3Blue1Brown