Sometimes a "believer" believes because of what he/she has experienced, and, no, every experience cannot be "proven" and good luck trying to convince one who HAS experienced something, that it doesn't exist. I speak from personal experience, NOT about a religious experience, but about a paranormal one, something strict empiricists would likely sneer at as quickly as they do religion.

To quote my very left-brained, science trained spouse, "Science doesn't yet know everything...They thought they did in the 19th century and, as time told, they were dead wrong".