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The grandfather paradox is a paradox of time travel in which inconsistencies emerge through changing the past. The name comes from the paradox's common description as a person who travels to the past and kills their own grandfather, preventing the existence of their father or mother and therefore their own existence. Despite its title, the grandfather paradox does not exclusively regard the contradiction of killing one's own grandfather to prevent one's birth. Rather, the paradox regards any action that alters the past, which would become inconsistent with the original version of the past.
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Early examples
The grandfather paradox was described as early as 1931, and even then it was described as "the age-old argument of preventing your birth by killing your grandparents". Early science fiction stories dealing with the paradox are the short story Ancestral Voices by Nathaniel Schachner, published in 1933, and the 1943 book by René Barjavel Future Times Three.
Variants
Garrison et al give a variation of the paradox of an electronic circuit which sends a signal through a time machine to shut itself off, and receives the signal before it sends it.
An equivalent paradox is known in philosophy as autoinfanticide, going back in time and killing oneself as a baby.
Another 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 after the war, it is likely that their birth was influenced in some way by its effects, and thus the lineage aspect of the paradox would directly apply in some way.
Some advocate a parallel universe approach to the grandfather paradox. When the time traveller kills their grandfather, they are actually killing a parallel universe version of their grandfather, and the time traveller's original universe is unaltered; it's been argued that since the traveler arrives in a different universe's history and not their own history, this is not "genuine" time travel. In other variants, the actions of the time traveller have no effect outside of their own personal experience, as depicted in Alfred Bester's short story The Men Who Murdered Mohammed.
Logical analysis
Even without knowing whether time travel to the past is physically possible, the grandfather paradox can be explored from a logical perspective. The paradox is a logical contradiction that stems from changing the past (or the present, or the future) from the way it is: if an event has occurred one way, there is no possibility for the event to have occurred a different way. Then, logically, changing the past (or the present, or the future) from what it is results in a contradiction, which means changing the past is impossible. There still exists the logical possibility of travelling back in time and setting events the way they are, for example a time traveller intending to kill their own grandfather but instead killing someone who is not their grandfather.
Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible. For example, the philosopher Bradley Dowden made this sort of argument in the textbook Logical Reasoning, where he wrote:
Nobody has ever built a time machine that could take a person back to an earlier time. Nobody should be seriously trying to build one, either, because a good argument exists for why the machine can never be built. The argument goes like this: suppose you did have a time machine right now, and you could step into it and travel back to some earlier time. Your actions in that time might then prevent your grandparents from ever having met one another. This would make you not born, and thus not step into the time machine. So, the claim that there could be a time machine is self-contradictory.
However, some philosophers and scientists believe that time travel into the past need not be logically impossible provided that there is no possibility of changing the past, as suggested, for example, by the Novikov self-consistency principle. Bradley Dowden himself revised the view above after being convinced of this in an exchange with the philosopher Norman Swartz.
Consideration of the possibility of backwards time travel in a hypothetical universe described by a Gödel metric led famed logician Kurt Gödel to assert that time might itself be a sort of illusion. He suggests something along the lines of the block time view in which time is just another dimension like space, with all events at all times being fixed within this 4-dimensional "block".
Novikov self-consistency principle
The Novikov self-consistency principle expresses one view on how backwards time travel would be possible without the generation of paradoxes. According to this hypothesis, physics in or near closed timelike curves (time machines) can only be consistent with the universal laws of physics, and thus only self-consistent events can occur. Anything a time traveller does in the past must have been part of history all along, and the time traveller can never do anything to prevent the trip back in time from happening, since this would represent an inconsistency. Novikov et al. used the example given by physicist Joseph Polchinski for the grandfather paradox, of a billiard ball heading towards a time machine: the ball's older self emerges from the time machine and strikes its younger self so its younger self never enters the time machine. Novikov et al. showed how this system can be solved in a self-consistent way which avoids the grandfather paradox, though it creates a causal loop.
Seth Lloyd and other researchers at MIT have proposed an expanded version of the Novikov principle, according to which probability bends to prevent paradoxes from occurring. Outcomes would become stranger as one approaches a forbidden act, as the universe must favor improbable events to prevent impossible ones.
Quantum physics
Physicist David Deutsch has argued that quantum computation with a negative delay—backwards time travel—produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning. In 2014, researchers published a simulation validating Deutsch's model with photons. Deutsch uses the terminology of "multiple universes" in his paper in an effort to express the quantum phenomena, but notes that this terminology is unsatisfactory. Others have taken this to mean that "Deutschian time travel" involves multiple universes in order to resolve the grandfather paradox.