Free Will Theorem

A theorem by John Conway and Simon Kochen stating that, under specified assumptions, if experimenters have free choice, certain particles’ responses are not determined by prior information.

SPIN theorem: A result about spin-1 particles: measurements along orthogonal directions yield one 1 and two 0s, regardless of measurement order. It supplies the spin-measurement constraint used in the theorem’s argument.
Spin (physics): An intrinsic form of angular momentum carried by quantum particles. The theorem uses spin-1 particles and their constrained measurement outcomes.
John Horton Conway: An English mathematician known for contributions to group theory, combinatorics, and recreational mathematics. He co-developed and presented the theorem with Simon Kochen.
Determinism: The view that the state of the world and its laws fix every later event. The theorem challenges a specific form of outcome determination, not determinism without qualification.
Quantum indeterminacy: The lack of uniquely determined outcomes for some measurements in quantum theory. The theorem gives a conditional argument that certain responses are not fixed by prior information.
TWIN theorem: A result showing that entangled spin-1 particles give matching answers when both are measured along the same direction. It links the two particles’ responses across spacelike-separated measurements.
Spin-1 particle: A particle whose intrinsic angular momentum has quantum number one. The theorem’s specific SPIN constraint concerns spin-1 measurements.
Simon Kochen: A mathematician whose work includes foundational results on quantum mechanics and the Kochen–Specker theorem. His earlier contextuality result is central to the theorem’s mathematical background.
Compatibilism: The philosophical position that free will can coexist with determinism. It addresses human agency, while the theorem’s free-choice premise concerns measurement settings.
Bell test: An experiment testing whether observed correlations violate inequalities implied by local hidden-variable models. Bell tests probe related assumptions about distant measurements and pre-existing information.

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