As a possibly interesting corollary to this....Some of these experiences seem to suggest to me that the mind is at least partially 'outside' of the system that is defined by current physics assumptions, since the mind seems to be able to produce occasional objectively demonstrable 'miracles' that don't happen much otherwise, apparently. The conventional scientific approach of course assumes that reality is absolutely immune to such interference, and experiments are designed accordingly. So it should be expected that such experiments are inadequate for studying such phenomena.

Anecdotally, it also seems to me that a moral component of the mind is outside the 'conventional' physical system. In other words, I speculate that if you could completely understand a person's genes and the physiological effects of their past experience, it would largely account for their moral character, but not entirely. Since the 'physical system' lacks knowledge of that other component, the multiverse of alternative outcomes includes some that would never actually be permitted to exist by the mind. But those outcomes still influence intuition and precognition, since they are physically possible. Maybe I'm too lazy to give specific examples. But there's the idea to play with anyway.