The Free Will Theorem of Conway and Kochen is an interesting argument that tries to suggest free will goes “all the way down”. If experimenters can make their choices freely on how to measure certain experiments then the elementary particles being measured can make “free choices” as well. But the contrapositive of this result seems more interesting to me: if some elementary particles are not free, then the experimenters aren’t either!

I’ve cheated some here because it is really based on three axioms or assumptions, and not four. All for the sake of science (and philosophy)!

Fin : Information transmission has a maximal (finite) speed, and obtains from causality

Twin : For two elementary particles, it is possible to quantum “entangle” them, separate them significantly, and measure the square of their spin in parallel directions (but “full entanglement” is not required)

Spin : For certain elementary particles of spin one (the vector or gauge bosons: gluons, photons, Z and W), the squared spin component (taken in three orthogonal directions) will be a permutation of (1,1,0)

Min : Instead of Fin, the weaker assumption Min states that the spin measurers need only be “space-like” separated and make choices independently of each other

Lin : Instead of Fin or Min, Lin is an even weaker assumption that rests on experimentally testable “Lorentz Covariance”

If nothing else, trying to understand this theorem teaches you a bit about elementary particles and quantum physics!