Logic would dictate that if time travel were possible some idiot would have already tried to use it and destroyed the universe in the process, or anything you do in the past must trigger the events that influence the future where you started your time machine. You probably couldn't do much if you made one.
Think about it, if you saved Sophie, the even that caused you to decide to go back in time and save her wouldn't happen. It must not be possible to do it, something would interfere with you trying because if creating such a paradox was possible, one would have occured long before the opportunity you had to create yours and we'd all be dead.