How do we know quantum entanglement really happens? Quantum entanglement says that we can entangle two particles with an opposite property, separate them, and that they exist in an indeterminate state until we observe one of them.
eg. If we create a left/right pair, separate them in space then observe one of the particles then the other particle of the pair will instantly resolve into the opposite state of the particle we observed.
Question: How do we know this is true? How do we know that something happened to the second particle as a result of observing the first?
A much simpler explanation is that both the particles flipped into fixed left/right states at the moment we started to separate them, we simply hadn't opened the containers yet to see which was which.
I assume that there can be no possible experiment to distinguish between these two explanations since we're not allowed to observe either particle.
What reason(s) do we have to believe the magical 'quantum' explanation when the simple explanation explains it just as well?
 A: It's a very good question, one that John Bell asked. In 1964, he proposed an experiment to distinguish between the two cases, one case where a hidden variable is carried along, and another case where the measurement result of one somehow propagates to the other. Bell derived "Bell's inequality" which would be violated if the second case turned out to be correct.
In 1982, Alain Aspect performed the first experiment to test the inequality, and the result confirmed entanglement, not hidden variables. Since then, many other experiments have also confirmed entanglement.
Like you, and most people who first come across this, I used to feel that "a simpler explanation is that both the particles flipped into fixed left/right states at the moment we started to separate them." So I went through the exercise of trying to come up with a function that maps the hidden variables to up/down (or left/right) in a way that violates the inequality like the entanglement experiments do. After enough playing around, I got a feel for how hidden variable cannot do this. I recommend this exercise for those who want to get better feel for how entanglement works.
