[simiones]

> that its operation does not involve currently-unknown laws of physics (because we have a good understanding of what happens at the scale of an entire atom or above)

Well, we know certain approximations of those laws. Purely theoretically, it is possible that the exact laws at some level of detail that we have not yet been able to observe involve functions that are not computable by a Turing machine, and then it is theoretically possible that the brain itself is computing functions which are not computable by a Turing machine (this would of course assume that the Church-Turing thesis is actually wrong).

As long as the Church-Turing thesis is not proven, we can't say with absolute certainty that the physical world can be simulated to any level of detail by a Turing machine.

Furthermore, even if the Church-Turing thesis was proven, is it possible that the physical world involves transformations that are not even computable at all (even if they can be approximated by computable functions)?

Just to be clear, I do not believe these things. But it is fun to think about the limits of our knowledge.