All religions provide at least some of their members with (what they understand as) direct experience of the non-empirical.
Biologically, these are trance states.
Trance can be brought on by music, dance, fasting, meditation, repetition, pain, drugs, and many other things.
Next: The variability of religion
picture: The Ecstasy of St. Teresa, Bernini, 1650. I saw in his [the angel's] hand a long spear of gold, and at the iron's point there seemed to be a little fire. He appeared to me to be thrusting it at times into my heart, and to pierce my very entrails; when he drew it out, he seemed to draw them out also, and to leave me all on fire with a great love of God. The pain was so great, that it made me moan; and yet so surpassing was the sweetness of this excessive pain, that I could not wish to be rid of it... The Life of St. Teresa of Jesus, 1565, ch 29, paragraph 17.