Now that we have a few more concepts under our belts, I would like to go back and revisit in some more detail just what John Bell proved in 1964 about entangled states. He considered a simple quantum situation like the entangled ions in Alice and Bob’s pocket watches and then set about to compare the predictions of quantum theory for such a setup to the predictions of a classical hidden variable theory that had all of Einstein’s constraints: reality, locality, and certainty. Remember-there was already the Bohm hidden variable theory, well known in 1964, which did predict the same outcome as quantum theory, but this Bohm theory doesn’t count because it violates Einstein’s locality condition. (Einstein thumbs his nose at the Bohmians.)
Bell’s goal was to see if he could construct a local classical hidden variable theory that would agree with all the predictions of quantum theory and satisfy Einstein’s three conditions. If such a hidden variable theory could be found, then it would be tempting to just replace quantum theory with that hidden variable theory and all the spookiness would just disappear. But in order for
this project to succeed, the classical hidden variable theory had to obey all three of Einstein’s reality, locality, and certainty conditions and reproduce all the predictions of quantum theory. at was just too tall of an order to ask of any local hidden variable theory, Bell discovered. Something, somewhere, had to give.