  Both deterministic and indeterministic physical laws are incompatible with
control by genuine (non-illusory) free will. We propose that an indeterministic
dynamics can be $weakly$ compatible with free will (FW), whereby the latter
acts by altering the probability distribution over allowed outcomes. In the
quantum physical world, such a FW can collapse the wave function, introducing
deviations from the Born rule. In principle, this deviation would stand in
conflict with both special relativity and (a variant of) the Strong
Church-Turing thesis, implying that the brain may be an arena of exotic,
non-standard physics. However, in practice, these deviations would not be
directly or easily observable, because they occur in sub-neuronal
superpositions in the brain, where they would be shrouded in random measurement
errors, noise and statistical fluctuations. Our result elucidates the
difference between the FW of human observers and that of observed particles in
the Free Will Theorem. This difference is a basic reason for why FW (and, in
general, consciousness) cannot be recreated by standard artificial intelligence
(AI) technology. We propose various neurobiological experiments to test our
proposed theory. We speculate that for observers to be aware of a physical
theory such as quantum mechanics, FW is necessary and that the theory must
therefore not be universal. We suggest that FW may be regarded as a primitive
principle in Nature for explaining quantum indeterminism.
