Novikov self-consistency principle

# Novikov self-consistency principle

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The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle
Principle
A principle is a law or rule that has to be, or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed...

developed by Russian physicist Igor Dmitriyevich Novikov
Igor Dmitriyevich Novikov
Igor Dmitriyevich Novikov is a Russian theoretical astrophysicist and cosmologist.Novikov formulated the Novikov self-consistency principle in the mid-1980s, an important contribution to the theory of time travel.Novikov gained his Ph.D. degree in astrophysics in 1965 and the Russian D.Sc....

in the mid-1980s to solve the problem of paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

es in time travel
Time travel
Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

, which is theoretically permitted in certain solutions of general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

(solutions containing what are known as closed timelike curve
Closed timelike curve
In mathematical physics, a closed timelike curve is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point...

s). Stated simply, the Novikov consistency principle asserts that if an event exists that would give rise to a paradox, or to any "change" to the past whatsoever, then the probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

of that event is zero. In short, it says that it's impossible to create time paradoxes.

## History of the principle

Physicists have long been aware that there are solutions to the theory of general relativity which contain closed timelike curve
Closed timelike curve
In mathematical physics, a closed timelike curve is a worldline in a Lorentzian manifold, of a material particle in spacetime that is "closed," returning to its starting point...

s, or CTCs—see for example the Gödel metric
Gödel metric
The Gödel metric is an exact solution of the Einstein field equations in which the stress-energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second associated with a nonzero cosmological constant...

. Novikov discussed the possibility of CTCs in books written in 1975 and 1983, offering the opinion that only self-consistent trips back in time would be permitted. In a 1990 paper by Novikov and several others, Cauchy problem in spacetimes with closed timelike curves, the authors state:
The only type of causality violation that the authors would find unacceptable is that embodied in the science-fiction concept of going backward in time and killing one's younger self ("changing the past"). Some years ago one of us (Novikov10) briefly considered the possibility that CTCs might exist and argued that they cannot entail this type of causality violation: Events on a CTC are already guaranteed to be self-consistent, Novikov argued; they influence each other around a closed curve in a self-adjusted, cyclical, self-consistent way. The other authors recently have arrived at the same viewpoint.

We shall embody this viewpoint in a principle of self-consistency, which states that the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent. This principle allows one to build a local solution to the equations of physics only if that local solution can be extended to a part of a (not necessarily unique) global solution, which is well defined throughout the nonsingular regions of the spacetime.

Among the coauthors of this 1990 paper were Kip Thorne
Kip Thorne
Kip Stephen Thorne is an American theoretical physicist, known for his prolific contributions in gravitation physics and astrophysics and for having trained a generation of scientists...

, Michael Morris
Michael Morris
Michael Morris may refer to:*Michael Morris, 1st Baron Killanin , Irish lawyer and political figure, became the first Lord Killanin in 1900....

, and Ulvi Yurtsever, who in 1988 had stirred up renewed interest in the subject of time travel in general relativity with their paper Wormholes, Time Machines, and the Weak Energy Condition, which showed that a new general relativity solution known as a traversable wormhole could lead to closed timelike curves, and unlike previous CTC-containing solutions it did not require unrealistic conditions for the universe as a whole. After discussions with another coauthor of the 1990 paper, John Friedman, they convinced themselves that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent through the wormhole.

In response, another physicist named Joseph Polchinski
Joseph Polchinski
Joseph Polchinski is a physicist working on string theory. He graduated from Canyon del Oro High School in Tucson, Arizona in 1971, obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley in 1980 under the supervision of Stanley Mandelstam...

sent them a letter in which he argued that one could avoid questions of free will by considering a potentially paradoxical situation involving a billiard ball
Billiard ball
A billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played...

sent through a wormhole which sends it back in time. In this scenario, the ball is fired into a wormhole
Wormhole
In physics, a wormhole is a hypothetical topological feature of spacetime that would be, fundamentally, a "shortcut" through spacetime. For a simple visual explanation of a wormhole, consider spacetime visualized as a two-dimensional surface. If this surface is folded along a third dimension, it...

at an angle such that, if it continues along that path, it will exit the wormhole in the past at just the right angle to collide with its earlier self, thereby knocking it off course and preventing it from entering the wormhole in the first place. Thorne deemed this problem "Polchinski's paradox".

