Grandfather paradox

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The grandfather paradox is a paradox of time travel, first conceived by the science fiction writer René Barjavel in his 1943 book "Le Voyageur Imprudent" ("The Imprudent Traveller") ^[1]. The paradox, stated in the second person, is this: Suppose you traveled back in time and killed your biological grandfather before he met your grandmother. As a result, one of your parents (and by extension, you) would never have been conceived, so you could not have traveled back in time after all. In that case, your grandfather would still be alive and you would have been conceived, allowing you to travel back in time and kill your grandfather, and so on. Thus each possibility seems to imply its own negation, a type of logical paradox.

An equivalent paradox is known (in philosophy) as autoinfanticide — that is, going back in time and killing oneself as a baby — though when the word was first coined in a paper by Paul Horwich it was in the malformed version autofanticide. ^{[citation needed]}

The grandfather paradox has been used to argue that backwards time travel must be impossible. However, other resolutions have also been advanced.

Contents 1 Scientific theories 1.1 Complementary time travel 1.2 Novikov self-consistency principle 1.3 Parallel universes 2 Theories in science fiction 2.1 Parallel universes resolution 2.2 Restricted action resolution 2.3 Relative timelines resolution 2.4 Destruction resolution 2.5 Observation resolution 2.6 Other examples 3 Other considerations 4 See also 5 References

[edit] Scientific theories

[edit] Complementary time travel

Since quantum mechanics is governed by probabilities, an unmeasured entity (in this case, your historical grandfather) has numerous probable states. When that entity is measured, the number of its probable states singularises, resulting in a single outcome (in this case, ultimately, you). Therefore, since the outcome of your grandfather is known, you killing your grandfather would be incompatible with that outcome. Thus, the outcome of one's trip backwards in time must be complementary with the state from which one left. ^[2]

[edit] Novikov self-consistency principle

See the Novikov self-consistency principle and Kip S. Thorne for one view on how backwards time travel could be possible without a danger of paradoxes. According to this hypothesis, the only possible timelines are those which are entirely self-consistent, so that anything a time traveler does in the past must have been part of history all along, and the time traveler can never do anything to prevent the trip back in time from being made since this would represent an inconsistency.

[edit] Parallel universes

There could be "an ensemble of parallel universes" such that when you travel back in time and kill your grandfather, you do so in (or your actions result in the creation of) a parallel universe in which you will never be conceived as a result. However, your existence is not erased from your original universe.

Examples of parallel universes postulated in physics are:

• In quantum mechanics, the many-worlds interpretation suggests that every seemingly random quantum event with a non-zero probability actually occurs in all possible ways in different "worlds", so that history is constantly branching into different alternatives. The physicist David Deutsch has argued that if backwards time travel is possible, it should result in the traveler ending up in a different branch of history than the one he departed from. ^[3] See also quantum suicide and quantum immortality.

• M-theory is put forward as a hypothetical master theory that unifies the five superstring theories, although at present it is largely incomplete. One possible consequence of ideas drawn from M-theory is that multiple universes in the form of 3-dimensional membranes known as branes could exist side-by-side in a fourth large spatial dimension (which is distinct from the concept of time as a fourth dimension) - see Brane cosmology. It is theorized that when two branes collide it sends a massive ripple of heat and energy throughout the two. This is a possible explanation of what caused the big bang according to the ekpyrotic scenario and the cyclic model. However, there is currently no argument from physics that there would be one brane for each physically possible version of history as in the many-worlds interpretation, nor is there any argument that time travel would take you to a different brane.

[edit] Theories in science fiction

[edit] Parallel universes resolution

The idea of preventing paradoxes by supposing that the time traveler is taken to a parallel universe while his original history remains intact, which is discussed above in the context of science, is also common in science fiction - see Time travel as a means of creating historical divergences. Some examples of this type of story:

• Michael Crichton's novel Timeline. Crichton's novel seems to imply that universes set in the past can affect the one we live in. The example given is when a professor trapped in the past sends a message to his graduate students at a medieval cathedral.

