This is the most common example of the Time Travel Paradox.

It describes how a Time Travelers action when traveling back in time alters the Time Travelers future creating a paradox.

Firstly the Time Traveler returns to a time before the birth of the Time Traveler's mother and therefore the Time Traveler. An action caused by the Time Traveler results in the death of the Time Traveler's grandmother. There is now a paradox.

....if you kill your grandmother then you would not be born, therefore you cannot travel to the past and kill your grandmother, so you would be born, so you could travel to the past and kill your grandmother....

An action occurs that changes the future in such a way that the action to change this future could not occur. This has been used in many science fiction books and films for example “Back To The Future”. Here the Time Traveler Marty McFly travels to the past and accidentally prevents his parents from meeting. As a result he cannot return to the present because he will not exist. So he spends the rest of the film trying to get them together.

It could be argued that at the moment he changes the past he should promptly disappear. After all this could be a logical termination of his timeline (and perhaps a good reason for people not to time travel). In the film however he simply begins to fade away represented by a photograph of himself with his brother and sister where they begin to loose parts of themselves. It is not until his parents fall in love and therefore his future birth is established that he returns to health.

There are also other aspects of Time Travel used in the film. Marty returns to ten minutes before the time he left and so for ten minutes there is an overlap with two Martys and two time travel cars. Also because of events witnessed by Marty prior to his time travel trip namely the shooting of Dr Emmett he is able to warn him. Knowing this Dr Emmett wears a bullet-proof vest which saves his life.

It all appears perfectly in order even when the timelines are drawn out as in the following chart. This shows the timelines of Marty and Dr Emmett in relation to the main events in the film.

Things begin to get a little unstuck when the events on the timeline of Dr Emmett are considered in more detail. In 1985 it would appear that he has already met Marty before and has a letter telling him of events in the future. But how can this be true? According to Marty’s timeline he has not yet traveled into the past. So how can Dr Emmett Know? How can he be wearing the vest? Now you can begin to see a paradox. Two versions of history.