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 Despite the experiment feeling arbitrary, as most statistical problems are, it’s a test in mechanical reality demonstraring that probabilities are not static 
 Theories have limits, and the theory is not the phenomena. 

How are you going to define free will or determinism? You need to find a scope for a definition which implies that the definition will fail outside of the scope. As such, and any mechanistic model of a Complex System can at most be a tangent plane approximation of the system's behavior. 

And then you have to factor in the assumption that the system cannot  be influenced by its observers. In the case of free will vs determinism you are essentially focusing the camera on the display, which is self referential - a feature that formal systems don't play nicely with.
 
 Wen I speak of determinism I refer to the mathematical properties of Einstein’s equations on time