• In the Marvel Universe comic books, any change made to the timeline results in an alternate timeline. Some characters know this and use it to their advantage (such as Vance Astro of the Guardians of the Galaxy, whose timeline shift allowed an alternate self to become Justice.)

[edit] Restricted action resolution

Another resolution, of which the Novikov self-consistency principle can be taken as an example, holds that if one were to travel back in time, the laws of nature (or other intervening cause) would simply forbid the traveller from doing anything that could later result in their time travel not occurring. For example, a shot fired at the traveler's grandfather will miss, or the gun will jam, or misfire, or the grandfather will be injured but not killed, or some other event will occur to prevent the attempt from succeeding. No action the traveller takes to affect change will ever succeed, as there will always be some form of "bad luck" or coincidence preventing the outcome. In effect, the traveller will be unable to change history. Very commonly in fiction, the time traveller does not merely fail to prevent the actions he seeks to prevent; he in fact precipitates them (see predestination paradox), usually by accident.

This theory might lead to concerns about the existence of free will (in this model, free will may be an illusion). This theory also assumes that causality must be constant: i.e. that nothing can occur in the absence of cause, whereas some theories hold that an event may remain constant even if its initial cause was subsequently eliminated.

Closely related but distinct is the notion of the time line as self-healing. The time-traveler's actions are like throwing a stone in a large lake; the ripples spread, but are soon swamped by the effect of the existing waves. For instance, a time traveler could assassinate a politician who led his country into a disastrous war, but the politician's followers would then use his murder as a pretext for the war, and the emotional effect of that would cancel out the loss of the politician's charisma. Or the traveller could prevent a car crash from killing a loved one, only to have the loved one killed by a mugger, or fall down the stairs, choke on a meal, killed by a stray bullet, etc. In some stories it is only the event that precipitated the time traveler's decision to travel back in time that cannot be substantially changed, in others all attempted changes will be "healed" in this way, and in still others the universe can heal most changes but not sufficiently drastic ones.

It also may not be clear whether the time traveler altered the past or precipitated the future he remembers, such as a time traveler who goes back in time to persuade an artist -- whose single surviving work is famous -- to hide the rest of the works to protect them. If, on returning to his time, he finds that these works are now well-known, he knows he has changed the past. On the other hand, he may return to a future exactly as he remembers, except that a week after his return, the works are found. Were they actually destroyed, as he believed when he traveled in time, and he has preserved them? Or was their disappearance occasioned by the artist's hiding them at his urging, and the skill with which they were hidden, and so the long time to find them, stemmed from his urgency?

Examples of this set of theories include:

• Oedipus Rex, where the actions undertaken to thwart a prophecy bring it about: Cronus' swallowing of his children to prevent their usurping his power is what encouraged Zeus to overthrow him, and Oedipus's being abandoned led him to meet his mother without being aware of her presence. This, and other folk tales involving prophecies (wherein the 'time travel' is of information), form the oldest known occurrences of the predestination paradox.
• The 2002 movie version of The Time Machine, in which the main character cannot save his girlfriend by going back in time, as he only started building the time machine out of frustration at her death. This loop is not present in the original book.
• In the film Twelve Monkeys, the main character not only is unable to prevent a tragic past event from occurring, but even realizes that, as a child, he witnessed his adult self failing in the attempt. Moreover the perpetrator of some of the related events was inspired to bring them about as a result of speaking to the protagonist
• Douglas Adams's Hitchhiker Series makes use of this resolution for light-hearted and comic plots.
• Harry Harrison's The Technicolor Time Machine uses this resolution for light-hearted and comic plots: when a film-maker goes back in time to make a film of the Viking colonization of America, it proves, in the end, to be the cause of the Vikings' colonization of America, with the film-maker himself appearing in the sagas they used as their source.
• In Castle Roogna, Piers Anthony has the magician Murphy persuade the time-traveler Dor to remain out of a conflict, because he might tamper with the past, but Dor's subsequent actions did affect it, and in his own time, while everything appears unaltered, a discussion points out that later disasters may have made his beneficial effect appear to have disappeared.
• In the 1969 science fiction novel Behold the Man by Micheal Moorcock,the protagonist Karl Glogauer builds a time machine in order to travel back to the Holy Land 2000 years in the past. His intention is to prove the existance of Jesus Christ. When he discovers that in fact Christ actually suffered from severe physical and learning disabilities, Glogauer decides to act out his role as recorded in the Bible, faking the miracles and finally being crucified.

