(Note: This post was designed to be read as a stand-alone, if desired.) Originally, the discoverers of quantum physics thought they had discovered an incomplete description of reality - that there was some deeper physical process they were missing, and this was why they couldn't predict exactly the results of quantum experiments. The math of Bell's Theorem is surprisingly simple, and we walk through it. Bell's Theorem rules out being able to locally predict a single, unique outcome of measurements - ruling out a way that Einstein, Podolsky, and Rosen once defined "reality". This shows how deep implicit philosophical assumptions can go. If worlds can split, so that there is no single unique outcome, then Bell's Theorem is no problem. Bell's Theorem does, however, rule out the idea that quantum physics describes our partial knowledge of a deeper physical state that could locally produce single outcomes - any such description will be inconsistent.
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This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Entangled Photons, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
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