Free will theorem

The free will theorem of John H. Conway and Simon B. Kochen states that, if we have a certain amount of "free will", then, subject to certain assumptions, so must some elementary particles. Conway and Kochen's paper was published in Foundations of Physics in 2006.^[1]

Axioms

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

1. Fin: There is a maximum speed for propagation of information (not necessarily the speed of light). This assumption rests upon causality.
2. 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).
3. Twin: It is possible to "entangle" two elementary particles, and separate them by a significant distance, so that they have the same squared spin results if measured in parallel directions. This is a consequence of (but more limited than) quantum entanglement.

In their later paper, "The Strong Free Will Theorem," Conway and Kochen weaken the Fin axiom (thereby strengthening the theorem) to a new axiom called Min, which asserts only that two experimenters separated in a space-like way can make choices of measurements independently of each other. In particular, they are not asserting that all information must travel finitely fast; only the particular information about choices of measurements.

The Theorem

The theorem states that, given the axioms, if the two experimenters in question are free to make choices about what measurements to take, then the results of the measurements cannot be determined by anything previous to the experiments. Since the theorem applies to any arbitrary physical theory consistent with the axioms, it would not even be possible to place the information into the universe's past in an ad hoc way. The argument proceeds from the Kochen-Specker theorem, which shows that the result of any individual measurement of spin was not fixed independently of the choice of measurements.

Limitations

Conway and Kochen do not prove that free will does exist. The definition of "free will" used in the proof of this theorem is simply that an outcome is "not determined" by prior conditions, and some philosophers strongly dispute the equivalence of "not determined" with free will. Some critics argue that the theorem only applies to deterministic models.^[2]

See also

• Einstein-Podolsky-Rosen paradox
• Bell's inequalities
• Compatibilism
• Contextualism
• Principle of locality
• No-communication theorem
• Libertarianism (metaphysics)

Notes

1. ^ Conway, John; Simon Kochen (2006). "The Free Will Theorem". Foundations of Physics 36 (10): 1441. arXiv:quant-ph/0604079. Bibcode 2006FoPh...36.1441C. doi:10.1007/s10701-006-9068-6. 
2. ^ What Does the Free Will Theorem Actually Prove? Sheldon Goldstein, Daniel V. Tausk, Roderich Tumulka, and Nino Zanghì, Notices of the AMS, Dec. 2010, http://www.ams.org/notices/201011/rtx101101451p.pdf

References

• Conway and Kochen, The Strong Free Will Theorem, published in Notices of the AMS. Volume 56, Number 2, Feb. 2009.
• Rehmeyer, Julie (August 15, 2008). "Do Subatomic Particles Have Free Will?". Science News. http://www.sciencenews.org/view/generic/id/35391/title/Math_Trek__Do_subatomic_particles_have_free_will%3F 
• Probing Free Will: A Video Lecture Guide, videos of six lectures given by J.H. Conway, Mar. 2009