how do we know quantum randomness isn't just hidden information?

How I got here

Started with

Could entanglement just be pre-set hidden information, like a pair of gloves in two boxes?

Ended at

Bell’s Theorem (Stanford Encyclopedia of Philosophy)

The Trail

1. “hidden variables vs entanglement explained simply” (google.com)
2. Einstein–Podolsky–Rosen paradox (en.wikipedia.org)
3. Bell's theorem (en.wikipedia.org)

   the inequality itself is like high school algebra. the implications are not

4. Bell test (en.wikipedia.org)
5. Alain Aspect (en.wikipedia.org)
6. Bell’s Theorem (Stanford Encyclopedia of Philosophy) (plato.stanford.edu)

What I came away with

Bell showed in 1964 that any local hidden-variable theory limits how correlated certain measurements can be, and quantum mechanics predicts beating that limit. Experiments from Clauser in the 70s, Aspect in the 80s, and the loophole-free tests of 2015 beat it, which is what the 2022 Nobel was for. Local hidden variables are out.

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