[edit] Relative timelines resolution

It could be that the universe does not have an absolute timeline that is permanently written after events happen (or, in the deterministic view, at the start of time). Instead, each particle has its own timeline and therefore, humans have their own timeline. This might be considered similar to the theory of relativity, except that it deals with a particle's history, rather than its velocity.

Physical forces affect physical particles. If your body's physical particles go back in time, you will be able to kill your grandfather (no physical forces will mystically stop you), and nothing will physically happen to you as a result, because there are no physical forces that can "figure out" what happened and this new timeline develops, because the universe simply has no mechanism for unmaking it. Your younger self does not need to be born in order to fulfill a destiny of going back in time, because there is no written-in-stone absolute timeline that needs to be followed. If you were able to find and observe the younger versions of the particles that make you up, they too would follow physical laws and hence wouldn't form into a younger version of you (because one of your parents wouldn't be there to form you).

This theory is similar to the parallel universes theory, except that it happens within one universe. If parallel universes cannot interact again after time travel occurs, then essentially the parallel universe resolution and the relative timelines resolution are the same as there is no way of proving a parallel universe still exists or ever did exist.

Examples include:

• Alfred Bester's short story The Men Who Murdered Mohammed, posits that, once you change the past, you create a solipsistic universe where you can make whatever changes you like, including preventing your own birth. Each time traveller has their own solipsistic time line.

• Orson Scott Card used this theory to allow his characters to travel back in time and prevent the European colonization of the New World in his novel Pastwatch: The Redemption of Christopher Columbus.
• Similarly, this model also appears in James P. Hogan's novel Thrice Upon a Time, although Hogan confusingly uses the term "universes" to describe different moments on the same timeline rather than separate timelines.
• In Anderson's Time Patrol, the Patrol's purpose is to prevent such changes in time, and when they have occurred, undo the changes as neatly as possible, to revert to the "normal" timeline. Such a Time Patrol, under one name or another, is a common feature in stories using this resolution.
• In the television series Seven Days, NSA Agent Frank Parker uses a device called the chronosphere to go back in time, usually one week, to "undo" catastrophic events. This would only be possible if the relative timelines resolution holds, because if Parker succeeds, there would never have been any reason to send him back in time.
• In the essay The Theory and Practice of Time Travel, Larry Niven proposes that, after some unknown number of revisions of history, the effect of some episode of time travel will be to create a universe where time travel, although possible, is simply never discovered. Such a timeline is stable, and in it no paradoxes occur, and so need no resolution.

In some works, the replacement is not complete. Characters may "remember" their lives in the original timeline, and more drastic effects may occur. In Jasper Fforde's Thursday Next books, time travelers caused Thursday's husband to drown as a child, but Thursday remained pregnant with his child.

[edit] Destruction resolution

Some science fiction stories suggest that causing any paradox will cause the destruction of the universe, or at least the parts of space and time affected by the paradox. The plots of such stories tend to revolve around preventing paradoxes.

