"their spin will be correlated" - in this case the billiard's spin is a per-ball property that is set before they are sent to Alice and Bob, and happens to be correlated. You can simulate this in the Python code, but you will not be able to break the Bell inequality like that. This is similar to the dice example I give, where the objects sent to Alice and Bob are random from their perspective (since the dice roll happens with Victor), and correlated.
In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. To be clear, I didn't prove this in the article, the approach the article takes is "here is some code, play around with it to get a feeling for why".
> In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices].
What if the particles have properties that mutate their state after they are sent to Alice and Bob?
Suppose, in the billiards example, that I put a small device into the balls that changes the spin of the ball to some predefined value.
Wouldn't that break the Bell inequalities without action at a distance?
The reason for the breaking would be that the state of the balls would be modified after they are sent to Alice and Bob. It would look like action at a distance without being 'action at a distance'.
It doesn't matter when the state of the ball changes (when Victor sends them, on the way, when it's measured). You can play around with this in the Python code, there is shows up like "it doesn't matter which function you put that line of code, the functions are called one after the other". The functions in question are generate_composite(), split(), and the 4 measure_X_Y(), called from bell_experiment().
In general, classical correlation cannot break the Bell inequalities [assuming no peeking, ie. no action-at-a-distance in the measurement devices]. To be clear, I didn't prove this in the article, the approach the article takes is "here is some code, play around with it to get a feeling for why".
Hope this helps.