Free will vs determinism argument makes sense if you've first assumed that you are separate from your environment, which seems true from a very local perspective. What happens if you consider the opposite?
Sure, science must encapsulate phenomena in some way to imply consequences, but an encapsulated and formalized nature is not nature.
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
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