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{{Short description|Assertion that timeTime-travel paradoxes are impossible, as paradox-causing events cannot occur}}

The '''Novikov self-consistency principle''', also known as the '''Novikov self-consistency conjecture''' and [[Larry Niven]]'s '''law of conservation of history''', is a [[principle]] developed by Russian physicist [[Igor Dmitriyevich Novikov]] in the mid-1980s. Novikov intended it to solve the problem of [[Temporal paradox]]es|paradoxes in [[time travel]], which is theoretically permitted in certain solutions of [[general relativity]] that contain what are known as [[closed timelike curve]]s. The principle asserts that if an event exists that would cause a paradox or any "change" to the past whatsoever, then the [[probability]] of that event is zero. It would thus be impossible to create [[time paradox]]es.

==History==

Physicists have long known that some solutions to the theory of general relativity contain [[closed timelike curve]]s&mdash;for example the [[Gödel metric]]. Novikov discussed the possibility of closed timelike curves (CTCs) in books he wrote in 1975 and 1983,<ref>See note 10 on p. 42 of Friedman et al., "Cauchy problem in space-times with closed timelike curves"</ref> offering the opinion that only self-consistent trips back in time would be permitted.<ref>On p. 169 of Novikov's ''Evolution of the Universe'' (1983), which was a translation of his Russian book '' Evolyutsiya Vselennoĭ'' (1979), Novikov's comment on the issue is rendered by translator M. M. Basko as "The close of time curves does not necessarily imply a violation of causality, since the events along such a closed line may be all 'self-adjusted'—they all affect one another through the closed cycle and follow one another in a self-consistent way."</ref> In a 1990 paper by Novikov and several others, "[[Cauchy problem]] in spacetimes with closed timelike curves",<ref name="friedman">{{cite journal | first=John | last=Friedman |author2=Michael Morris |author3=Igor Novikov |author4=Fernando Echeverria |author5=Gunnar Klinkhammer |author6=Kip Thorne |author7=Ulvi Yurtsever | url=http://authors.library.caltech.edu/3737/ | title=Cauchy problem in spacetimes with closed timelike curves | journal = Physical Review D | volume = 42 | year=1990 | issue=6 | doi=10.1103/PhysRevD.42.1915 | pages=19151915–1930 | bibcode=1990PhRvD..42.1915F | pmid=10013039| url-access=subscription }}</ref> the authors state:

{{quote|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 space-time.

}}

Among the co-authors of this 1990 paper were [[Kip Thorne]], [[Mike Morris (physicist)|Mike 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",<ref>{{cite journal | first=Kip | last=Thorne |author2=Michael Morris |author3=Ulvi Yurtsever | journal=[[Physical Review Letters]] | volume = 61 | issue=13| pages=1446–1449 | doi= 10.1103/PhysRevLett.61.1446 | title= Wormholes, Time Machines, and the Weak Energy Condition | year=1988 | url=http://authors.library.caltech.edu/9262/1/MORprl88.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://authors.library.caltech.edu/9262/1/MORprl88.pdf |archive-date=2022-10-09 |url-status=live | bibcode=1988PhRvL..61.1446M | pmid=10038800}}</ref> which showed that a new general relativity solution known as a [[Wormhole#Traversable wormholes|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 the lead author of the 1990 paper, John Friedman, they convinced themselves that time travel needn'tneed not lead to unresolvable paradoxes, regardless of the object sent [[Through the Wormhole|through the wormhole]].<ref name = "time warps">{{cite book| first= Kip S. | last= Thorne|title=Black Holes and Time Warps: Einstein's Outrageous Legacy|url=https://archive.org/details/blackholestimewa0000thor| url-access= registration | quote= Polchinski's paradox. |year=1994|publisher=W. W. Norton|isbn=978-0-393-31276-8|pages=[https://archive.org/details/blackholestimewa0000thor/page/510 510]–}}</ref>{{rp|509}}

[[File:Grandfather paradox billiard ball.svg|thumb|right|150pxupright=0.7|"Polchinski's paradox"]] [[File:Causal loop billiard ball.svg|thumb|right|150pxupright=0.7|Echeverria and Klinkhammer's resolution]]
By way of response, physicist [[Joseph Polchinski]] wrote them a letter arguing that one could avoid the issue of free will by employing a potentially paradoxical thought experiment involving a [[billiard ball]] sent back in time through a wormhole. In Polchinski's scenario, [[The Billiard Ball|the billiard ball]] is fired into the [[wormhole]] at an angle such that, if it continues along its path, it will exit in the past at just the right angle to collide with its earlier self, knocking it off track and preventing it from entering the wormhole in the first place. Thorne would refer to this scenario as "[[Polchinski's paradox]]" in 1994.<ref name = "timewarps">{{cite book | last = Thorne | first = Kip S. | author-link = Kip Thorne | title = [[Black Holes and Time Warps]] | publisher = W. W. Norton | year= 1994 | isbn = 0-393-31276-3}}</ref>{{rp|510–511}}