After considering the problem, two students at Caltech (where Thorne taught), Fernando Echeverria and Gunnar Klinkhammer, were able to find a solution beginning with the original billiard ball trajectory proposed by Polchinski which managed to avoid any inconsistencies. In this situation, the billiard ball emerges from the future at a different angle than the one used to generate the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole, a blow which changes its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self this glancing blow. Echeverria and Klinkhammer actually found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each case. Later analysis by Thorne and Robert Forward
Robert Forward
Robert Lull Forward — known as Robert L. Forward — was an American physicist and science fiction writer...

showed that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.

Echeverria, Klinkhammer and Thorne published a paper discussing these results in 1991; in addition, they reported that they had tried to see if they could find any initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so. Thus it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven. This only applies to initial conditions which are outside of the chronology-violating region of spacetime, which is bounded by a Cauchy horizon
Cauchy horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem...

. This could mean that the Novikov self-consistency principle does not actually place any constraints on systems outside of the region of spacetime where time travel is possible, only inside it.

Even if self-consistent extensions can be found for arbitrary initial conditions outside the Cauchy Horizon, the finding that there can be multiple distinct self-consistent extensions for the same initial condition—indeed, Echeverria et al. found an infinite number of consistent extensions for every initial trajectory they analyzed—can be seen as problematic, since classically there seems to be no way to decide which extension the laws of physics will choose. To get around this difficulty, Thorne and Klinkhammer analyzed the billiard ball scenario using quantum mechanics, performing a quantum-mechanical sum over histories (path integral
Path integral formulation
The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...

) using only the consistent extensions, and found that this resulted in a well-defined probability for each consistent extension. The authors of Cauchy problem in spacetimes with closed timelike curves write:
The simplest way to impose the principle of self-consistency in quantum mechanics (in a classical space-time) is by a sum-over-histories formulation in which one includes all those, and only those, histories that are self-consistent. It turns out that,14 at least formally (modulo such issues as the convergence of the sum), for every choice of the billiard ball's initial, nonrelativistic wave function before the Cauchy horizon
Cauchy horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem...

, such a sum over histories produces unique, self-consistent probabilities for the outcomes of all sets of subsequent measurements. ... We suspect, more generally, that for any quantum system in a classical wormhole spacetime with a stable Cauchy horizon, the sum over all self-consistent histories will give unique, self-consistent probabilities for the outcomes of all sets of measurements that one might choose to make.

## Potential implications for paradoxes

The Novikov Principle is able to circumvent most commonly-cited paradoxes which are often alleged to exist should time travel be possible (and are often claimed to make it impossible). A common example of the principle in action is the idea of preventing disasters from happening in the past and the potential paradoxes this may cause (notably the idea that preventing the disaster would remove the motive for the traveller to go back and prevent it and so on). The Novikov self-consistency principle states that a time traveller would not be able to do so. An example is the Titanic sinking; even if there were time travellers on the Titanic, they obviously failed to stop the ship from sinking. The Novikov Principle does not allow a time traveller to change the past in any way at all, but it does allow them to affect past events in a way that produces no inconsistencies—for example, a time traveller could rescue people from a disaster, and replace them with realistic corpses if history recorded that bodies of victims had been found. Provided that the rescuees were not known to have survived prior to the date that the time traveler stepped into the time machine (perhaps because they were taken forward in time to a later date, or because their identities were hidden), the time traveler's motivation to travel back in time and save them will be preserved. In this example, it must always have been true that the people were rescued by a time traveller and replaced with realistic corpses, and there would be no "original" history where they were actually killed, since the notion of "changing" the past is deemed impossible by the self-consistency principle.

## Assumptions of the Novikov self-consistency principle

The Novikov consistency principle assumes certain conditions about what sort of time travel is possible. Specifically, it assumes either that there is only one timeline
Chronology
Chronology is the science of arranging events in their order of occurrence in time, such as the use of a timeline or sequence of events. It is also "the determination of the actual temporal sequence of past events".Chronology is part of periodization...

, or that any alternative timelines (such as those postulated by the many-worlds interpretation
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...

of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

) are not accessible.

