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Locality and quantum mechanics

Locality is the denial of action at a distance It requires that all the information useful in predicting what will happen at a given location and time is contained in a sphere of influence. For an event that will occur in one second the sphere has a radius of 300,000 kilometers, the distance light travels in one second8.1.

Locality is the most powerful simplifying assumption in physics. Without it any event no matter how distant can influence any other event. Prediction would be impossible without locality or some other powerful restriction on what events can affect other events. Otherwise one would need to know the state of the universe to predict anything. Quantum mechanics is a local theory in configuration space but not in physical space.

As mentioned in Section 7.10 Bell refuted von Neumann's proof that no more complete theory could be consistent with quantum mechanics. In proving this Bell was influenced by Bohm's development of a more complete theory that was explicitly nonlocal. This led him to a proof that no local theory with hidden variables could reproduce the statistical predictions of quantum mechanics. Hidden variables were defined by Bell in a general way to include any more complete theory with a mechanism for explaining the conservation laws. He suggested that it should be possible to test some of the nonlocal predictions experimentally[5].


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