Is (theoretical) timetravel possible without automatically creating a paradox?

[Clint]

So your either stuck in another world (umm... what?) or you just vanish, cause you don' exist anymore. (But then who made the changes? ---> paradox. yeah ^_^)

I realize that it doesn't matter what theories any of us throw out there concerning time travel and paradoxes, because in the end, everything is just really confusing. I would just like to add to that confusion a little bit.

It's impossible for somebody to just vanish, even if they don't technically exist any more in that one timeline, because the person already exists. That was probably the thinking when the time travel part of quantum theory was being established, because if a person doesn't exist in a certain timeline, yet still exists, doesn't that mean that there has to be another timeline in which that person does exists?