Paradox in time travel

Paradox in time travel movies is serious. For example, you go back and your grand pa no longer marries granny. Oh wow, poof you are gone.  Hey, so how did you get their in the first place any way. This is know as the grandfather paradox in time travel and a problem we want to solve for you. First off, the time line splits into two pieces. Just that allows you to go back and make changes to the original one.