well, hypothetically, if time travel were possible, and you went back in time and killed yourself. what would happen?

because if you were to kill yourself you would be dead, which means you couldn't have gone back in time in the first place, which means you couldn't have killed yourself which means you couldn't have died.

well?

some say the universe would seize to exist, and that a parallel universe would carry on with an alternate way of things (i.e. you decided not to go back in time), some say you would just die.

i am partly asking this to see what you guys think, and partly because maybe there is an actual answer which is most widely believed by scientists.