[magicalhippo]

Yes, that's what I was trying to say.

Hidden variables, like my "electron objects", would give a linear relationship.

However what quantum mechanics predicts and what we measure in the lab is a non-linear relationship that for some angles yield stronger correlations. Hence the phrase "violating Bell's inequality".

After Bell people devised other inequalities for other experimental setups which also can be used to rule out local hidden variables. A popular example are the CHSH inequalities[1], which is easier to realize experimentally, and give a stronger disagreement with hidden variables.

I've never seen the particles not paired up, and I don't see how that would work.

The whole point is that according to quantum mechanics, the pair of entangled particles aren't two separate systems, but that they must be treated as having a single state.

[1]: https://en.wikipedia.org/wiki/CHSH_inequality