Grandfather paradox

The grandfather paradox is a paradox of time travel in which inconsistencies emerge through changing the past. The name comes from the paradox's description: a person travels to the past and kills their own grandfather before the conception of their father or mother, which prevents the time traveller's 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, since there is a contradiction whenever the past becomes different from the way it was.
Early examples.
The grandfather paradox was mentioned in written stories as early as 1929. In 1931, it was described as "the age-old argument of preventing your birth by killing your grandparents" in a letter to American science fiction magazine "Amazing Stories". Early science-fiction stories dealing with the paradox are the short story "Ancestral Voices" by Nathaniel Schachner, published in 1933, and the 1944 book "Future Times Three" by René Barjavel, although a number of other works from the 1930s and 1940s touched upon the topic in various degrees of detail.
Variants.
The grandfather paradox encompasses any change to the past, and it is presented in many variations. Physicist John Garrison et al. give a variation of the paradox of an electronic circuit that 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 the "retro-suicide paradox" or "autoinfanticide", going back in time and killing a younger version of oneself (such 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 and the Holocaust. Rather than necessarily physically preventing time travel, the action removes any "reason" for the travel, along with any knowledge that the reason ever existed. 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, the traveller is actually killing a parallel universe version of the grandfather, and the time traveller's original universe is unaltered; it has been argued that since the traveller arrives in a different universe's history and not their own history, this is not "genuine" time travel. In other variants, the actions of time travellers have no effects outside of their own personal experience, as depicted in Alfred Bester's short story "The Men Who Murdered Mohammed".
Philosophical analysis.
Even without knowing whether time travel to the past is physically possible, it is possible to show using modal logic that changing the past results in a logical contradiction. If it is necessarily true that the past happened in a certain way, then it is false and impossible for the past to have occurred in any other way. A time traveller would not be able to change the past from the way it "is;" they would only act in a way that is already consistent with what "necessarily" happened.
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", arguing that the possibility of creating a contradiction rules out time travel to the past entirely. 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. This principle is illustrated in Ted Chiang's novelette The Merchant and the Alchemist's Gate. Dowden revised his view after being convinced of this in an exchange with the philosopher Norman Swartz.
General relativity.
Consideration of the possibility of backward 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 four-dimensional "block".
Causal loops.
Backward time travel that does not create a grandfather paradox creates a causal loop. The Novikov self-consistency principle expresses one view as to how backward 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, that of a billiard ball heading toward a time machine. The ball's older self emerges from the time machine and strikes its younger self so that its younger self never enters the time machine. Novikov et al. showed how this system can be solved in a self-consistent way that avoids the grandfather paradox, though it creates a causal loop. Some physicists suggest that causal loops only exist in the quantum scale, in a fashion similar to that of the chronology protection conjecture proposed by Stephen Hawking, so histories over larger scales are not looped. Another conjecture, the cosmic censorship hypothesis, suggests that every closed timelike curve passes through an event horizon, which prevents such causal loops from being observed.
Seth Lloyd and other researchers at MIT have proposed an expanded version of the Novikov principle by 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.
Some physicists, such as Daniel Greenberger, and David Deutsch, have proposed that quantum theory allows for time travel where the past must be self-consistent. Deutsch argues that quantum computation with a negative delay—backward 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 the time traveller emerging in a different universe, which avoids the grandfather paradox.
The interacting-multiple-universes approach is a variation of Everett's many-worlds interpretation (MWI) of quantum mechanics. It involves time travellers arriving in a different universe than the one from which they came; it has been argued that, since travellers arrive in a different universe's history and not their own history, this is not "genuine" time travel. Stephen Hawking has argued that even if the MWI is correct, we should expect each time traveller to experience a single self-consistent history, so that time travellers remain within their own world rather than travelling to a different one. Allen Everett argued that Deutsch's approach "involves modifying fundamental principles of quantum mechanics; it certainly goes beyond simply adopting the MWI", and that even if Deutsch's approach is correct, it would imply that any macroscopic object composed of multiple particles would be split apart when traveling back in time, with different particles emerging in different worlds.
However, it was shown in an article by Tolksdorf and Verch that Deutsch's CTC self-consistency condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic quantum field theory on spacetimes where CTCs are excluded, casting doubts on whether Deutsch's condition is really characteristic of quantum processes mimicking CTCs in the sense of general relativity.