The paradox never happens because all the relavent events already happened, had always happened, and are part of the timeline. There's just a twist in the universal plot. You didn't kill your great-grandfather, because the person you are descended from the playboy your great-grandmother was seeing on the side. Or maybe you fail to kill him because you miss, or he pulls through afterwards, or another time traveller comes back and revives him, explaining the old family tale of the mysterious doctor who treated your ancestor. There's your quantum vacuum effect. It is simply observed as a mundane event.

Pretty much what everyone has been saying is:
Time travel is impossible, but if it were, we wouldn't really be able to change it massively because going back in time would only create the current world you live in instead of a completely different one because it has already happened.Certain holes and such may happen while doing stuff in the past, but ultimately it wouldn't change the present/future. and going forward in time hasn't been explained because it doesn't really need to be.

you should all read "a brief history of time" by stephen hawking. it´s all there.