Upon considering the scenario, Fernando Echeverria and Gunnar Klinkhammer, two students at [[California Institute of Technology|Caltech]] (where Thorne taught), arrived at a solution to the problem, that managedlays toout avoidthe anysame elements as the solution Feynman and Wheeler<ref>{{cite journal | first1=John | last1=Wheeler | first2=Richard | last2=Feynman | title=Classical Electrodynamics in Terms of Direct Interparticle Action | journal = Reviews of Modern Physics | volume = 21 | year=1949 | issue=3 | pages=425–433| doi=10.1103/RevModPhys.21.425 | bibcode=1949RvMP...21..425W | doi-access=free }}</ref> termed the "glancing blow" solution, to evade inconsistencies arising from causality loops. In the revised scenario, the ball from the future emerges at a different angle than the one that generates the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole. This blow alters its trajectory by just the right degree, meaning it will travel back in time with the angle required to deliver its younger self the necessary 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 situation. Later analysis by Thorne and [[Robert Forward]] illustrated that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.<ref name = "timewarps" />{{rp|511–513}}

Echeverria, Klinkhammer, and Thorne published a paper discussing these results in 1991;<ref>{{cite journal | first=Fernando | last= Echeverria |author2=Gunnar Klinkhammer |author3=Kip Thorne | url=http://authors.library.caltech.edu/6469/ | title=Billiard balls in wormhole spacetimes with closed timelike curves: Classical theory | journal = Physical Review D | volume = 44 | year=1991 | issue=4 | doi= 10.1103/PhysRevD.44.1077 | pages=10771077–1099| pmid= 10013968 |bibcode = 1991PhRvD..44.1077E | url-access=subscription }}</ref> 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.<ref name = "earman">{{cite book | last = Earman | first = John | title = Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausalities in Relativistic Spacetimes | publisher = Oxford University Press |year= 1995 | isbn = 0-19-509591-X}}</ref>{{rp|184}} This only applies to initial conditions outside of the chronology-violating region of spacetime,<ref name = "earman" />{{rp|187}} which is bounded by a [[Cauchy horizon]].<ref>{{cite book | last = Nahin | first =Paul J. | title = Time Machines: Time Travel in Physics, Metaphysics, and Science Fiction | publisher =American Institute of Physics |year= 1999 | pages = 508 | isbn = 0-387-98571-9}}</ref> This could mean that the Novikov self-consistency principle does not actually place any constraints on systems outside of the region of space-time where time travel is possible, only inside it.

Even if self-consistent extensions can be found for arbitrary initial conditions outside the Cauchy Horizonhorizon, 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<ref name = "earman" />{{rp|184}}—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,<ref name = "timewarps" />{{rp|514–515}} performing a quantum-mechanical sum over histories ([[path integral formulation|path integral]]) 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:

{{quote|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, 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]], 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.}}

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The Novikov consistency principle assumes certain conditions about what sort of time travel is possible. Specifically, it assumes either that there is only one [[Chronology|timeline]], or that any alternative timelines (such as those postulated by the [[many-worlds interpretation]] of [[quantum mechanics]]) are not accessible.

Given these assumptions, the constraint that time travel must not lead to inconsistent outcomes could be seen merely as a [[Tautology (logic)|tautology]], a self-evident truth that can notcannot possibly be false. 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 space-time that lack closed timelike curves. This is clarified in the above-mentioned "Cauchy problem in spacetimes with closed timelike curves",<ref name="friedman" /> where the authors write:

{{quote|That the principle of self-consistency is not totally tautological becomes clear when one considers the following alternative: The laws of physics might permit CTCs; and when CTCs 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 CTCs: 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.}}

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===Quantum computation with a negative delay===