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a tautology
Tautology (logic)
In logic, a tautology is a formula which is true in every possible interpretation. Philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921; it had been used earlier to refer to rhetorical tautologies, and continues to be used in that alternate sense...

, a self-evident truth that cannot possibly be false, because if you make the assumption that it is false this would lead to a logical paradox
Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

. However, the Novikov self-consistency principle is intended to go beyond just the statement that history must be consistent, making the additional nontrivial assumption that the universe obeys the same local laws of physics in situations involving time travel that it does in regions of spacetime that lack closed timelike curves. This is made clear in the above-mentioned Cauchy problem in spacetimes with closed timelike curves, where the authors write:
That the principle of self-consistency is not totally tautological becomes clear when one considers the following alternative: The laws of physics might permit CTC's; and when CTC's occur, they might trigger new kinds of local physics which we have not previously met. ... The principle of self-consistency is intended to rule out such behavior. It insists that local physics is governed by the same types of physical laws as we deal with in the absence of CTC's: the laws that entail self-consistent single valuedness for the fields. In essence, the principle of self-consistency is a principle of no new physics. If one is inclined from the outset to ignore or discount the possibility of new physics, then one will regard self-consistency as a trivial principle.

## Time loop logic

Time loop logic, coined by the roboticist
Roboticist
A roboticist designs, builds, programs, and experiments with robots. Since robotics is a highly interdisciplinary field, roboticists often have backgrounds in a number of disciplines including computer science, mechanical engineering, electrical engineering, and computer engineering...

and futurist Hans Moravec
Hans Moravec
Hans Moravec is an adjunct faculty member at the Robotics Institute of Carnegie Mellon University. He is known for his work on robotics, artificial intelligence, and writings on the impact of technology. Moravec also is a futurist with many of his publications and predictions focusing on...

, is the name of a hypothetical system of computation that exploits the Novikov self-consistency principle to compute answers much faster than possible with the standard model of computational complexity
Computational complexity theory
Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other...

using Turing machine
Turing machine
A Turing machine is a theoretical device that manipulates symbols on a strip of tape according to a table of rules. Despite its simplicity, a Turing machine can be adapted to simulate the logic of any computer algorithm, and is particularly useful in explaining the functions of a CPU inside a...

s. In this system, a computer sends a result of a computation backwards through time
Time travel
Time travel is the concept of moving between different points in time in a manner analogous to moving between different points in space. Time travel could hypothetically involve moving backward in time to a moment earlier than the starting point, or forward to the future of that point without the...

and relies upon the self-consistency principle to force the sent result to be correct.

A program exploiting time loop logic can be quite simple in outline. For example, to compute one prime factor of the natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...

N in polynomial time (no polynomial time factorization algorithm is known in traditional complexity theory; see integer factorization):
1. If N is 0 or 1, abort.
2. Allocate a communication channel c.
3. Receive one prime factor, F, of N from the future on channel c.
4. Test that FN, that F divides
Division (digital)
Several algorithms exist to perform division in digital designs. These algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring,...

N (time complexity O
Big O notation
In mathematics, big O notation is used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. It is a member of a larger family of notations that is called Landau notation, Bachmann-Landau notation, or...

(log N)), and that F is prime (polynomial time; see AKS primality test
AKS primality test
The AKS primality test is a deterministic primality-proving algorithm created and published by three Indian Institute of Technology Kanpur computer scientists, Manindra Agrawal, Neeraj Kayal, and Nitin Saxena, on August 6, 2002, in a paper titled "PRIMES is in P"...

).
1. If so, send F backwards in time on channel c.
2. If not, send F + 1 backwards in time on channel c. Note that this results in a paradox, as the number received in step 3 above is not the same as that sent in this step.

The self-consistency principle guarantees that the sequence of events generating the paradox in the nested conditional has zero probability. Note that if N is itself prime, i.e., there is no such prime FN, then some event will prevent the execution of step 3 that receives the value F from the future. Assuming the machine executing the program itself continues to function, it can detect this failure and abort.

