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The Novikov self-consistency principle, also known as the Novikov self-consistency conjecture, is a principle

Principle

A principle is either:* a descriptive comprehensive and fundamental law, doctrine, or assumption,* a normative rule or code of conduct, or* a law or fact of nature underlying the working of an artificial device.-Principle as cause:...

developed by Dr. Igor 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 in astrophysics in 1965 and Doctoral Degree in...

in the mid-1980s to solve the problem of paradox

Paradox

A paradox is a statement or group of statements that leads to a contradiction or a situation which defies intuition. The term is also used for an apparent contradiction that actually expresses a non-dual truth...

es in time travel

Time travel

Time travel is the concept of moving between different moments in time in a manner analogous to moving between different points in space, either sending objects backwards in time to a moment before the present, or sending objects forward from the present to the future without the need to...

, 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. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a...

(solutions containing what are known as closed timelike curve

Closed timelike curve

In a Lorentzian manifold, a closed timelike curve is a worldline 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 a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy...

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 curves, 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 written by a number of authors including Novikov, Cauchy problem in spacetimes with closed timelike curves, the authors write:

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, 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 is fundamentally a 'shortcut' through space and time. Spacetime can be viewed as a 2D surface that, when 'folded' over, allows the formation of a wormhole bridge. A wormhole has at least two mouths that are connected...

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. It should be noted, though, that 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

RMS Titanic

The RMS Titanic was an Olympic-class passenger liner owned by British shipping company White Star Line and built at the Harland and Wolff shipyard in Belfast, United Kingdom...

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, 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 seconds before it occurs. Providing that the rescuees do not re-emerge until after the time traveller first journeyed into the past, his/her motivation to create the time machine and travel into the past will be preserved. (See Millennium.) In this example, it must always have been true that the people were rescued by a time traveller and replaced with realistic corpses, there was no "original" history where they were actually killed, since the notion of "changing" the past is ruled out completely 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 a chronicle or arrangement of events in their order of occurrence in time, such as a timeline. 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.It is also known as MWI, the relative state formulation, theory of the universal wavefunction, parallel universes, many-universes interpretation or just many worlds.Many-worlds asserts the objective reality of the...

of quantum mechanics

Quantum mechanics

Quantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...

) 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 propositional logic, a tautology is a propositional formula that is true under any possible valuation of its propositional variables. For example, the propositional formula is a tautology, because the statement is true for any valuation of A...

, 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

Paradox

. 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 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 computer science that focuses on classifying computational problems according to their inherent difficulty. In this context, a computational problem is understood to be a task that is in principle amenable to being solved...

using Turing machine

Turing machine

A Turing machine is a theoretical device that manipulates symbols contained on a strip of tape. 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 of a computer. The Turing...

s. In this system, a computer sends a result of a computation backwards through time

Time travel

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, there are two conventions for the set of natural numbers: it is either the set of positive integers {, , , ...} according to the traditional definition or the set of non-negative integers {, 1, 2, ...} according to...

N in polynomial time (no polynomial time factorization algorithm is known in traditional complexity theory; see integer factorization):

If N is 0 or 1, abort.
Allocate a communication channel c.
Receive one prime factor, F, of N from the future on channel c.
Test that F ≠ N, 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, computer science, and related fields, big O notation describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions...

(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.The authors received many accolades,...

).
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 F ≠ N, 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 a 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, Clarendon Laboratory...

showed in 1991 that this model of computation could not only solve NP problems in a reasonable time, but also the larger class of 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.

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."-Derivation:Historical...

Science fiction
Science fiction
Science fiction is a genre of fiction. It differs from fantasy in that, within the context of the story, its imaginary elements are largely possible within scientifically-established or scientifically-postulated laws of nature...

author Larry Niven
Larry Niven
Laurence van Cott Niven is a US science fiction author. Perhaps 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. It also often includes elements of detective...

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.
A very early example 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 prophesy by Apollo
Apollo
In Greek and Roman mythology, Apollo , is one of the most important and many-sided of the Olympian deities...

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.The Cassandra Complex may also refer to:* The Cassandra Complex , an electronic music band...

."

Fictional usage

This kind of principle is used in the fifth season of the TV series, Lost
Lost (TV series)
Lost is an American serial drama television series. It follows the lives of plane crash survivors on a mysterious tropical island, after a commercial passenger jet flying between Sydney, Australia, and Los Angeles, United States, crashes somewhere in the South Pacific...

. It is often referred to as 'Whatever Happened, Happened.'

External links

Notion of the Past & Can We Change It? - speech by Novikov
From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture, which also addresses the Novikov self-consistency principle
Einstein Physics prevent paradoxical time travel
Time Travel and Modern Physics