Examples include:

• It was speculated by Doc Brown that "the encounter could create a time paradox, the results of which could cause a chain reaction that would unravel the very fabric of the space-time continuum and destroy the entire universe. Granted, that's a worst-case scenario. The destruction might, in fact, be very localized, limited merely to our own galaxy". However, it must be noted that actual paradoxes were averted in the Back to the Future trilogy, so it was never shown if Doc's speculations were correct.
• The 2005 Doctor Who series episode Father's Day provided a unique version of the destruction resolution. A paradox causes a wound in space-time, which attracts flying carnivorous monsters, Reapers. The Reapers act like bacteria around a real wound, devouring everything, starting with the youngest people and objects, until the wound is "sterilized" and the paradox resolved by its destruction.
• In Beast Wars, the present-day Megatron traveled back in time to prehistoric Earth where the Transformers from the original show hibernated. In order to prevent the Autobots from winning the historic war, he fired a lethal blast at Optimus Prime's body. Immediately, a reality-destroying time storm erupted and steadily spread from Earth to the rest of the galaxy and beyond. Fortunately, the Maximals were able to repair Prime's body before all of history was altered and they were erased from existence.

[edit] Observation resolution

Some speculations suggest that, under no circumstances whatsoever you would be able to "kill your grandfather". The only result of the time travel would be your knowledge that you've caused some event in the past. For example, if a protagonist kills their grandfather, it would turn out that the victim is not their grandfather at all.

[edit] Other examples

The Grandfather Paradox, or similar, is also used in the following:

• A well known, typical example of the paradox is the first Back to the Future film: Marty McFly travels to 1955 and accidentally prevents the first meeting of his parents. While trying to find out a way to return to his own year, he observes that his siblings begin to fade out from a picture he was carrying with him since he averted their own birth. Towards the end of the film, he starts to fade from reality as well, until he manages to make his parents fall in love "again".
• The Futurama episode, Roswell That Ends Well, episode 3ACV19, in which a main protagonist, Philip Fry, travels back in time and humorously solves the paradox by (accidentally) becoming his own grandfather (an action that would, indirectly, result in him getting cryogenically frozen and setting up the entire series).
• Robert A. Heinlein's short story "—All You Zombies—"
• Spider Robinson's short story Father Paradox
• Connie Willis's novel To Say Nothing of the Dog
• The Terminator series of movies
• Star Trek episode The City On The Edge Of Forever - This was when McCoy, with an accidental overdose on medicine, went through a time portal causing the death of a woman not to happen which would alter the past causing the crew up above in space not to exist along with what the changes on Earth, where Kirk and Spock must find the point in time which McCoy altered time and stop him. In a sad twist of fate, the very same woman that Kirk would later fall in love with is the woman that McCoy saved causing the time change and now Kirk with grief in his heart must let her die in order to set time right again. In the Star Trek: Deep Space Nine episode "Trials and Tribble-ations", which used footage from the original series to create a time travel episode with Kirk and crew in it, Julian Bashir flirts with a girl he later realizes may be his ancestor and, in a spoof of the paradox, begins to worry that he may be faced with the choice of becoming his own progeny or ceasing to exist.
• The popular webtoon Bonus Stage episode 87, Bonus Stages, where main character, Phil Argus, goes back in time to the first episode of the series, and kills his old self, putting a slightly different twist on the paradox, and destroying the rest of the Bonus Stage universe.
• The online machinima comedy series Red vs. Blue - The character Church travels back in time to prevent his own death, and to avert the events and disasters that put the characters into their current situation. He ends up causing all of the problems and situations of the first 48 episodes — including his own death — entirely by accident.
• The Red Dwarf episode, Tikka To Ride, episode 7.1, in which The future version of the crew destroyed the present crew; therefore, the future crew no longer existed and therefore were unable to go back in time and kill themselves, hence they survived.
• The Red Dwarf episode, Ouroboros, episode 7.3, in which Lister discovers he is his own father and travels back in time to place his son, aka himself, under the pool table where his adoptive parents first found him.
