I'd go for ESP in the form of telepathy.
If one person has a thought or feeling that produces a brain state in that person which is physical (it may be electrical but chemically based) it should give rise to an associated field.
That field (I'll assume an EM field) could be sensed or picked up by someone close by whose brain is configured in the same way and so the thought-pattern field would fit the recipient's brain (a bit like a hand in a glove) and they could experience the same thought or feeling.
I think that at least sounds plausible (to someone who's not a neuroscientist ) but I very much doubt it's true.
I think the point is: if some evidence came to light that that is what really happens it would be easier to convince me of it than say someone receiving a highly unlikely message in a psychic reading proving the afterlife.