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Free will theorem

The free will theorem of John H. Conway and Simon Kochen states that, if we have a certain amount of "free will", then, subject to certain assumptions, so do some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.

Axioms

The proof of the theorem relies on three axioms, Conway calls "fin", "spin", and "twin". The spin and twin axioms can be verified experimentally.

Fin: There is a maximum speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
Spin: The squared spin component of certain elementary particles of spin one, taken in three orthogonal directions, will be a permutation of (1,1,0).
Twin: It is possible to quantum entangle two elementary particles, and separate them by a significant distance, so that they have the same squared spin results, without permutation.

The theorem

The Kochen-Specker theorem shows that the results of probing the particle cannot be determined ahead of time, if the questions are not. Therefore the orientation is not determined, although the answers from the two particles will agree (quantum entanglement). Because the answers agree, and there is no communication, the answers cannot depend on the order of the questions. Therefore, unless the questions are predetermined (and the particles can acquire that information), the results are non-deterministic.

Problems and limitations

The proof does not assert that free will exists at all. A fully deterministic view of the universe could imply that both our questions about the particles and the answers to those questions are pre-ordained.

The definition of "free will" used in the proof of this theorem is simply that an outcome is "not determined" by prior conditions, and may therefore be equivalent to the possibility that the outcome is simply random. Thus, the definition of "free will" may not coincide with other definitions or intuitions about free will. Indeed, some philosophers strongly dispute the equivalence of "not determined" with the existence of free will.