Physicist David Deutsch
David Deutsch
David Elieser Deutsch, FRS is an Israeli-British physicist at the University of Oxford. He is a non-stipendiary Visiting Professor in the Department of Atomic and Laser Physics at the Centre for Quantum Computation in the Clarendon Laboratory of the University of Oxford...

showed in 1991 that this model of computation could solve NP problems in polynomial time, and Scott Aaronson
Scott Aaronson
Scott Joel Aaronson is a theoretical computer scientist and faculty member in the Electrical Engineering and Computer Science department at the Massachusetts Institute of Technology.-Education:...

later extended this result to show that the model could also be used to solve PSPACE
PSPACE
In computational complexity theory, PSPACE is the set of all decision problems which can be solved by a Turing machine using a polynomial amount of space.- Formal definition :...

problems in polynomial time.

## Pre-Novikov examples

Claims, arguments, or philosophical principles logically equivalent to the Novikov self-consistency principle have been published before Novikov's own publication. This makes the principle an example of Stigler's law of eponymy
Stigler's law of eponymy
Stigler's law of eponymy is a process proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication "Stigler’s law of eponymy". In its simplest and strongest form it says: "No scientific discovery is named after its original discoverer." Stigler named the...

.
• Something resembling the idea can be found in Greek mythology
Greek mythology
Greek mythology is the body of myths and legends belonging to the ancient Greeks, concerning their gods and heroes, the nature of the world, and the origins and significance of their own cult and ritual practices. They were a part of religion in ancient Greece...

, in the story of Cassandra
Cassandra
In Greek mythology, Cassandra was the daughter of King Priam and Queen Hecuba of Troy. Her beauty caused Apollo to grant her the gift of prophecy...

. Cassandra was given the gift of prophecy
Prophecy
Prophecy is a process in which one or more messages that have been communicated to a prophet are then communicated to others. Such messages typically involve divine inspiration, interpretation, or revelation of conditioned events to come as well as testimonies or repeated revelations that the...

by Apollo
Apollo
Apollo is one of the most important and complex of the Olympian deities in Greek and Roman mythology...

but also cursed such that no one would believe her predictions. This left her unable to avert any of the disastrous events she foresaw. The metaphor has been adopted in modern times into the notion of a "Cassandra Complex
Cassandra complex
The Cassandra Complex is a psychological phenomenon in which an individual's accurate prediction of a crisis is ignored or dismissed.Cassandra Complex may also refer to:* The Cassandra Complex , an electronic music band...

".
• H. P. Lovecraft
H. P. Lovecraft
Howard Phillips Lovecraft --often credited as H.P. Lovecraft — was an American author of horror, fantasy and science fiction, especially the subgenre known as weird fiction....

discussed this idea of time travel in a 1930 letter to Clark Ashton Smith
Clark Ashton Smith
Clark Ashton Smith was a self-educated American poet, sculptor, painter and author of fantasy, horror and science fiction short stories. He achieved early local recognition, largely through the enthusiasm of George Sterling, for traditional verse in the vein of Swinburne...

, where he wrote:
• In "Via the Time Accelerator" by F. J. Bridge (a pseudonym of Francis J. Brueckel), from the January 1931 issue of Amazing Stories
Amazing Stories
Amazing Stories was an American science fiction magazine launched in April 1926 by Hugo Gernsback's Experimenter Publishing. It was the first magazine devoted solely to science fiction...

, a time traveler in 1930 wonders if he should travel to the future, and then he sees himself returning from the future, which reassures him about the success of his voyage. Later, in a situation where he finds himself in danger, he tells himself "I would escape ... It was so decreed. Had I not, with my own eyes, seen myself appear out of the fourth dimension back there in the Twentieth Century, and glide down to my landing-field? Surely, then, I was destined to return to my own age safe and sound." The time traveler eventually arrives in a ruined city in A.D. 1,001,930, where he is met by an old man who claims to be the Last Man still alive, and who says he knew the time traveler was coming because he read in an ancient history book that he himself (the Last Man) had arrived from the future in A.D. 502,101 in the same time machine the time traveler was using. When the time traveler goes to sleep, the Last Man does indeed take the time machine back to A.D. 502,101, leaving the time traveler stranded. The time traveler then wanders around the ruined city until he finds a museum, where preserved in a glass case is his time machine, which had been put there after it had appeared in A.D. 502,101. The time traveler adds some oil to its engine, and uses it to travel back to 1930, arriving there just as he had seen himself do.
• Robert A. Heinlein
Robert A. Heinlein
Robert Anson Heinlein was an American science fiction writer. Often called the "dean of science fiction writers", he was one of the most influential and controversial authors of the genre. He set a standard for science and engineering plausibility and helped to raise the genre's standards of...

