Novikov self-consistency principle: Difference between revisions

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==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=1915–1930 | 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 (Novikov) 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.

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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 lays out the same 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=1077–1099| 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 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<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:

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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...5.4145R| 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