As Marty McFly explores the world of 1955, he is confronted with the fact that the history of his parent's life is changing before his eyes, and his own existence is in jeopardy. He has interfered with the meeting of his parents, and must correct the situation before it's too late, or he will cease to exist. Back to the Future is essentially the classic grandfather paradox: a man goes back in time and undoes his own birth. However, Back to the Future's theory of time travel suggests a different resolution than a never-ending loop.
Like the Terminator series, Back to the Future insists there can only be one timeline and rejects a many worlds interpretation. Both series also allow 'temporal refugees,' visitors from possible future timelines who by virtue of their presence in the past, nullify their own creations. In T2 we have the T800 that comes from a world where Cyberdyne created Skynet, In BttF we have Marty. The difference between the two theories of time travel, however, is that Marty immeadiately feels the consequnces of his temporal mischief and begins to dissappear whereas the terminator persists even after destroying Cyberdyne.
Unlike the traditional grandfather paradox solution, where a time traveler who undoes their own existence thereby nullifies their own trip, in Back to the Future, the consequences of Marty's time travel aren't felt until after he meddles with his parents meeting. Marty exists long enough to mess up the past, but its not until the moment of divergence between his past and the new past that his continued existence is put in jeopardy. Of course, Marty is given a chance to redeem his timeline by getting his parents back together before he blinks out of existance (imagine his increasingly vanishing presence as representing the diminishing probability of his conception). This is what allows for the suspense in the Back to the Future movies, Marty could concievably nullfy his own existance without nullifying his trip altogether--the universe will only reconcile his anarchorismic presence after the point he meddled with his parent's meeting.
In the Back to the Future theory of time travel, a grandfather paradox would be resolved like this: one day, Papy Joe would be walking home, when someone who sorta looks like him pops out of thin air, murders him and then proceeds to fade out of existance. In a Terminator universe, the assailiant wouldn't dissappear but could linger around the timeline indefinetly, even though his origin had been nullified. If Terminator gives refugees a passport, Back to the Future only gives them a travel visa.
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