Physicist [[David Deutsch]] showed in 1991 that this model<!-- details required --> of computation could solve NP problems in [[Time complexity#Polynomial time|polynomial time]],<ref name="Deutsch1991">{{cite journal | first=David | last=Deutsch | url= http://journals.aps.org/prd/abstract/10.1103/PhysRevD.44.3197 | title= Quantum mechanics near closed timelike lines | journal = Physical Review D | volume = 44 | issue = 10 | year=1991 | doi= 10.1103/PhysRevD.44.3197 | pages=3197–3217 | bibcode=1991PhRvD..44.3197D | pmid= 10013776| url-access= subscription }}</ref> and [[Scott Aaronson]] later extended this result to show that the model could also be used to solve [[PSPACE]] problems in polynomial time.<ref>{{cite journal|journal=Scientific American|date=March 2008 | first= Scott | last= Aaronson| title= The Limits of Quantum Computers |volume=298 |issue=3 |pages=68–69 |doi=10.1038/scientificamerican0308-62 |pmid=18357822 |bibcode=2008SciAm.298c..62A |url= http://www.scottaaronson.com/writings/limitsqc-draft.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.scottaaronson.com/writings/limitsqc-draft.pdf |archive-date=2022-10-09 |url-status=live | via= scottaaronson.com }}</ref><ref>{{cite journal | first1= Scott | last1= Aaronson | first2= John |last2= Watrous | url=http://www.scottaaronson.com/papers/ctc.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.scottaaronson.com/papers/ctc.pdf |archive-date=2022-10-09 |url-status=live | title=Closed Timelike Curves Make Quantum and Classical Computing Equivalent | journal = Proceedings of the Royal Society A | volume = 465 | year=2009 | issue = 2102 | doi= 10.1098/rspa.2008.0350 | pages= 631–647 | bibcode=2009RSPSA.465..631A|arxiv = 0808.2669 | s2cid= 745646 | via= scottaaronson.com}}</ref> Deutsch shows that quantum computation with a negative delay&mdash;backwards time travel&mdash;produces only self-consistent solutions, and the chronology-violating region imposes constraints that are not apparent through classical reasoning.<ref name="Deutsch1991" /> Researchers published in 2014 a simulation in which they claim to have validated Deutsch's model with photons.<ref name=RingbauerEtAl2014>{{cite journal| first1= Martin | last1= Ringbauer | first2= Matthew A. | last2= Broome | first3= Casey R. | last3= Myers | first4= Andrew G. | last4= White | first5= Timothy C. | last5= Ralph|title=Experimental simulation of closed timelike curves|journal=Nature Communications| date= 19 June 2014| volume= 5| doi= 10.1038/ncomms5145|arxiv = 1501.05014 |bibcode = 2014NatCo...5E4145R5.4145R| pmid= 24942489| page= 4145| s2cid= 12779043 }}</ref> However, it was shown in an article by Tolksdorf and Verch that Deutsch's self-consistency condition can be fulfilled to arbitrary precision in any quantum system described according to relativistic [[quantum field theory]] even on spacetimes which do not admit closed timelike curves, casting doubts on whether Deutsch's model is really characteristic of quantum processes simulating closed timelike curves in the sense of [[general relativity]].<ref>{{cite journal

| last1 = Tolksdorf

| first1 = Juergen

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| volume = 357

| issue = 1

| pages = 319-351319–351

| arxiv = 1609.01496

| bibcode =2018CMaPh.357..319T

| doi = 10.1007/s00220-017-2943-5

| s2cid = 253751446

}}</ref>

In a later article,<ref>{{cite journal

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| issue = 93

| series =

| pages page = 93

| arxiv = 1912.02301

| bibcode = 2021FoPh...51...93T

| doi = 10.1007/s10701-021-00496-z

| s2cid = 208637445

}}</ref>

the same authors show that Deutsch's CTC fixed point condition can also be fulfilled in any system

subject to the laws of classical [[statistical mechanics]], even if it is not built up by quantum systems. The authors conclude that hence,

Deutsch's condition is not specific to quantum physics, nor does it depend on the quantum nature of a [[physical system]] so that it can be fulfilled.

In consequence, Tolksdorf and Verch argue that Deutsch's condition is not sufficiently specific to allow statements about time travel scenarios or their hypothetical realization by quantum physics.

=== Lloyd's prescription ===

An alternative proposal was later presented by [[Seth Lloyd]]<ref>{{cite journal

| last1 = Lloyd

| first1 = Seth

| authorlink1 = Seth Lloyd

| last2 = Maccone

| first2 = Lorenzo

| last3 = Garcia-Patron

| first3 = Raul

| last4 = Giovannetti

| first4 = Vittorio

| last5 = Shikano

| first5 = Yutaka

| last6 = Pirandola

| first6 = Stefano

| last7 = Rozema

| first7 = Lee A.

| last8 = Darabi

| first8 = Ardavan

| last9 = Soudagar

| first9 = Yasaman

| last10 = Shalm

| first10 = Lynden K.

