Grandfather Paradox

A Grandfather Paradox is a an often cited example of the problems potentially caused by time travel. Theoretically, a person could travel back in time and kill their own grandfather before the conception of one of their parents. However, if the time traveler succeeds in killing his/her grandfather, the time traveller was then never born and would cease to exist. Following this logic, the time traveler never existed and was unable to travel in time to kill their grandfather. In that case, the grandfather must be alive and the time traveler must exist. This sequence of events continues to circle in an unending paradox that can only be solved through the collapse of the space-time continuum or the introduction of the possibilities of alternate timelines and universes.