's By His Bootstraps
By His Bootstraps
"By His Bootstraps" is a science fiction short story by Robert A. Heinlein that plays with some of the inherent paradoxes that would be caused by time travel. It was originally published in the October 1941 issue of Astounding Science Fiction under the pen name Anson MacDonald...

(1941) features a plot in which a man interacts with different older versions of himself that travel by way of a "Time Gate", with all the interactions revisited later in the story from the perspective of the now-older man, everything being tied together in a completely self-consistent way. Heinlein later revisited a similar theme in his 1958 story —All You Zombies—, in which the main character's interactions with sex-changed versions of himself/herself at various points in his/her life result in a bizarre version of the ontological paradox in which the character becomes his/her own mother and father.
• In Harry Harrison
Harry Harrison
Harry Harrison is an American science fiction author best known for his character the Stainless Steel Rat and the novel Make Room! Make Room! , the basis for the film Soylent Green...

's The Technicolor Time Machine (1967), main characters go back in time to shoot a movie about founding a Viking colony in North America, only to discover to their surprise that the colony they founded turned out to be written into the history as the original Viking colony in North America—and some of them are even featured in Norse sagas.
• In Michael Moorcock
Michael Moorcock
Michael John Moorcock is an English writer, primarily of science fiction and fantasy, who has also published a number of literary novels....

's Behold the Man
Behold the Man
Behold the Man is a science fiction novel by Michael Moorcock. It originally appeared as a novella in a 1966 issue of New Worlds; later, Moorcock produced an expanded version which was first published in 1969 by Allison & Busby.. The title derives from the Gospel of John, Chapter 19, Verse 5:...

(1969), a time traveler goes back to 28 A.D. in hopes of meeting Jesus, only to end up playing the role of Jesus himself, just as described in the Bible.
• Science fiction
Science fiction
Science fiction is a genre of fiction dealing with imaginary but more or less plausible content such as future settings, futuristic science and technology, space travel, aliens, and paranormal abilities...

author Larry Niven
Larry Niven
Laurence van Cott Niven / ˈlæri ˈnɪvən/ is an American science fiction author. His best-known work is Ringworld , which received Hugo, Locus, Ditmar, and Nebula awards. His work is primarily hard science fiction, using big science concepts and theoretical physics...

called this idea the "law of conservation of history" in an essay titled "The Theory and Practice of Time Travel," which was published in his book "All the Myriad Ways" in 1971.

## Fictional usage

• The movie 12 Monkeys appears to obey Novikov's principle. All attempts by the main character James Cole (played by Bruce Willis
Bruce Willis
Walter Bruce Willis , better known as Bruce Willis, is an American actor, producer, and musician. His career began in television in the 1980s and has continued both in television and film since, including comedic, dramatic, and action roles...

) to change the past prove unsuccessful, and in the end his death is witnessed by his own childhood self in exactly the way he had remembered earlier in the movie. Additionally, the scientists in charge of the time travel mission have no interest in attempting to avert the release of the deadly virus which killed most of the human population, and are instead only trying to obtain a pure strain of the original virus, in hopes that it will help them to cure the disease in their own time.

• Something close to this principle is used in season 5 of the TV series Lost
Lost (TV series)
Lost is an American television series that originally aired on ABC from September 22, 2004 to May 23, 2010, consisting of six seasons. Lost is a drama series that follows the survivors of the crash of a commercial passenger jet flying between Sydney and Los Angeles, on a mysterious tropical island...

. The show's version is often referred to by characters and fans as "Whatever Happened, Happened" (also the title of an episode). It is supported by various implications in-show, chief of which is the fact that, in travelling to the past to prevent the 'future' crashing of their plane, the survivors actually set in motion the chain of events that ultimately caused it. However, the episode "Flashes Before Your Eyes
Flashes Before Your Eyes
"Flashes Before Your Eyes" is the 8th episode of the third season of the American drama television series Lost, and the show's 57th episode overall. The episode was written by the series co-creator, show runner and executive producer Damon Lindelof and supervising producer Drew Goddard, and...