• In Metal Gear Solid 3: Snake Eater, after Revolver Ocelot and the Ocelots are knocked out, it is possible to shoot Ocelot. This however results in an instant game over screen, with the words "TIME PARADOX" replacing "GAME OVER". This occurs due to the fact that Ocelot is a vital factor in the Metal Gear Solid games, and that none of them would have happened if Ocelot died. Also, if the main character, Naked Snake, dies in any way, the "TIME PARADOX" message also replaces the "SNAKE IS DEAD" screen. This is due to the fact that Naked Snake is actually Big Boss, the father of Solid Snake, who is the most critical character in the previous Metal Gear games.
• The Invader Zim episode, Bad, Bad Rubber Piggy, in which Zim tries to use a space-time object replacement device to send a Hunter-Destroyer robot to destroy Dib before he becomes Zim's enemy. GIR warns Zim that if Dib doesn't become Zim's enemy, Zim won't send the robot, and then Dib won't be destroyed and will become Zim's enemy, and then Zim will send the robot, Dib will be destroyed and won't become Zim's enemy (Gir keeps telling it until his head explodes). the paradox never occurs because Zim had failed at destroying Dib.
• K. A. Applegate's Megamorphs #3: Elfangor's Secret (of the Animorphs series) featured a storyline wherein the Animorphs are shown an alternate universe where slavery and disease are rampant, which will become reality unless they can follow a certain alien foe, Visser Four, through time in order to stop him. Visser Four travels to world events such as Washington's crossing of the Delaware and D-Day attempting and succeeding in altering the timeline with the Time Matrix to make it favorable for the invading Yeerks. The successful Yeerk abandons his host, and the Animorphs take that opportunity to ask the dying human when his parents met with the intention of preventing his birth to save the timeline, which they do.
• In The Legend of Zelda: Oracle of Ages, when Link gets possessed Impa to the area where Nayru is singing, Veran emerges from Impa and possesses Nayru. After Ralph puts away his sword and steps away from possessed Nayru, possessed Nayru goes back in time and turns almost everyone into stones and possesses Queen Ambi to make the Black Tower, thus causing a paradox to change the future. Link goes back in time to fix the paradox.
• In Harry Potter and the Prisoner of Azkaban, Harry sees a figure on the other side of the lake (who he believed to be his deceased father) which saves him and Sirius Black with a Patronus Charm. Later he travels back in time and discovers that the figure was himself. He casts the Patronus and saves himself and Sirius. In fact, only because Harry saw himself already conjure the Patronus was he able to muster the self confidence to be able to conjure the Patronus.
• In Prince of Persia In the first part of the new Prince of Persia trilogy, the Prince releases the Sands of Time. The second game reveals that whoever releases the Sands must die. The Prince attempts to reverse his fate by going back in time to before the sands were made, at which point he discovers that he himself makes the Sands. He finally overcomes his fate when he puts on a mask that sends him back in time again, stopping his action that made the sands. As the Prince acts in paradox (if the sands were never created, he wouldn't be trying to destroy them), he is pursued by a beast called the Dahaka, a guardian of the timeline who ensures consistency through force.
• Though not a reference to the time travel paradox, Tom Arnold's character in The Stupids sings a short nonsensical song about being his own grandfather. In the song he explains how he became "his own grandpa."

[edit] Other considerations

Consideration of the grandfather paradox has led some to the idea that time travel is by its very nature paradoxical and therefore logically impossible, on the same order as round squares. 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, most philosophers and scientists agree that time travel into the past need not be logically impossible as long as 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 which is recorded here.

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. ^[4][5] He seems to have been suggesting something along the lines of the block time view in which time does not really "flow" but is just another dimension like space, with all events at all times being fixed within this 4-dimensional "block".

[edit] See also

• Chronology protection conjecture
• Time loop
• Time travel in fiction
• I'm my own Grandpa

[edit] References

1. ^ Barjavel, René (1943). Le voyageur imprudent ("The imprudent traveller").
2. ^ Kettlewell, Julianna. "New model 'permits time travel'", BBC News, 2005-06-17. Retrieved on 2006-05-25.
3. ^ Deutsch, David (1991). "Quantum mechanics near closed timelike curves". Physical Review D 44: 3197-3217.
4. ^ Yourgrau, Palle (2004). A World Without Time: The Forgotten Legacy Of Godel And Einstein. Basic Books. ISBN 0-465-09293-4.
5. ^ Holt, Jim. "Time Bandits", The New Yorker, 2005-02-21. Retrieved on 2006-10-19.