Editing Temporal paradox (section)

==== Novikov self-consistency principle ====
{{main|Novikov self-consistency principle}}
The self-consistency principle developed by [[Igor Dmitriyevich Novikov]]<ref name="Friedman1990">{{cite journal |ref={{harvid|Friedman|1990}}|last1=Friedman|first1=John |last2=Morris|first2=Michael S.|last3=Novikov|first3=Igor D.|last4=Echeverria|first4=Fernando |last5=Klinkhammer|first5=Gunnar |last6=Thorne|first6=Kip S.|last7=Yurtsever|first7=Ulvi| 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>{{Rp|at=p. 42 note 10}} expresses one view as to how backward [[time travel]] would be possible without the generation of paradoxes. According to this hypothesis, even though [[general relativity]] permits some [[exact solutions in general relativity|exact solutions]] that allow for [[time travel]]<ref>{{citation|last=Krasnikov|first=S.|year=2002|title=No time machines in classical general relativity|journal=Classical and Quantum Gravity|volume=19|issue=15|page=4109|arxiv = gr-qc/0111054 |bibcode = 2002CQGra..19.4109K |doi = 10.1088/0264-9381/19/15/316 |s2cid=16517920}}</ref> that contain [[closed timelike curves]] that lead back to the same point in spacetime,<ref>{{cite journal |last=Gödel|first=Kurt| title=An Example of a New Type of Cosmological Solution of Einstein's Field Equations of Gravitation | journal=Rev. Mod. Phys. | year=1949 | volume=21 | pages=447–450 | doi=10.1103/RevModPhys.21.447 | issue=3|bibcode = 1949RvMP...21..447G | doi-access=free }}</ref> physics in or near [[closed timelike curves]] (time machines) can only be consistent with the universal laws of physics, and thus only self-consistent events can occur. Anything a time traveler does in the past must have been part of history all along, and the time traveler can never do anything to prevent the trip back in time from happening, since this would represent an inconsistency. The authors concluded that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent to the past.<ref name="Thorne" />

[[File:Grandfather_paradox_billiard_ball.svg|right|thumb|Top: original billiard ball trajectory. Middle: the billiard ball emerges from the future, and delivers its past self a strike that averts the past ball from entering the time machine. Bottom: The billiard ball never enters the time machine, giving rise to the paradox, putting into question how its older self could ever emerge from the time machine and divert its course.]]
Physicist [[Joseph Polchinski]] considered a potentially paradoxical situation involving a [[billiard ball]] that is fired into a [[wormhole]] at just the right angle such that it will be sent back in time and collides with its earlier self, knocking it off course, which would stop it from entering the wormhole in the first place. [[Kip Thorne]] referred to this problem as "Polchinski's paradox".<ref name="Thorne">{{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|pages=509–513| title-link = Black Holes and Time Warps }}</ref> Thorne and two of his students at Caltech, Fernando Echeverria and Gunnar Klinkhammer, went on to find a solution that avoided any inconsistencies, and found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each case.<ref>{{cite journal |ref={{harvid|Echeverria|1991}}| 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> Later analysis by Thorne and [[Robert Forward]] showed that for certain initial trajectories of the billiard ball, there could be an infinite number of self-consistent solutions.<ref name="Thorne" /> It is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven.<ref name="Earman1995187188">{{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}} The lack of constraints on initial conditions only applies to spacetime outside of the [[Chronology protection conjecture|chronology-violating region of spacetime]]; the constraints on the chronology-violating region might prove to be paradoxical, but this is not yet known.<ref name="Earman1995187188" />{{Rp|187–188}}

Novikov's views are not widely accepted. Visser views causal loops and Novikov's self-consistency principle as an ''ad hoc'' solution, and supposes that there are far more damaging implications of time travel.<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 | isbn = 0-387-98571-9|pages=345–352}}</ref> Krasnikov similarly finds no inherent fault in causal loops but finds other problems with time travel in general relativity.<ref name="Krasnikov2001" />{{Rp|14–16}} Another conjecture, the [[cosmic censorship hypothesis]], suggests that every closed timelike curve passes through an [[event horizon]], which prevents such causal loops from being observed.<ref>{{cite journal |last1=Visser |first1=Matt |date=15 April 1997 |title=Traversable wormholes: The Roman ring |journal=Physical Review D |volume=55 |issue=8 |pages=5212–5214 |arxiv=gr-qc/9702043 |bibcode=1997PhRvD..55.5212V |doi=10.1103/PhysRevD.55.5212 |s2cid=2869291}}</ref>