" suggests that minor changes are possible, unlike the totally fixed timeline postulated by Novikov's principle: in this episode Desmond's consciousness time travels back to a point in his past, where he ends up in a bar, where he remembers (from his previous experience of this time) a man named Jimmy Lennon entering and attacking the bartender; in his attempt to warn the bartender, he himself gets attacked instead. Additionally, when Desmond meets a mysterious woman with apparent knowledge of the future (later revealed as Eloise Hawking), she points out a man with red shoes, who moments later is killed by falling scaffolding; when Desmond asks why she didn't try to save the man, she says that "it wouldn't matter. Had I warned him about the scaffolding, tomorrow he'd be hit by a taxi. If I warned him about the taxi, he'd fall in the shower and break his neck. The universe, unfortunately, has a way of course correcting. That man was supposed to die." Again, this suggests that although major events (like the man's death) are unchangeable, minor ones (like the precise cause of his death) can be changed, in violation of Novikov's principle.

• The first-season 2002 TV series Twilight Zone
Twilight zone
-Television series and spinoffs:*The Twilight Zone, the anthology television series and its franchise:**The Twilight Zone , the 1959–1964 original television series***Twilight Zone: The Movie, a 1983 film based on the original series...

episode "Cradle of Darkness" featured a woman who traveled from the modern day back in time to kill the infant Adolf Hitler
Adolf Hitler was an Austrian-born German politician and the leader of the National Socialist German Workers Party , commonly referred to as the Nazi Party). He was Chancellor of Germany from 1933 to 1945, and head of state from 1934 to 1945...

to prevent his future atrocities. The woman, posing as the family nurse, disposes of the Hitlers' baby and replaces him with a beggar woman's child so as not to arouse suspicion. This replacement infant is the child who then grows up to become the infamous Adolf Hitler.

• Each episode of the Irwin Allen
Irwin Allen
Irwin Allen was a television and film director and producer nicknamed "The Master of Disaster" for his work in the disaster film genre. He was also notable for creating a number of television series.- Biography :...

series The Time Tunnel
The Time Tunnel
The Time Tunnel is a 1966–1967 U.S. color science fiction TV series. The show was created and produced by Irwin Allen, his third science fiction television series. The show's main theme was Time Travel Adventure. The Time Tunnel was released by 20th Century Fox and broadcast on ABC. The show ran...

(less the few set in the future) depicted the time-traveling duo arriving at the scene of an historic tragedy, days or hours before the event, and invariably failing in their attempts to prevent it. This was also true in the 1976 revival pilot, and the similar 1982–83 series, Voyagers!
Voyagers!
Voyagers! is an American science fiction time travel-based television series that aired on NBC during the 1982–1983 season. The series stars Jon-Erik Hexum and Meeno Peluce.-Plot:...

.

• In the Star Trek: The Next Generation
Star Trek: The Next Generation
Star Trek: The Next Generation is an American science fiction television series created by Gene Roddenberry as part of the Star Trek franchise. Roddenberry, Rick Berman, and Michael Piller served as executive producers at different times throughout the production...

episode "Time's Arrow", a 500-year old copy of the android Data's head is unearthed in an excavation near San Francisco on Earth. In the sequence of events that ensues upon investigation, Data is sent back in time to 19th century San Francisco. Later in this time frame, the shock of another temporal event causes his head to be split from his body and remain in the 19th century, while the rest of his body travels forward to the original point in time, when it is re-attached to the 500 year old head. Thus Data remains, as does the causality of time. However, the series does not consistently obey the Novikov principle in episodes featuring time travel, as episodes like Time Squared and Yesterday's Enterprise
Yesterday's Enterprise
"Yesterday's Enterprise" is the fifteenth episode of the third season of the science fiction television show Star Trek: The Next Generation. The episode first aired in syndication the week of February 19, 1990...

show history being changed as a result of time travel.

• The video game series Legacy of Kain
Legacy of Kain
Legacy of Kain is a series of action-adventure video games developed initially by Silicon Knights in association with Crystal Dynamics. After a legal battle, Crystal Dynamics continued the series without Silicon Knights and Eidos Interactive became the publisher...

uses the same principle, although one can possibly break away from the timeline during a temporal distortion, that is, whenever two identical bodies meet in time and space.