| last11 = Steinberg

| first11 = Aephraim M.

| authorlink11 = Aephraim M. Steinberg

| date = 27 January 2011

| title = Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency

| journal = Physical Review Letters

| volume = 106

| issue = 4

| pages = 040403

| doi = 10.1103/PhysRevLett.106.040403

|bibcode = 2011PhRvL.106d0403L

|arxiv = 1005.2219

| pmid=21405310

| s2cid = 18442086

}}</ref><ref>{{cite journal

| last1 = Lloyd

| first1 = Seth

| authorlink1 = Seth Lloyd

| last2 = Maccone

| first2 = Lorenzo

| last3 = Garcia-Patron

| first3 = Raul

| last4 = Giovannetti

| first4 = Vittorio

| last5 = Shikano

| first5 = Yutaka

| year = 2011

| title = The quantum mechanics of time travel through post-selected teleportation

| arxiv = 1007.2615

| doi=10.1103/PhysRevD.84.025007

| volume=84

| issue=2

| pages = 025007

| journal=Physical Review D

| bibcode= 2011PhRvD..84b5007L

| s2cid = 15972766

}}</ref> based upon [[post-selection]] and path integrals. In particular, the path integral is over single-valued fields, leading to self-consistent histories.

== In popular culture ==

* ''[[The Final Countdown (film)|The Final Countdown]]'' (1980): A science-fiction time-travel movie in which the aircraft carrier [[USS Nimitz|USS ''Nimitz'']] passes through a wormhole back to the eve of the [[Attack on Pearl Harbor|Japanese attack on Pearl Harbor]]. The anomaly returns and sends it back into the present, before it has a chance to affect the outcome.

* ''[[Harry Potter and the Methods of Rationality]]''. In Eliezer Yudkowsky's exposition on rationality, framed as a piece of Harry Potter fanfiction, Harry attempts to use his Time Turner to influence the past and comes to the conclusion that the Novikov self-consistency principle applies.

* The story ''[[Steins;The Merchant and the Alchemist's Gate]]'': Cited(2007) by Makise[[Ted KurisuChiang]] duringexplores herthe presentationinterplay onbetween timefree will and self-consistent time-travel.

* ''[[Steins;Gate]]'' (2009): Cited by Makise Kurisu during her presentation on time travel.

* ''[[Orthogonal (series)|Orthogonal]]'': A science-fiction novel series that applies the principle.

* ''[[Harry Potter and the Methods of Rationality]]''.: In [[Eliezer Yudkowsky]]'s exposition on rationality, framed as a piece of Harry Potter fanfiction, Harry attempts to use his Time Turner to influence the past and comes to the conclusion that the Novikov self-consistency principle applies.

* ''[[Outer Wilds]]'' a video game involving time travel which does not follow the principle, causing a game over if the player experiments to test it.

* ''[[Orthogonal (series)|Orthogonal]]'': A science-fiction novel series by [[Greg Egan]] that applies the principle.

* The [[Netflix]] series ''[[Dark (TV series)|Dark]]'' is largely based on the notion that the possibility of time travel tempts the characters to try to change the past, which only leads them to cause the events they were trying to prevent in the first place.

* ''[[Quantum Break]]'' (2016): A video game by [[Remedy Entertainment]], centers heavily on the question whether the past can be changed or not. Some of the characters in the plot are driven to change it, whereas others, who have already tried doing so in vain, have resigned themselves to come to the conclusion that the Novikov self-consistency principle seemingly applies.

* ''[[Outer Wilds]]'' a(2019): A video game involving time travel which does not follow the principle, causing a game over if the player experiments to test it.

* All time travel in the [[Hallmark Channel]] original series ''[[The Way Home (TV series)|The Way Home]]'' follows the Novikov self-consistency principle. Two of the main characters can travel backwards in time by jumping into a pond, but they are unable to change anything in the past. All of their actions become part of history, and they actually end up causing the tragic events they were trying to prevent in the first place.

* ''[[Doctor Who]]'': a British science fiction television series that sometimes follows the Novikov self-consistency principle.

== See also ==

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* [[Many-worlds interpretation]]

* [[Grandfather paradox]]

* [[Quantum mechanics of time travel]]

* [[Time viewer]]

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* [http://news.bbc.co.uk/2/hi/science/nature/4097258.stm Einstein Physics prevent paradoxical time travel]

* [http://plato.stanford.edu/entries/time-travel-phys/ Time Travel and Modern Physics]

{{Time travel}}

{{DEFAULTSORT:Novikov Self-Consistency Principle}}