Editing Novikov self-consistency principle (section)

===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
| last2        = Verch
| first2       = Rainer
|date=2018
| title        = Quantum physics, fields and closed timelike curves: The D-CTC condition in quantum field theory
| journal      = Communications in Mathematical Physics
| volume       = 357
| issue        = 1
| pages        = 319–351
| arxiv        = 1609.01496
| bibcode      =2018CMaPh.357..319T 
| doi          =  10.1007/s00220-017-2943-5
| s2cid = 253751446
}}</ref>
In a later article,<ref>{{cite journal
| last1        = Tolksdorf
| first1       = Juergen
| authorlink1  = 
| last2        = Verch
| first2       = Rainer
| authorlink2  = 
|date=2021
| title        = The D-CTC condition is generically fulfilled in classical (non-quantum) statistical systems
| journal      = Foundations of Physics
| volume       = 51
| issue        = 93
| series       = 
| 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.