Bell’s theorem

Bell’s theorem asserts that if certain predictions of quantum theory are correct then our world is non-local. “Non-local” here means that there exist interactions between events that are too far apart in space and too close together in time for the events to be connected even by signals moving at the speed of light. This theorem was proved in 1964 by John Stewart Bell and has been in recent decades the subject of extensive analysis, discussion, and development by both physicists and philosophers of science. The relevant predictions of quantum theory were first convincingly confirmed by the experiment of Aspect et al. in 1982; they have been even more convincingly reconfirmed many times since. In light of Bell’s theorem, the experiments thus establish that our world is non-local. This conclusion is very surprising, since non-locality is normally taken to be prohibited by the theory of relativity. Pre-existing values are thus the only local way to account for perfect anti-correlations in the outcomes of spin measurements along identical axes. But a simple argument shows that pre-existing values are incompatible with the predictions of quantum theory (for a pair of particles prepared in the singlet state) when we allow also for the possibility of spin measurements along different axes. According to quantum theory, when spin measurements along different axes are performed on the pair of particles in the singlet state, the probability that the two results will be opposite (one “up” and one “down”) is equal to (1+cosθ)/2, where θ∈[0,π] is the angle between the chosen (oriented) axes. It follows from the simple mathematical result below, Bell’s inequality theorem, that this is not compatible with the pre-existing values we have been discussing.