I think time travel could be possible at some point in the future, we may indeed be visiting ourselves from the future, but I doubt that we are visiting in the touchable, feet on the ground sense. No real physical presence in the past.
History is replete with stories, myths and legends of ghost, apparitions, and spirits. We assume that these are our ancestors from the past, perhaps they are our great great great grandchildren from the present coming back to take a look at what life was like back then, but almost completely unable to interact with the physical world they are visiting.
That's a really interesting point. That could very well be the case! We might not exist in physical forms in the future and traveling to the past would make us seem like ghosts and apparitions.