It’s probably a similar phenomenon to hypnotism. You let the rational part of your brain go and just let yourself go as wacky as you feel you’re supposed to – either because a hypnotist told you to, or because you know what the routine is already. Also related is Koro, where people convince themselves that their penis is missing. Ultimately, your senses are just the interpretations of the world by your brain. If you convince your brain to lie to yourself, you’ll see what isn’t there.
That is a promise of God, that He will reveal these things to you. The process is we get the Holy Spirit, which is the same spirit that Jesus has, the same spirit that the Father has (this is why God is one). A person recognizes the spirit of their Creator. It is something our soul embraces. In this world we search for things to satisfy the longing of our soul, the only thing that can fill it is God’s spirit.
On a similar note I was watching a friend’s in a very noisy place (many children), all of a sudden she (the child) turned to me and told me that her mother was calling her. This place was so noisy that any such calling would be drowned out, but the child heard her mother’s call somehow. I’ve seen other examples of this, particularly between mother and child, a bond that is beyond what we can see.
It depends on the circumstances. If school officials knew that it was likely to happen or arranged circumstances so that it was likely to happen, then it may still be considered government sponsorship of religion.
