The grandfather paradox is a proposed paradox of time travel first described by the science fiction writer René Barjavel in his 1943 book Le Voyageur Imprudent (Future Times Three). The paradox is described as following: the time traveller went back in time to the time when his grandfather had not married yet. At that time, the time traveller kills his grandfather, and therefore, the time traveller is never born when he was meant to be. If he is never born, then he is unable to travel through time and kill his grandfather, which means he would be born, and so on.
Despite the name, the grandfather paradox does not exclusively regard the impossibility of one’s own birth. Rather, it regards any action that makes impossible the ability to travel back in time in the first place. The paradox’s namesake example is merely the most commonly thought of when one considers the whole range of possible actions. Another example would be using scientific knowledge to invent a time machine, then going back in time and (whether through murder or otherwise) impeding a scientist’s work that would eventually lead to the very information that you used to invent the time machine. An equivalent paradox is known (in philosophy) as autoinfanticide, going back in time and killing oneself as a baby.
Assuming the causal link between the time traveller’s present and future, the grandfather paradox that disrupts that link may be regarded as impossible (thus precluding the arbitrary alteration of one’s fate). However, a number of hypotheses have been postulated to avoid the paradox, such as the idea that the past is unchangeable, so the grandfather must have already survived the attempted killing (as stated earlier); or the time traveller creates—or joins—an alternate timeline or parallel universe in which the traveller was never born.
A variant of the grandfather paradox is the Hitler paradox or Hitler’s murder paradox, a fairly frequent trope in science fiction, in which the protagonist travels back in time to murder Adolf Hitler before he can instigate World War II. Rather than necessarily physically preventing time travel, the action removes any reason for the travel, along with any knowledge that the reason ever existed, thus removing any point in travelling in time in the first place. Additionally, the consequences of Hitler’s existence are so monumental and all-encompassing that for anyone born in the decades after World War II, it is likely that the grandfather paradox would directly apply in some way (say, if your great-grandparents were Holocaust refugees, or even if the train your parents met on was constructed as part of the war effort).