Just think of all the technology we have now that would have seemed completely ridiculous just a century ago. It has been proven that time does not move at a uniform rate. It is affected by gravity, notably highly dense bodies. People are researching the possibilities. It is beyond our current means, but times do change, and the way tech has evolved in just the last three or four decades shows that. We can't say for certainty that it will never be possible. Also, if people did invent time travel, and use it to travel back in time, they wouldn't want to draw attention to themselves. As for the "documented paranormal experiences" - as you said, that's not conclusive evidence. People's minds play tricks on them, and a lot of the time they see what they want to see.