Upvote:0
The psychic powers of a Buddhist monk cannot be tested by science because it is forbidden for a Buddhist monk to demonstrate psychic powers to lay people, i.e., to scientists.
Displaying psychic powers. A related rule at Cv.V.8.2 states that to display psychic powers to lay people is a dukkaΛa. In the origin story leading up to that rule, the Buddha levels strong criticism at such an act: βJust as a woman might expose her v***na for a miserable wooden masaka coin, so too have you displayed a superior human state, a wonder of psychic power, to lay people for the sake of a miserable wooden bowl.β
Upvote:4
"Can a buddha communicate with someone in far away places?"
Question falls under the Four Imponderables, namely the first Acinteyya, i.e. the range of powers of a Buddha:
The Buddha-range of the Buddhas [i.e., the range of powers a Buddha develops as a result of becoming a Buddha];
The jhana-range of one absorbed in jhana [i.e., the range of powers that one may obtain while absorbed in jhana];
The [precise working out of the] results of kamma;
Speculation about [the origin, etc., of] the cosmos is an imponderable that is not to be speculated about.
-- Acintita Sutta, Anguttara Nikaya 4.77.
These imponderables the Buddha advices not to contemplate since they will only serve to agitate and destabilize the mind making it less suitable for meditation practice.