Some light quantum mechanics (with minutephysics)

What you are describing is a "hidden variable" theory. They are disproved by the experiments of the Bell's inequality. It's more weird, much more weird. Let's continue with your experiment about the pair of red or green socks. If you and your friend measure if they are red-or-green, both will get the same results. This can be explained with a classical theory. Nobody disagree with that. The weird part is that you can measure if they are 50%red and 50%green! Can I call it yellow? This makes no sense with classical socks and colors, but it makes sense for quantum particles and other properties. But there are two ways to combine 50%red and 50%green, the technical notation is (R+G)/sqrt(2) and (R-G)/sqrt(2), one with a plus and one with a minus. Can I call them good-yellow and bad-yellow? Or you prefer yellow and blue? In one of the experiments, red means vertical and green horizontal, so one of the combinations is a 45° diagonal like this / and the other is a 45° diagonal like this \. You don't need fancy equipment to measure the combinations, it's just a polarizer rotated 45°. Can I call them yellow and backyelow? I prefer good-yellow and bad-yellow because it's more clear that something weird is happening. If you measure red-or-green and your friends measures good-yellow-or-bad-yellow, then the results will not be correlated. If you got "red", your friend has a 50% probability of getting good-yellow and a 50% probability of getting bad-yellow. There is nothing to explain here.

> I have a lot of trouble imagining any experiment which could completely rule out every other influencing factor It's called Bell's theorem and it can even be tested at home[4]. There are no local hidden variables in quantum mechanics.[1][2][3] 1. link 2. link 3. link 4a. link 4b. ▶ this video

I found these two videos very helpful in understanding the quantum nature of light after being stuck in the same spot: link ▶ this video (Watch those in order, because they're a collaboration between two YouTubers)

Minute Physics and 3brown1blue did a two part collab that simplifies some of it down to a counting problem that'd be suitable for grade school. link ▶ this video