• While predating Novikov's thesis, the film Timerider: The Adventure of Lyle Swann presents a similar predestination paradox
A predestination paradox is a paradox of time travel that is often used as a convention in science fiction. It exists when a time traveller is caught in a loop of events that "predestines" or "predates" them to travel back in time...

, wherein the title character becomes his own great-great-grandfather thus causing his own existence and time-travel. The same film, however, contains an ontological paradox in that Swann's heirloom necklace which his great-great-grandmother took from his great-great-grandfather (i.e., himself) is never created and is perpetually in the time-loop.

• The events of the first Terminator film appear to respect the self-consistency principle. In the film, a sentient computer called Skynet
Skynet (Terminator)
Skynet is the main antagonist in the Terminator franchise—an artificially intelligent system which became self-aware and revolted against its creators...

attempts to exterminate the human race, but faces difficulty in dealing with a human resistance effort led by a man called John Connor
John Connor
John Connor is a character appearing in the American science fiction Terminator franchise and he serves as the series main protagonist. Created by writer and director James Cameron, the character is first referred to in the 1984 film The Terminator and first appears portrayed by teenage actor...

. In a last-ditch attempt to win the war, Skynet sends a cybernetic assassin called a Terminator back through time to murder Connor's mother Sarah before he is born, thereby preventing Connor's existence and the success of his future rebellion. Connor sends a soldier named Kyle Reese
Kyle Reese
Kyle Reese is the primary character in the first Terminator film, the posthumous father of John Connor, and the love of Sarah Connor. He is played by Michael Biehn in the first Terminator films, Jonathan Jackson in the television series, and played as a teenager by Anton Yelchin in Terminator...

back to the same time to protect Sarah. Rather than altering history, these time travellers end up creating the timeline as it was meant to be. While on the run from the Terminator, Kyle and Sarah have sex and conceive the child who will become John Connor. Likewise, the Terminator is destroyed in a factory and its remains are claimed by Cyberdyne Systems, the factory's owner. This company uses the Terminator's remains as the basis for a research project that will ultimately result in the creation of the malevolent computer Skynet. (It should be noted, however, that only the first film respects this principle. In the sequels, the main characters are able to significantly alter the timeline. Also, even in the first film Skynet's plan would not really make sense unless it believed that history could be changed, and when Sarah Connor asks Kyle Reese if he's saying the Terminator is from the future, he responds 'One possible future. From your point of view. I don't know tech stuff.')

• In The Final Countdown, the aircraft carrier USS Nimitz, based at Pearl Harbor
Pearl Harbor
Pearl Harbor, known to Hawaiians as Puuloa, is a lagoon harbor on the island of Oahu, Hawaii, west of Honolulu. Much of the harbor and surrounding lands is a United States Navy deep-water naval base. It is also the headquarters of the U.S. Pacific Fleet...

, is sent back in time from 1980 to December 6, 1941. Aboard is a civilian consultant from one of the companies which contributed to the design of the ship. One of the ship's officers, a historian, is lost and presumed dead while transporting a rescued senator and his secretary to a small island for safety in advance of the coming battle; according to history, the pair and his chief of staff were believed to have been killed by the Japanese. The senator dies trying to escape the island. Just as the ship's complement prepare to go into battle the next morning to stop the Japanese attack, the ship returns to 1980 – their minor involvement having had no net effect on history. Back in port, the consultant meets his reclusive boss who helped design the ship – he and his wife are the pilot and the senator's secretary who assumed false names during the war.

• Throughout the plot of Harry Potter and the Prisoner of Azkaban
Harry Potter and the Prisoner of Azkaban
Harry Potter and the Prisoner of Azkaban is the third novel in the Harry Potter series written by J. K. Rowling. The book was published on 8 July 1999. The novel won the 1999 Whitbread Book Award, the Bram Stoker Award, the 2000 Locus Award for Best Fantasy Novel, and was short-listed for other...

, two unexplained events that greatly affect the plot are later seen to be caused by the protagonists using a time-turner, a small hourglass allowing its user to travel back in time. Hermione Granger
Hermione Granger
Hermione Jean Granger is a fictional character and one of the three protagonists in J. K. Rowling's Harry Potter series. She initially appears in the first novel, Harry Potter and the Philosopher's Stone, as a new student on her way to Hogwarts...

uses the time-turner to go back in time and do a different lesson than the current Hermione is doing and thus appears to be in multiple places at once. In the same book, Harry Potter saved himself from a Dementor attack, realizing at the last moment that his savior was not his father as he had initially thought, but was in fact, himself.

