The physical and spiritual world would have to be connected by immaterial means?
Probably. But we don't have any idea how. There's no satisfactory view about this. But Saint Aquinas talked about an intermediate mortal soul. He just not made clear if this mortal soul is physical or spiritual. This mortal soul (anima) can be the link of the brain and the immortal soul.
Therefore, it might be possible that the scientific method could, at some point in the future, be used to study this immaterial connection between the physical and spiritual/non-physical, if such a connection exists at all.
I know what you mean. You are talking about scientific falseability about some metaphysical entity.
Well there's a way to test the causation of consciousness.
When we reach the exascale computing we will have, in theory, the same capacity of the brain (this exascale is predicted to be reached between 2025 and 2040).
Combining the exascale computing with the brain simulation in the ongoing Blue Brain Project, we can try to run a virtual brain and see if a consciousness (strong artificial intelligence capable to pass the Turing test) emerges from it.
This would be the ultimate experiment.
I bet a consciousness will not arise. But I'm not sure about the birth of Skynet. Lol
https://en.m.wikipedia.org/wiki/Exascale_computing
https://en.m.wikipedia.org/wiki/Blue_Brain_Project