Neuroscience, both the single-neuron probes and the amazing brain imaging by PET scans and functional MRI, allows us to see (though the pictures are still very blurry and far from the temporal and spatial resolution needed) what is happening in the brain as the mind thinks about various things.
It is unlikely that even the most detailed study of the brain will let us see the
indeterministic effects of quantum physics. Looking at a single event is never enough to say that the event was
uncaused. Random
chance shows up only in the statistics of multiple identical effects. And even then, it is only an inference. It is the standard theory of quantum physics that supports the inference of irreducible chance in the universe.
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