• Novikov is alluded to by name in the comic Nth Man: The Ultimate Ninja
Nth Man: the Ultimate Ninja
Nth Man: The Ultimate Ninja is a comic book about an American ninja set in an unspecified near future where World War III has started. It was written by Larry Hama between 1989 and 1990, based largely on his success writing the G.I. Joe: A Real American Hero comic, which he wrote concurrently with...

. One of the characters is Colonel Vavara Novikova (Russian surnames having masculine and feminine forms), who accompanies the protagonist and antagonist back in time to their birth so that they can be delivered to the orphanage where their story begins.

• In the film The Time Traveler's Wife
The Time Traveler's Wife (film)
The Time Traveler's Wife is a 2009 romantic film based on Audrey Niffenegger's 2003 novel of the same name. Directed by Robert Schwentke, the film stars Eric Bana as Henry DeTamble, a Chicago librarian with a genetic disorder that causes him to time travel randomly as he tries to build a romantic...

(2009), the main character's mother is killed in a car crash while he is young. He escapes injury by time travelling out of the car. Although he frequently revisits the scene and time of the accident throughout his life, he can never alter the outcome as to do so would remove his desire to be there.

• In Season 4 episode 2 of the TV series Eureka
Eureka (TV series)
Eureka is an American science fiction television series that premiered on Syfy on July 18, 2006. Since then four seasons have aired, and a fifth is currently being filmed. The second half of season 4 began on SyFy on July 11, 2011 and ended on September 19, 2011...

The Novikov Self Consistency Principle is explicitly mentioned to justify the many similarities between the "alternative timeline" experienced by the protagonists and their "original timeline". In the brief discussion the character Dr. Henry Deacon (Joe Morton
Joe Morton
Joseph Thomas "Joe" Morton, Jr. is an American stage, television, and film actor.-Early life:Morton was born in The Bronx, a borough of New York City, New York. He is the son of Evelyn, a secretary, and Joseph Thomas Morton, Sr., a U.S. army intelligence officer. Because of his father's...

), using the analogy of ripples in a pond, explains that the further one travels from the point where the timeline is changed the less noticeable are the effects of that change. This is not however an accurate depiction of the principle, since the principle actually forbids any changes to the timeline.

• In The Time Machine (2002)
The Time Machine (2002 film)
The Time Machine is a 2002 American science fiction film loosely adapted from the 1895 novel of the same name by H. G. Wells, and the 1960 film screenplay by David Duncan...

, the protagonist invented a time machine in order to go back and save his sweetheart, only to find that he couldn't do it, as that would remove his reason to invent the time machine. Again, this is not exactly the principle, as he changes the method of her death.

• Principle of non-contradiction
• Causality in physics
Causality (physics)
Causality is the relationship between causes and effects. It is considered to be fundamental to all natural science, especially physics. Causality is also a topic studied from the perspectives of philosophy and statistics....

Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

es
• Probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

• Probability distribution
Probability distribution
In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

A predestination paradox is a paradox of time travel that is often used as a convention in science fiction. It exists when a time traveller is caught in a loop of events that "predestines" or "predates" them to travel back in time...

• Many-worlds interpretation
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...

• Self-fulfilling prophecy
Self-fulfilling prophecy
A self-fulfilling prophecy is a prediction that directly or indirectly causes itself to become true, by the very terms of the prophecy itself, due to positive feedback between belief and behavior. Although examples of such prophecies can be found in literature as far back as ancient Greece and...

• Blinovitch Limitation Effect
Blinovitch Limitation Effect
The Blinovitch Limitation Effect is a fictional principle of time travel physics in the universe of the long-running British science fiction television series Doctor Who....

(fictional)
• The chicken or the egg
The chicken or the egg
The Chicken or the egg causality dilemma is commonly stated as "which came first, the chicken or the egg?" To ancient philosophers, the question about the first chicken or egg also evoked the questions of how life and the universe in general began....

• Cassandra (metaphor)
Cassandra (metaphor)
The Cassandra metaphor , is a term applied in situations in which valid warnings or concerns are dismissed or disbelieved....